Forecasting Trends
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Transcript of Forecasting Trends
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Q1 Draw the graphs of series and explain the behaviour of the series.
Exp Imp WR
Jul-01 951.9 791.6 84.74 Exp: Pakistan's Exports in million
Aug-01 683.9 938.0 96.89 Imp: Pakistan's Imports in million
Sep-01 780.5 774.5 158.42 WR: Pakistan's Worker's Remittan
Oct-01 800.2 838.3 188.93
Nov-01 760.0 825.3 260.12
Dec-01 711.1 707.7 193.22
Jan-02 722.2 854.8 180.80
Feb-02 699.6 738.1 236.33
Mar-02 654.9 886.6 227.17
Apr-02 725.8 890.1 238.79
May-02 786.0 1119.3 255.10
Jun-02 846.1 975.3 268.54
Jul-02 816.7 927.2 307.41
Aug-02 902.8 969.3 392.44Sep-02 869.0 880.3 353.04
Oct-02 891.7 1018.0 377.77
Nov-02 854.1 960.2 353.83
Dec-02 863.2 1032.6 363.19
Jan-03 946.5 1053.1 383.22
Feb-03 776.4 918.7 342.77
Mar-03 935.6 1270.5 356.41Apr-03 990.2 1068.0 306.85
May-03 1049.6 969.8 336.42
Jun-03 1264.4 1152.6 363.50
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Dec-04 1130.0 1673.7 336.38
Jan-05 1148.2 1610.3 321.38
Feb-05 1166.1 1783.0 339.29
Mar-05 1346.8 2135.2 443.70Apr-05 1297.9 1902.6 401.00
May-05 1378.2 2019.8 358.30
Jun-05 1532.2 2229.6 358.98
Jul-05 1269.3 1996.3 313.14
Aug-05 1400.7 2233.8 348.41
Sep-05 1483.3 2321.8 341.10
Oct-05 1325.0 2325.3 372.50
Nov-05 1113.5 2299.0 308.81
Dec-05 1455.3 2474.7 371.24
Jan-06 1224.7 2144.3 391.32
Feb-06 1228.9 2210.4 358.13
Mar-06 1512.9 2681.9 423.56
Apr-06 1443.2 2258.6 401.47
May-06 1484.1 2648.5 506.57
Jun-06 1510.1 2986.4 463.87Jul-06 1342.0 2459.9 377.01
Aug-06 1498.5 2523.6 434.84
Sep-06 1412.8 2442.3 421.74
Oct-06 1262.6 2131.1 410.61
Nov-06 1374.9 2773.6 448.61
Dec-06 1516.6 2564.2 475.21
Jan-07 1175.6 2329.9 391.33Feb-07 1271.9 2572.3 457.18
Mar-07 1523.1 2622.6 520.24
Apr-07 1469.3 2573.5 513.35
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Nov-08 1527.1 2716.9 620.52
Dec-08 1256.5 2125.4 673.50
Jan-09 1346.0 2528.4 637.30
Feb-09 1249.6 2122.7 641.32Mar-09 1311.8 2354.7 739.43
Apr-09 1321.5 2798.4 697.52
May-09 1462.7 2561.4 720.68
Jun-09 1522.0 3339.3 735.17
Jul-09 1467.6 2639.2 744.85
Aug-09 1462.3 2528.2 780.53
Sep-09 1508.0 2419.3 806.12
Oct-09 1577.2 2971.6 758.29
Nov-09 1518.0 2528.4 742.79
Dec-09 1566.1 2907.6 697.60
Jan-10 1684.8 3320.9 667.90
Feb-10 1518.6 2504.6 589.03
Mar-10 1769.6 3287.0 763.72
Apr-10 1700.8 3015.7 755.77
May-10 1753.6 3363.3 757.86Jun-10 1780.6 3224.2 841.44
Jul-10 1726.2 3238.8 791.18
Aug-10 1738.4 3010.0 933.06
Sep-10 1593.0 2780.6 922.06
Oct-10 1938.1 3193.3 855.11
Nov-10 1776.7 3125.0 926.89
Dec-10 2126.6 3751.0 863.13Jan-11
Feb-11
Mar-11
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The behaviour of the series is inclining and the best fitted trend line is linear covering the m
The peak point of the graph is at May 2008 reaching upto 2000m US $.
The behaviour of the series is inclining and the best fitted trend line is quadratic covering th
The peak point of the graph is at Apr 2008 reaching upto 4100m US $.
0.0
500.0
1000.0
1500.0
2000.0
2500.03000.0
3500.0
4000.0
4500.0
Ju
l-01
Ma
r-02
No
v-02
Ju
l-03
Ma
r-04
No
v-04
Ju
l-05
Ma
r-06
No
v-06
Ju
l-07
Ma
r-08
No
v-08
Ju
l-09
Ma
r-10
No
v-10
Import
Import
Linear (Import)
Poly. (Import)
700.00
800.00
900.001000.00
Workers Remittance
Workers Remittance
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S $
S $
ces in million US $
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ximum points in the graph.
e maximum points in the graph.
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Q2: Calculate month on month (MoM) and year on year (YoY) growth of the series,
MoM
Exp Imp WR MoM-X MoM-Y MoM-Z
Jul-01 951.9 791.6 84.74
Aug-01 683.9 938.0 96.89 -28.1493 18.4904 14.33797
Sep-01 780.5 774.5 158.42 14.11524 -17.4302 63.50501
Oct-01 800.2 838.3 188.93 2.526632 8.241223 19.25893
Nov-01 760.0 825.3 260.12 -5.02321 -1.55476 37.68062
Dec-01 711.1 707.7 193.22 -6.43617 -14.2429 -25.7189
Jan-02 722.2 854.8 180.80 1.572672 20.7777 -6.42791
Feb-02 699.6 738.1 236.33 -3.13176 -13.6543 30.7135
Mar-02 654.9 886.6 227.17 -6.39901 20.11744 -3.87594
Apr-02 725.8 890.1 238.79 10.82681 0.395277 5.115112
May-02 786.0 1119.3 255.10 8.296869 25.75697 6.830269
Jun-02 846.1 975.3 268.54 7.648602 -12.8638 5.268522
Jul-02 816.7 927.2 307.41 -3.47894 -4.9329 14.47457Aug-02 902.8 969.3 392.44 10.54697 4.534281 27.66013
Sep-02 869.0 880.3 353.04 -3.74623 -9.17609 -10.0398
Oct-02 891.7 1018.0 377.77 2.621034 15.63955 7.004872
Nov-02 854.1 960.2 353.83 -4.22083 -5.67685 -6.33719
Dec-02 863.2 1032.6 363.19 1.067515 7.539198 2.645338
Jan-03 946.5 1053.1 383.22 9.650087 1.983941 5.51502
Feb-03 776.4 918.7 342.77 -17.9737 -12.7654 -10.5553Mar-03 935.6 1270.5 356.41 20.50586 38.30192 3.979345
Apr-03 990.2 1068.0 306.85 5.836828 -15.942 -13.9053
May-03 1049.6 969.8 336.42 5.994016 -9.18879 9.63663
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Nov-04 909.0 1476.9 291.81 -8.8989 1.411228 -12.8405
Dec-04 1130.0 1673.7 336.38 24.31838 13.32386 15.27364
Jan-05 1148.2 1610.3 321.38 1.612737 -3.7886 -4.45924
Feb-05 1166.1 1783.0 339.29 1.558354 10.72637 5.572842Mar-05 1346.8 2135.2 443.70 15.49685 19.75088 30.77308
Apr-05 1297.9 1902.6 401.00 -3.63095 -10.8932 -9.62362
May-05 1378.2 2019.8 358.30 6.186528 6.162415 -10.6484
Jun-05 1532.2 2229.6 358.98 11.17521 10.38732 0.189785
Jul-05 1269.3 1996.3 313.14 -17.1571 -10.4659 -12.7695
Aug-05 1400.7 2233.8 348.41 10.34907 11.89914 11.26333
Sep-05 1483.3 2321.8 341.10 5.896624 3.937526 -2.0981
Oct-05 1325.0 2325.3 372.50 -10.6708 0.152082 9.205512
Nov-05 1113.5 2299.0 308.81 -15.9664 -1.13081 -17.098
Dec-05 1455.3 2474.7 371.24 30.70335 7.641919 20.21631
Jan-06 1224.7 2144.3 391.32 -15.8495 -13.35 5.4089
Feb-06 1228.9 2210.4 358.13 0.348772 3.081954 -8.48155
Mar-06 1512.9 2681.9 423.56 23.10472 21.33007 18.2699
Apr-06 1443.2 2258.6 401.47 -4.6042 -15.782 -5.21532
May-06 1484.1 2648.5 506.57 2.833677 17.2598 26.17879Jun-06 1510.1 2986.4 463.87 1.748846 12.75941 -8.42924
Jul-06 1342.0 2459.9 377.01 -11.1306 -17.6291 -18.7251
Aug-06 1498.5 2523.6 434.84 11.66438 2.588966 15.33912
Sep-06 1412.8 2442.3 421.74 -5.72226 -3.22129 -3.0126
Oct-06 1262.6 2131.1 410.61 -10.6324 -12.7425 -2.63907
Nov-06 1374.9 2773.6 448.61 8.897373 30.14557 9.254524
Dec-06 1516.6 2564.2 475.21 10.30473 -7.54965 5.929426
Jan-07 1175.6 2329.9 391.33 -22.4865 -9.13438 -17.6511
Feb-07 1271.9 2572.3 457.18 8.194537 10.40112 16.82723
Mar-07 1523.1 2622.6 520.24 19.7515 1.955827 13.79325
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Oct-08 1475.2 3460.3 466.13 -16.7543 -9.08606 -29.4117
Nov-08 1527.1 2716.9 620.52 3.517732 -21.4831 33.12166
Dec-08 1256.5 2125.4 673.50 -17.7191 -21.7714 8.538
Jan-09 1346.0 2528.4 637.30 7.11823 18.96127 -5.37491Feb-09 1249.6 2122.7 641.32 -7.15989 -16.0447 0.630786
Mar-09 1311.8 2354.7 739.43 4.973494 10.92615 15.29814
Apr-09 1321.5 2798.4 697.52 0.746085 18.84232 -5.66788
May-09 1462.7 2561.4 720.68 10.68121 -8.46739 3.320335
Jun-09 1522.0 3339.3 735.17 4.056153 30.36964 2.010601
Jul-09 1467.6 2639.2 744.85 -3.57671 -20.9654 1.316702
Aug-09 1462.3 2528.2 780.53 -0.35756 -4.20421 4.790226
Sep-09 1508.0 2419.3 806.12 3.123394 -4.30856 3.278542
Oct-09 1577.2 2971.6 758.29 4.589074 22.82653 -5.93336
Nov-09 1518.0 2528.4 742.79 -3.75154 -14.9135 -2.04407
Dec-09 1566.1 2907.6 697.60 3.166538 14.99602 -6.08382
Jan-10 1684.8 3320.9 667.90 7.579602 14.21592 -4.25745
Feb-10 1518.6 2504.6 589.03 -9.8677 -24.581 -11.8086
Mar-10 1769.6 3287.0 763.72 16.52875 31.23914 29.65699
Apr-10 1700.8 3015.7 755.77 -3.88793 -8.25448 -1.04086May-10 1753.6 3363.3 757.86 3.104861 11.52822 0.276929
Jun-10 1780.6 3224.2 841.44 1.541624 -4.13537 11.02812
Jul-10 1726.2 3238.8 791.18 -3.05518 0.451735 -5.97321
Aug-10 1738.4 3010.0 933.06 0.707575 -7.06335 17.93271
Sep-10 1593.0 2780.6 922.06 -8.36328 -7.62257 -1.17892
Oct-10 1938.1 3193.3 855.11 21.65964 14.84357 -7.26092
Nov-10 1776.7 3125.0 926.89 -8.32784 -2.1394 8.394242
Dec-10 2126.6 3751.0 863.13 19.69413 20.03092 -6.87892
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Point: 54
Value: 30.70
Lowest position:
Point: 35Value: -29.6
The series exhibits fluctuating behaviour
Highest position:
Point: 12Value: 49.44
Lowest position:
Point: 81
-30
-20
-10
0
10
20
30
40
50
60
YoY-X
YoY-X
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draw graph and explain behavior of series
MoM YoY
YoY-X YoY-Y YoY-Z
-14.204 17.13041 262.768532.00264 3.334477 305.0366
11.34141 13.66433 122.8507
11.44392 21.43333 99.95236
12.38542 16.34869 36.02568
21.39857 45.90099 87.96708
31.05261 23.19789 111.958
10.97298 24.46616 45.03872
42.87129 43.309 56.89131
36.43851 19.98835 28.50203
33.53724 -13.3544 31.8777
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5.490971 48.94742 15.30346
8.119007 26.43407 -12.7894
4.957564 19.66578 -15.9373
28.67876 56.48793 17.2026731.52949 51.63758 34.58913
18.44283 26.11135 19.59083
29.57478 17.16192 17.0915
22.7139 19.7619 1.118278
7.229497 36.94862 -5.25551
17.93427 51.42282 2.564027
33.22601 68.52933 8.99853
32.80287 59.6658 11.26045
22.50017 55.66351 5.825709
28.79176 47.8587 10.36328
6.65875 33.16459 21.7624
5.388421 23.97106 5.552772
12.33043 25.6059 -4.5391
11.19598 18.71468 0.117207
7.684953 31.12417 41.38152-1.44548 33.94188 29.2189
5.724 23.22584 20.39663
6.984187 12.97326 24.80698
-4.75403 5.192105 23.64116
-4.71308 -8.35134 10.23087
23.48034 20.6409 45.27055
4.209001 3.614779 28.00614
-4.00997 8.65579 0.002555
3.495003 16.37072 27.65755
0.675931 -2.2116 22.82557
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7.043342 2.233132 -19.666
-0.78413 -14.0558 22.73429
-4.82457 -9.51088 40.52915
-8.07725 -28.3545 14.40214-18.758 -41.9681 27.55987
-25.9574 -38.3848 22.78607
-26.2045 -31.7453 18.08163
-23.8493 -34.0241 23.24583
-20.253 -17.012 34.2997
-21.9114 -25.6322 18.75608
-6.50207 -26.9178 31.7795
-14.9043 -36.4366 22.07466
6.913418 -14.1247 62.67779
-0.5943 -6.93928 19.70444
24.63815 36.79928 3.578322
25.17499 31.34238 4.801506
21.52408 17.98794 -8.15341
34.90119 39.5941 3.284864
28.69614 7.765752 8.35101519.88663 31.30755 5.159426
16.98956 -3.4457 14.4553
17.62233 22.71894 6.220044
18.87966 19.05624 19.54185
5.637935 14.93305 14.38247
22.87969 7.463117 12.7682
17.03716 23.59657 24.78493
35.78686 29.00803 23.7285
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Point: 79
Value: 50.25
Lowest position:
Point: 78Value: -25.70
The series exhibits fluctuating behaviour The series
Highest position: Highest p
Point: 23 Point: 2Value: 77.76 Value: 305.
Lowest position: Lowest pos
Point: 80 Point: 17
-60
-40
-20
0
20
40
60
80
100
YoY-Y
YoY-Y
-50
0
50
100
150
200
250
300
350
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Point: 3
Value: 63.51
Lowest position:
Point: 88Value: -29.41
exhibits fluctuating behaviour
sition:
3
ition:
YoY-Z
YoY-Z
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Q3: Regress the three series with time trend and identify the trend i.e. it is linear or quadratic.
Exp Imp WR t t^2
Jul-01 951.9 791.6 84.74 1 1
Aug-01 683.9 938.0 96.89 2 4
Sep-01 780.5 774.5 158.42 3 9
Oct-01 800.2 838.3 188.93 4 16
Nov-01 760.0 825.3 260.12 5 25
Dec-01 711.1 707.7 193.22 6 36
Jan-02 722.2 854.8 180.80 7 49
Feb-02 699.6 738.1 236.33 8 64
Mar-02 654.9 886.6 227.17 9 81
Apr-02 725.8 890.1 238.79 10 100
May-02 786.0 1119.3 255.10 11 121
Jun-02 846.1 975.3 268.54 12 144Jul-02 816.7 927.2 307.41 13 169
Aug-02 902.8 969.3 392.44 14 196
Sep-02 869.0 880.3 353.04 15 225
Oct-02 891.7 1018.0 377.77 16 256
Nov-02 854.1 960.2 353.83 17 289
Dec-02 863.2 1032.6 363.19 18 324
Jan-03 946.5 1053.1 383.22 19 361
Feb-03 776.4 918.7 342.77 20 400
Mar-03 935.6 1270.5 356.41 21 441
Apr-03 990.2 1068.0 306.85 22 484
May-03 1049.6 969.8 336.42 23 529
Jun-03 1264.4 1152.6 363.50 24 576
Jul-03 890.2 999.8 307.23 25 625
Aug-03 1038.7 1035.1 280.87 26 676
Sep-03 1038.8 1077.6 318.38 27 729
Oct-03 1006.6 1176.5 328.52 28 784
Nov-03 861.6 991.6 253.08 29 841
Dec-03 1045.1 1323.8 385.71 30 900
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Jan-04 1094.0 1345.7 382.31 31 961
Feb-04 906.2 1139.4 289.49 32 1024
Mar-04 1024.0 1408.1 329.67 33 1089
Apr-04 1095.8 1508.7 335.31 34 1156
May-04 1063.6 1724.0 306.00 35 1225
Jun-04 1248.6 1861.7 355.01 36 1296
Jul-04 1183.8 1457.7 330.51 37 1369
Aug-04 1187.7 1475.2 339.70 38 1444
Sep-04 1113.4 1377.7 312.94 39 1521
Oct-04 997.7 1456.4 334.80 40 1600
Nov-04 909.0 1476.9 291.81 41 1681
Dec-04 1130.0 1673.7 336.38 42 1764
Jan-05 1148.2 1610.3 321.38 43 1849
Feb-05 1166.1 1783.0 339.29 44 1936
Mar-05 1346.8 2135.2 443.70 45 2025
Apr-05 1297.9 1902.6 401.00 46 2116May-05 1378.2 2019.8 358.30 47 2209
Jun-05 1532.2 2229.6 358.98 48 2304
Jul-05 1269.3 1996.3 313.14 49 2401
Aug-05 1400.7 2233.8 348.41 50 2500
Sep-05 1483.3 2321.8 341.10 51 2601
Oct-05 1325.0 2325.3 372.50 52 2704
Nov-05 1113.5 2299.0 308.81 53 2809
Dec-05 1455.3 2474.7 371.24 54 2916
Jan-06 1224.7 2144.3 391.32 55 3025
Feb-06 1228.9 2210.4 358.13 56 3136
Mar-06 1512.9 2681.9 423.56 57 3249
Apr-06 1443.2 2258.6 401.47 58 3364
May-06 1484.1 2648.5 506.57 59 3481
Jun-06 1510.1 2986.4 463.87 60 3600
Jul-06 1342.0 2459.9 377.01 61 3721
Aug-06 1498.5 2523.6 434.84 62 3844
Sep-06 1412.8 2442.3 421.74 63 3969
Oct-06 1262.6 2131.1 410.61 64 4096
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Nov-06 1374.9 2773.6 448.61 65 4225
Dec-06 1516.6 2564.2 475.21 66 4356
Jan-07 1175.6 2329.9 391.33 67 4489
Feb-07 1271.9 2572.3 457.18 68 4624
Mar-07 1523.1 2622.6 520.24 69 4761
Apr-07 1469.3 2573.5 513.35 70 4900
May-07 1584.8 2750.3 537.98 71 5041
Jun-07 1544.1 2796.5 505.55 72 5184
Jul-07 1471.6 2573.8 495.69 73 5329
Aug-07 1464.6 2747.4 489.51 74 5476
Sep-07 1484.5 2734.9 516.05 75 5625
Oct-07 1378.2 3384.7 580.24 76 5776
Nov-07 1539.2 3161.3 505.58 77 5929
Dec-07 1320.2 2348.8 479.26 78 6084
Jan-08 1464.2 3529.1 557.07 79 6241
Feb-08 1538.1 3657.9 502.76 80 6400Mar-08 1771.6 3821.6 602.21 81 6561
Apr-08 1790.8 4099.9 590.71 82 6724
May-08 1920.8 3882.3 584.75 83 6889
Jun-08 1908.6 4023.8 547.41 84 7056
Jul-08 1879.4 3548.9 627.21 85 7225
Aug-08 1564.0 3459.5 592.30 86 7396
Sep-08 1772.1 3806.1 660.35 87 7569
Oct-08 1475.2 3460.3 466.13 88 7744
Nov-08 1527.1 2716.9 620.52 89 7921
Dec-08 1256.5 2125.4 673.50 90 8100
Jan-09 1346.0 2528.4 637.30 91 8281
Feb-09 1249.6 2122.7 641.32 92 8464
Mar-09 1311.8 2354.7 739.43 93 8649
Apr-09 1321.5 2798.4 697.52 94 8836
May-09 1462.7 2561.4 720.68 95 9025
Jun-09 1522.0 3339.3 735.17 96 9216
Jul-09 1467.6 2639.2 744.85 97 9409
Aug-09 1462.3 2528.2 780.53 98 9604
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Sep-09 1508.0 2419.3 806.12 99 9801
Oct-09 1577.2 2971.6 758.29 100 10000
Nov-09 1518.0 2528.4 742.79 101 10201
Dec-09 1566.1 2907.6 697.60 102 10404
Jan-10 1684.8 3320.9 667.90 103 10609
Feb-10 1518.6 2504.6 589.03 104 10816
Mar-10 1769.6 3287.0 763.72 105 11025
Apr-10 1700.8 3015.7 755.77 106 11236
May-10 1753.6 3363.3 757.86 107 11449
Jun-10 1780.6 3224.2 841.44 108 11664
Jul-10 1726.2 3238.8 791.18 109 11881
Aug-10 1738.4 3010.0 933.06 110 12100
Sep-10 1593.0 2780.6 922.06 111 12321
Oct-10 1938.1 3193.3 855.11 112 12544
Nov-10 1776.7 3125.0 926.89 113 12769
Dec-10 2126.6 3751.0 863.13 114 12996Export
Linear Trend
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.89
R Square 0.79 Y=772.3+9.05t
Adjusted R Squa 0.79
Standard Error 154.54
Observations 114
ANOVA
df SS MS F Significance F
Regression 1 10108922.0 10108922.0 423.3 7.64325E-40
Residual 112 2674999.7 23883.9
Total 113 12783921.6
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Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 772.316 29.140 26.503 0.000 714.579 830.054
X Variable 1 9.049 0.440 20.573 0.000 8.178 9.921
Quadratic Trend
SUMMARY OUTPUT
Regression Statistics Y=671.68+14.25t-0.045t^2
Multiple R 0.898827528
R Square 0.8079
Adjusted R Squa 0.8044
Standard Error 148.7457
Observations 114
ANOVAdf SS MS F Significance F
Regression 2 10328014.25 5164007.125 233.3983761 1.72547E-40
Residual 111 2455907.366 22125.29158
Total 113 12783921.62
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 671.68 42.5380 15.7900 0.0000 587.3831 755.9671
X Variable 1 14.25 1.7076 8.3480 0.0000 10.8710 17.6383
X Variable 2 -0.045 0.0144 -3.1468 0.0021 -0.0738 -0.0168
Conclusion
The trend of this series is linear because in the quadratic trend the value of X variable 2 is very small and negative.
Import
Linear Trend
SUMMARY OUTPUT
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Regression Statistics
Multiple R 0.89
R Square 0.79
Adjusted R Squa 0.79 Y=720.84+25.06t
Standard Error 431.41
Observations 114
ANOVA
df SS MS F Significance F
Regression 1 77550331.42 77550331.42 416.6875156 1.52792E-39
Residual 112 20844486.08 186111.4829
Total 113 98394817.5
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 720.84 81.34 8.86 0.00 559.66 882.01X Variable 1 25.064 1.23 20.41 0.00 22.63 27.50
Quadratic trend
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9058R Square 0.8205
Adjusted R Squa 0.8173
Standard Error 398.8947 Y=337.26+44.9t-0.172t^2
Observations 114
ANOVA
df SS MS F Significance F
Regression 2 80732832.81 40366416.41 253.6901883 3.98781E-42
Residual 111 17661984.69 159116.9792
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Total 113 98394817.5
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 337.27 114.08 2.96 0.00 111.22 563.31
X Variable 1 44.90 4.58 9.81 0.00 35.83 53.98
X Variable 2 -0.17 0.04 -4.47 0.00 -0.25 -0.10
Conclusion
The trend of this series is linear because in the quadratic trend the value of X variable 1 is very small and negative.
Workers remittances
Linear Trend
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.93
R Square 0.86
Adjusted R Squa 0.86 Y=154.107+5.4389t
Standard Error 71.91
Observations 114
ANOVA
df SS MS F Significance F
Regression 1 3651906.496 3651906.496 706.2378262 3.48882E-50
Residual 112 579144.1812 5170.930189
Total 113 4231050.678
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 154.1 13.6 11.4 0.0 127.2 181.0
X Variable 1 5.4 0.2 26.6 0.0 5.0 5.8
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Quadratic trend
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.954
R Square 0.911
Adjusted R Squa 0.909 Y=250.64+0.44t+0.043t^2
Standard Error 58.321
Observations 114
ANOVA
df SS MS F Significance F
Regression 2 3853495.968 1926747.984 566.4583724 5.68208E-59Residual 111 377554.7095 3401.393779
Total 113 4231050.678
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 250.64 16.68 15.03 0.00 217.59 283.69
X Variable 1 0.45 0.67 0.67 0.51 -0.88 1.77
X Variable 2 0.04 0.01 7.70 0.00 0.03 0.05
Conclusion
The trend of this series is Linear because in quadratic trend the calculated value of X variable 1 lies in the acceptance region,
which means that regression coefficient is not significant. This model is not fit for forecasting
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Q4: Estimate simple linear regression of combination of three series given to you. Test the sig
apply the goodness of fit test for these combinations and if both tests show significance of re
then forecast the respective dependent variables.
X Y Z
Exp Imp WR
Jul-01 951.9 791.6 84.74
Aug-01 683.9 938.0 96.89
Sep-01 780.5 774.5 158.42
Oct-01 800.2 838.3 188.93
Nov-01 760.0 825.3 260.12
Dec-01 711.1 707.7 193.22
Jan-02 722.2 854.8 180.80
Feb-02 699.6 738.1 236.33
Mar-02 654.9 886.6 227.17
Apr-02 725.8 890.1 238.79
May-02 786.0 1119.3 255.10
Jun-02 846.1 975.3 268.54Jul-02 816.7 927.2 307.41
Aug-02 902.8 969.3 392.44
Sep-02 869.0 880.3 353.04
Oct-02 891.7 1018.0 377.77
Nov-02 854.1 960.2 353.83
Dec-02 863.2 1032.6 363.19
Jan-03 946.5 1053.1 383.22
Feb-03 776.4 918.7 342.77
Mar-03 935.6 1270.5 356.41
Apr-03 990.2 1068.0 306.85
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Oct-04 997.7 1456.4 334.80
Nov-04 909.0 1476.9 291.81
Dec-04 1130.0 1673.7 336.38
Jan-05 1148.2 1610.3 321.38
Feb-05 1166.1 1783.0 339.29
Mar-05 1346.8 2135.2 443.70
Apr-05 1297.9 1902.6 401.00
May-05 1378.2 2019.8 358.30
Jun-05 1532.2 2229.6 358.98
Jul-05 1269.3 1996.3 313.14
Aug-05 1400.7 2233.8 348.41
Sep-05 1483.3 2321.8 341.10Oct-05 1325.0 2325.3 372.50
Nov-05 1113.5 2299.0 308.81
Dec-05 1455.3 2474.7 371.24
Jan-06 1224.7 2144.3 391.32
Feb-06 1228.9 2210.4 358.13
Mar-06 1512.9 2681.9 423.56
Apr-06 1443.2 2258.6 401.47May-06 1484.1 2648.5 506.57
Jun-06 1510.1 2986.4 463.87
Jul-06 1342.0 2459.9 377.01
Aug-06 1498.5 2523.6 434.84
Sep-06 1412.8 2442.3 421.74
Oct-06 1262.6 2131.1 410.61
Nov-06 1374.9 2773.6 448.61
Dec-06 1516.6 2564.2 475.21
Jan-07 1175.6 2329.9 391.33
Feb-07 1271.9 2572.3 457.18
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Sep-08 1772.1 3806.1 660.35
Oct-08 1475.2 3460.3 466.13
Nov-08 1527.1 2716.9 620.52
Dec-08 1256.5 2125.4 673.50
Jan-09 1346.0 2528.4 637.30
Feb-09 1249.6 2122.7 641.32
Mar-09 1311.8 2354.7 739.43
Apr-09 1321.5 2798.4 697.52
May-09 1462.7 2561.4 720.68
Jun-09 1522.0 3339.3 735.17
Jul-09 1467.6 2639.2 744.85
Aug-09 1462.3 2528.2 780.53Sep-09 1508.0 2419.3 806.12
Oct-09 1577.2 2971.6 758.29
Nov-09 1518.0 2528.4 742.79
Dec-09 1566.1 2907.6 697.60
Jan-10 1684.8 3320.9 667.90
Feb-10 1518.6 2504.6 589.03
Mar-10 1769.6 3287.0 763.72Apr-10 1700.8 3015.7 755.77
May-10 1753.6 3363.3 757.86
Jun-10 1780.6 3224.2 841.44
Jul-10 1726.2 3238.8 791.18
Aug-10 1738.4 3010.0 933.06
Sep-10 1593.0 2780.6 922.06
Oct-10 1938.1 3193.3 855.11
Nov-10 1776.7 3125.0 926.89
Dec-10 2126.6 3751.0 863.13
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Coefficients Standard Error t Stat P-value Lower 95%
Intercept 562.80 28.0954 20.0316 0.0000 507.1282
X Variable 0.338 0.0119 28.2741 0.0000 0.3139
Results
Calculated T-Stats= 28.2741 Greater than 2
P-Value 8.24469E-53 smaller than 0.05
Conclusions Significant b0
Coeffecient of determination 0.88 Greater than 0.65
Conclusions Significant Model is fit for forecasting
Forecasting
For X on Y X=562.79+0.338Y Forecasted value
For Y= 3444 X= 562.80+0.338(3444)= 1726.87
For Y= 3053 X= 562.80+0.338(3053)= 1594.71
For Y= 3417 X= 562.80+0.338(3417)= 1717.75
Export on WR
SUMMARY OUTPUT
Regression Statistics X=638.67+1.40Z
Multiple R 0.805887
R Square 0.649454Adjusted R 0.646324
Standard E 200.030310
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Coeffecient of determination 0.65 Greater than 0.65
Conclusions Significant Model is fit for forecasting
ForecastingFor X on Z X=638.67+1.40Z Forecasted value
For Z= 826.57 X=638.67+1.40(826.57) 1795.87
For Z= 845.28 X=638.67+1.40(845.28) 1822.06
For Z= 1052.88 X=638.67+1.40(1052.88) 2112.7
Import on WR
SUMMARY OUTPUT
Regression Statistics Y= 437.03+3.695Z
Multiple R 0.7662
R Square 0.5871
Adjusted R 0.5834
Standard E 602.3014
Observatio 114
ANOVA
df SS MS F Significance F
Regression 1 57764917 57764917 159.2342216 3.00811E-23
Residual 112 40629901 362767
Total 113 98394818
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 437.0326 147.8795 2.9553 0.0038 144.0284
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Line fit plot
For X on Y For X on Z For Y on Z
Export on Import Export on WR Import on WR
RESIDUAL OUTPUT RESIDUAL OUTPUT RESIDUAL OUT
Observation Predicted Y Residuals Predicted Y Residuals Predicted Y
1 830.03 121.84 830.03 121.84 750.14
2 879.44 -195.52 879.44 -195.52 795.04
3 824.25 -43.79 824.25 -43.79 1022.39
4 845.79 -45.62 845.79 -45.62 1135.125 841.39 -81.41 841.39 -81.41 1398.16
6 801.71 -90.65 801.71 -90.65 1150.97
7 851.35 -129.10 851.35 -129.10 1105.08
8 811.95 -112.32 811.95 -112.32 1310.26
9 862.08 -207.22 862.08 -207.22 1276.41
10 863.26 -137.50 863.26 -137.50 1319.35
11 940.65 -154.67 940.65 -154.67 1379.6112 892.05 -45.95 892.05 -45.95 1429.27
13 875.80 -59.14 875.80 -59.14 1572.90
14 890.00 12.80 890.00 12.80 1887.08
15 859.97 9.00 859.97 9.00 1741.50
16 906.45 -14.70 906.45 -14.70 1832.87
17 886.94 -32.83 886.94 -32.83 1744.41
18 911.38 -48.15 911.38 -48.15 1779.00
19 918.29 28.23 918.29 28.23 1853.01
20 872.91 -96.51 872.91 -96.51 1703.55
21 991.69 -56.09 991.69 -56.09 1753.95
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39 1027.87 85.51 1027.87 85.51 1593.33
40 1054.43 -56.69 1054.43 -56.69 1674.10
41 1061.37 -152.42 1061.37 -152.42 1515.25
42 1127.80 2.19 1127.80 2.19 1679.94
43 1106.39 41.82 1106.39 41.82 1624.51
44 1164.70 1.41 1164.70 1.41 1690.69
45 1283.58 63.24 1283.58 63.24 2076.48
46 1205.07 92.85 1205.07 92.85 1918.71
47 1244.65 133.57 1244.65 133.57 1760.93
48 1315.47 216.76 1315.47 216.76 1763.44
49 1236.70 32.65 1236.70 32.65 1594.07
50 1316.89 83.83 1316.89 83.83 1724.3951 1346.58 136.73 1346.58 136.73 1697.38
52 1347.77 -22.74 1347.77 -22.74 1813.40
53 1338.89 -225.43 1338.89 -225.43 1578.07
54 1398.20 57.14 1398.20 57.14 1808.74
55 1286.68 -62.00 1286.68 -62.00 1882.94
56 1308.98 -80.04 1308.98 -80.04 1760.30
57 1468.15 44.74 1468.15 44.74 2002.0658 1325.26 117.97 1325.26 117.97 1920.44
59 1456.87 27.26 1456.87 27.26 2308.78
60 1570.94 -60.86 1570.94 -60.86 2151.01
61 1393.22 -51.21 1393.22 -51.21 1830.06
62 1414.72 83.82 1414.72 83.82 2043.74
63 1387.27 25.52 1387.27 25.52 1995.34
64 1282.21 -19.64 1282.21 -19.64 1954.21
65 1499.09 -124.17 1499.09 -124.17 2094.62
66 1428.40 88.19 1428.40 88.19 2192.91
67 1349.33 -173.77 1349.33 -173.77 1882.98
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86 1730.63 -166.60 1730.63 -166.60 2625.55
87 1847.67 -75.53 1847.67 -75.53 2876.99
88 1730.92 -255.70 1730.92 -255.70 2159.36
89 1479.97 47.15 1479.97 47.15 2729.82
90 1280.29 -23.76 1280.29 -23.76 2925.58
91 1416.34 -70.36 1416.34 -70.36 2791.82
92 1279.39 -29.79 1279.39 -29.79 2806.67
93 1357.68 -45.93 1357.68 -45.93 3169.19
94 1507.46 -185.92 1507.46 -185.92 3014.33
95 1427.47 35.22 1427.47 35.22 3099.91
96 1690.07 -168.05 1690.07 -168.05 3153.45
97 1453.73 13.85 1453.73 13.85 3189.2198 1416.28 46.06 1416.28 46.06 3321.05
99 1379.50 128.51 1379.50 128.51 3415.60
100 1565.93 11.29 1565.93 11.29 3238.87
101 1416.33 101.72 1416.33 101.72 3181.60
102 1544.32 21.79 1544.32 21.79 3014.63
103 1683.86 0.96 1683.86 0.96 2904.89
104 1408.29 110.28 1408.29 110.28 2613.47105 1672.41 97.15 1672.41 97.15 3258.93
106 1580.82 119.95 1580.82 119.95 3229.56
107 1698.18 55.39 1698.18 55.39 3237.29
108 1651.23 129.38 1651.23 129.38 3546.11
109 1656.14 70.06 1656.14 70.06 3360.40
110 1578.92 159.50 1578.92 159.50 3884.64
111 1501.46 91.57 1501.46 91.57 3843.99
112 1640.79 297.28 1640.79 297.28 3596.62
113 1617.73 158.95 1617.73 158.95 3861.84
114 1829.05 297.53 1829.05 297.53 3626.25
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nificance of regression coefficients,
ression equation,
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Upper 95%
618.4631
0.3612
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Upper 95%
730.0368
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UT
Residuals
41.47
142.95
-247.90
-296.80-572.88
-443.23
-250.29
-572.18
-389.86
-429.29
-260.30-453.95
-645.68
-917.82
-861.18
-814.88
-784.21
-746.40
-799.92
-784.89
-483.43
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-215.66
-217.74
-38.34
-6.24
-14.23
92.32
58.69
-16.12
258.90
466.19
402.21
509.43624.40
511.91
720.95
665.96
261.39
450.12
679.84
338.20
339.70
835.41
629.87
479.88
446.99
176.90
678.93
371.25
446.96
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833.91
929.16
1300.96
-12.89
-800.16
-263.40
-683.93
-814.51
-215.97
-538.50
185.85
-550.01-792.80
-996.29
-267.31
-653.20
-107.07
416.01
-108.88
28.06
-213.89
126.03
-321.87
-121.60
-874.60
-1063.40
-403.29-736.83
124.73
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Q5: Estimate multiple regression of combination of three series given to you. Test the significance of regression coeffecients,
and if they are significant then forecasting the respective dependent variables. Also apply goodness of fit test for these regressio
X Y Z
Exp Imp WR
Jul-01 951.9 791.6 84.74Aug-01 683.9 938.0 96.89
Sep-01 780.5 774.5 158.42
Oct-01 800.2 838.3 188.93
Nov-01 760.0 825.3 260.12
Dec-01 711.1 707.7 193.22
Jan-02 722.2 854.8 180.80
Feb-02 699.6 738.1 236.33
Mar-02 654.9 886.6 227.17
Apr-02 725.8 890.1 238.79
May-02 786.0 1119.3 255.10
Jun-02 846.1 975.3 268.54
Jul-02 816.7 927.2 307.41
Aug-02 902.8 969.3 392.44
Sep-02 869.0 880.3 353.04
Oct-02 891.7 1018.0 377.77
Nov-02 854.1 960.2 353.83
Dec-02 863.2 1032.6 363.19
Jan-03 946.5 1053.1 383.22
Feb-03 776.4 918.7 342.77Mar-03 935.6 1270.5 356.41
Apr-03 990.2 1068.0 306.85
May-03 1049.6 969.8 336.42
Jun-03 1264.4 1152.6 363.50
Jul-03 890.2 999.8 307.23
Aug-03 1038.7 1035.1 280.87
Sep-03 1038.8 1077.6 318.38
Oct-03 1006.6 1176.5 328.52
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Nov-03 861.6 991.6 253.08
Dec-03 1045.1 1323.8 385.71
Jan-04 1094.0 1345.7 382.31
Feb-04 906.2 1139.4 289.49
Mar-04 1024.0 1408.1 329.67
Apr-04 1095.8 1508.7 335.31
May-04 1063.6 1724.0 306.00Jun-04 1248.6 1861.7 355.01
Jul-04 1183.8 1457.7 330.51
Aug-04 1187.7 1475.2 339.70
Sep-04 1113.4 1377.7 312.94
Oct-04 997.7 1456.4 334.80
Nov-04 909.0 1476.9 291.81
Dec-04 1130.0 1673.7 336.38
Jan-05 1148.2 1610.3 321.38
Feb-05 1166.1 1783.0 339.29
Mar-05 1346.8 2135.2 443.70
Apr-05 1297.9 1902.6 401.00
May-05 1378.2 2019.8 358.30
Jun-05 1532.2 2229.6 358.98
Jul-05 1269.3 1996.3 313.14
Aug-05 1400.7 2233.8 348.41
Sep-05 1483.3 2321.8 341.10
Oct-05 1325.0 2325.3 372.50
Nov-05 1113.5 2299.0 308.81
Dec-05 1455.3 2474.7 371.24Jan-06 1224.7 2144.3 391.32
Feb-06 1228.9 2210.4 358.13
Mar-06 1512.9 2681.9 423.56
Apr-06 1443.2 2258.6 401.47
May-06 1484.1 2648.5 506.57
Jun-06 1510.1 2986.4 463.87
Jul-06 1342.0 2459.9 377.01
Aug-06 1498.5 2523.6 434.84
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Sep-06 1412.8 2442.3 421.74
Oct-06 1262.6 2131.1 410.61
Nov-06 1374.9 2773.6 448.61
Dec-06 1516.6 2564.2 475.21
Jan-07 1175.6 2329.9 391.33
Feb-07 1271.9 2572.3 457.18
Mar-07 1523.1 2622.6 520.24Apr-07 1469.3 2573.5 513.35
May-07 1584.8 2750.3 537.98
Jun-07 1544.1 2796.5 505.55
Jul-07 1471.6 2573.8 495.69
Aug-07 1464.6 2747.4 489.51
Sep-07 1484.5 2734.9 516.05
Oct-07 1378.2 3384.7 580.24
Nov-07 1539.2 3161.3 505.58
Dec-07 1320.2 2348.8 479.26
Jan-08 1464.2 3529.1 557.07
Feb-08 1538.1 3657.9 502.76
Mar-08 1771.6 3821.6 602.21
Apr-08 1790.8 4099.9 590.71
May-08 1920.8 3882.3 584.75
Jun-08 1908.6 4023.8 547.41
Jul-08 1879.4 3548.9 627.21
Aug-08 1564.0 3459.5 592.30
Sep-08 1772.1 3806.1 660.35
Oct-08 1475.2 3460.3 466.13Nov-08 1527.1 2716.9 620.52
Dec-08 1256.5 2125.4 673.50
Jan-09 1346.0 2528.4 637.30
Feb-09 1249.6 2122.7 641.32
Mar-09 1311.8 2354.7 739.43
Apr-09 1321.5 2798.4 697.52
May-09 1462.7 2561.4 720.68
Jun-09 1522.0 3339.3 735.17
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Jul-09 1467.6 2639.2 744.85
Aug-09 1462.3 2528.2 780.53
Sep-09 1508.0 2419.3 806.12
Oct-09 1577.2 2971.6 758.29
Nov-09 1518.0 2528.4 742.79
Dec-09 1566.1 2907.6 697.60
Jan-10 1684.8 3320.9 667.90Feb-10 1518.6 2504.6 589.03
Mar-10 1769.6 3287.0 763.72
Apr-10 1700.8 3015.7 755.77
May-10 1753.6 3363.3 757.86
Jun-10 1780.6 3224.2 841.44
Jul-10 1726.2 3238.8 791.18
Aug-10 1738.4 3010.0 933.06
Sep-10 1593.0 2780.6 922.06
Oct-10 1938.1 3193.3 855.11
Nov-10 1776.7 3125.0 926.89
Dec-10 2126.6 3751.0 863.13
Exp=f(Imp,WR)
For X=f(Y,Z)
SUMMARY OUTPUT
Regression Statistics X= 516.95+0.278Y+0.37ZMultiple R 0.946571
R Square 0.895997
Adjusted R Square 0.894123
Standard Error 109.444
Observations 114
ANOVA
df SS MS F Significance F
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Regression 2 11454361 5727180 478.1406 2.79221E-55
Residual 111 1329561 11978
Total 113 12783922
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 516.95 27.90 18.53 0.00 461.67 572.24
X Variable 1 0.28 0.02 16.22 0.00 0.24 0.31X Variable 2 0.37 0.08 4.49 0.00 0.21 0.54
Calculated X Variable 1 16.22133 Greater
T-Stats= X Variable 2 4.48915 than 2
P-Value X Variable 1 0.00000 Smaller
X Variable 2 0.00002 than 0.05
Conclusions X Variable 1 Significant Model fit
X Variable 2 Significant for forecasting
Coeffecient of determination 0.90 Greater than 0.65
Conclusions Significant fit for forecasting
Imp=g(Exp,WR)
For Y=g(X,Z)
SUMMARY OUTPUT
Regression Statistics Y= -1175.7+0.15X+2.52Z
Multiple R 0.94
R Square 0.88
Adjusted R Square 0.88
Standard Error 329.54
Observations 114
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ANOVA
df SS MS F Significance F
Regression 2 86340452.5 43170226.2 397.523643 2.47487E-51
Residual 111 12054365.0 108597.9
Total 113 98394817.5
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -1175.7351 128.1849 -9.1722 0.0000 -1429.7420 -921.7282
X Variable 1 0.1576 0.2706 0.5825 0.5614 -0.3786 0.6938
X Variable 2 2.5252 0.1557 16.2213 0.0000 2.2167 2.8337
Calculated T-Stats=X Variable 1 0.5825 Smaller than
X Variable 2 16.2213 Greater than 2
P-Value X Variable 1 0.5614 Greater than 0.05X Variable 2 0.0000 Smaller than 0.05
Conclusions X Variable 1 Insignificant Model is not fit
X Variable 2 Significant for forecasting
Coeffecient of determination 0.88 Model is fit
Conclusions Significant for forecasting
WR=h(Exp,Imp)For Z=h(X,Y)
SUMMARY OUTPUT
Regression Statistics Z= -109.3+0.41X+0.019Y
Multiple R 0.807
R Square 0.651
Adjusted R Square 0.644225
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Standard Error 115.417745
Observations 114
ANOVA
df SS MS F Significance F
Regression 2 2752391.3 1376195.6 103.3 4.56884E-26
Residual 111 1478659.4 13321.3Total 113 4231050.7
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -109.3182 58.6135 -1.8651 0.0648 -225.4647 6.8284
X Variable 1 0.4134 0.0921 4.4892 0.0000 0.2309 0.5959
X Variable 2 0.0193 0.0332 0.5825 0.5614 -0.0464 0.0851
Calculated T-Stats=X Variable 1 4.4892 Greater than 2
X Variable 2 0.5825 Smaller than 2
P-Value X Variable 1 0.0000 Smaller than 0.05
X Variable 2 0.5614 Greater than 0.05
Conclusions X Variable 1 Significant model is not fit
X Variable 2 Insignificant for forecasting
Coeffecient of determination 0.65 Model is fitConclusions Significant for forecasting
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Forecasting
For X=f(Y,Z)
RESIDUAL OUTPUT
Observation Predicted Y Residuals
1 768.9293063 182.93211792 814.212978 -130.2938457
3 791.5480576 -11.09208653
4 820.6659308 -20.49070578
5 843.4973096 -83.51654647
6 785.891922 -74.82478232
7 822.2322408 -99.98234878
8 8 10.3652928 -110.734517
9 848.315641 -193.4542977
10 853.6108644 -127.8489513
11 923.5248338 -137.5474074
12 888.4174701 -42.32375855
13 889.4654442 -72.80686465
14 932.7810623 -29.98978493
15 893.36438 -24.39373609
16 940.9026185 -49.15595666
17 915.9083549 -61.80077309
18 939.5500721 -76.32476365
19 952.7010855 -6.173784026
20 900.2241437 -123.82302321 1003.294791 -67.68595169
22 9 28.4600722 61.75864705
23 9 12.1191854 137.4533979
24 9 73.0872626 291.3275167
25 909.6021899 -19.43012574
26 9 09.6537288 129.0234672
27 9 35.4225454 103.3940956
28 9 66.7492117 39.83843638
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29 887.193947 -25.55500734
30 1 029.017937 16.12068985
31 1 033.849098 60.13335336
32 941.8999001 -35.68147111
33 1031.668636 -7.69970355
34 1 061.777799 34.04094699
35 1110.851213 -47.2068368536 1 167.437109 81.18523589
37 1045.79854 137.9671936
38 1 054.098342 133.6069459
39 1 016.981713 96.39415062
40 1047.023946 -49.28488366
41 1036.768731 -127.8174513
42 1 108.143251 21.85025194
43 1084.906848 63.3104802
44 1 139.671506 26.43911482
45 1 276.564765 70.25631734
46 1195.91225 102.0064792
47 1 212.695608 165.5192226
48 1271.38349 260.849717
49 1189.35159 79.99444924
50 1 268.621309 132.0902294
51 1 290.402034 192.9041981
52 1303.05697 21.96912952
53 1272.059541 -158.5926541
54 1344.19785 111.140700455 1259.645925 -34.97167633
56 1265.715727 -36.77016183
57 1 421.353911 91.53605009
58 1295.25738 147.9760335
59 1 442.900915 41.22907283
60 1521.149638 -11.06450831
61 1342.228947 -0.225541686
62 1381.46261 117.077238
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63 1 353.951555 58.83788941
64 1263.135512 -0.558945457
65 1456.19182 -81.2791128
66 1 407.758868 108.8348937
67 1311.345396 -135.7802649
68 1403.318548 -131.4212961
69 1 440.770307 82.3457495370 1424.523713 44.7900165
71 1 482.940625 101.8488247
72 1483.740448 60.4033394
73 1 418.066803 53.49152971
74 1464.11088 0.451109146
75 1470.48051 13.98011293
76 1675.344417 -297.1863093
77 1585.355969 -46.16565661
78 1349.285076 -29.06071962
79 1706.935019 -242.6926924
80 1722.626407 -184.5029111
81 1805.184985 -33.56824532
82 1878.417755 -87.60750898
83 1 815.615132 105.1717679
84 1 841.143289 67.42160897
85 1 738.513535 140.8705646
86 1700.638757 -136.6076285
87 1822.493878 -50.35770079
88 1653.981449 -178.754958289 1 504.321315 22.79968491
90 1359.265443 -102.736294
91 1458.055044 -112.083255
92 1346.559676 -96.9579529
93 1447.625798 -135.8752069
94 1555.620443 -234.0830723
95 1498.234408 -35.54087969
96 1720.278382 -198.2557642
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97 1528.885714 -61.30150241
98 1511.244194 -48.90743601
99 1 490.416636 17.59466751
100 1626.449451 -49.23439043
101 1497.258569 20.78668247
102 1586.064675 -19.94994245
103 1690.147397 -5.327396852104 1433.473055 85.09399363
105 1716.322298 53.24485567
106 1637.798273 62.96926372
107 1735.404511 18.16948922
108 1727.732518 52.87500794
109 1713.106987 13.09979446
110 1702.127792 36.2931928
111 1634.134891 -41.10289108
112 1724.205393 213.8716072
113 1731.858324 44.81867608
114 1882.50336 244.0746405
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s.
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Q6: Estimate autoregressive model for each series using Specific to general approach and test its significance and forecast for
Exp Imp
y x z y x z
Jul-01 951.9 0 0 791.6 0 0
Aug-01 683.9 951.9 0.0 938.0 791.6 0.0Sep-01 780.5 683.9 951.9 774.5 938.0 791.6
Oct-01 800.2 780.5 683.9 838.3 774.5 938.0
Nov-01 760.0 800.2 780.5 825.3 838.3 774.5
Dec-01 711.1 760.0 800.2 707.7 825.3 838.3
Jan-02 722.2 711.1 760.0 854.8 707.7 825.3
Feb-02 699.6 722.2 711.1 738.1 854.8 707.7
Mar-02 654.9 699.6 722.2 886.6 738.1 854.8
Apr-02 725.8 654.9 699.6 890.1 886.6 738.1
May-02 786.0 725.8 654.9 1119.3 890.1 886.6
Jun-02 846.1 786.0 725.8 975.3 1119.3 890.1
Jul-02 816.7 846.1 786.0 927.2 975.3 1119.3
Aug-02 902.8 816.7 846.1 969.3 927.2 975.3
Sep-02 869.0 902.8 816.7 880.3 969.3 927.2
Oct-02 891.7 869.0 902.8 1018.0 880.3 969.3
Nov-02 854.1 891.7 869.0 960.2 1018.0 880.3
Dec-02 863.2 854.1 891.7 1032.6 960.2 1018.0
Jan-03 946.5 863.2 854.1 1053.1 1032.6 960.2
Feb-03 776.4 946.5 863.2 918.7 1053.1 1032.6
Mar-03 935.6 776.4 946.5 1270.5 918.7 1053.1Apr-03 990.2 935.6 776.4 1068.0 1270.5 918.7
May-03 1049.6 990.2 935.6 969.8 1068.0 1270.5
Jun-03 1264.4 1049.6 990.2 1152.6 969.8 1068.0
Jul-03 890.2 1264.4 1049.6 999.8 1152.6 969.8
Aug-03 1038.7 890.2 1264.4 1035.1 999.8 1152.6
Sep-03 1038.8 1038.7 890.2 1077.6 1035.1 999.8
Oct-03 1006.6 1038.8 1038.7 1176.5 1077.6 1035.1
Nov-03 861.6 1006.6 1038.8 991.6 1176.5 1077.6
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Dec-03 1045.1 861.6 1006.6 1323.8 991.6 1176.5
Jan-04 1094.0 1045.1 861.6 1345.7 1323.8 991.6
Feb-04 906.2 1094.0 1045.1 1139.4 1345.7 1323.8
Mar-04 1024.0 906.2 1094.0 1408.1 1139.4 1345.7
Apr-04 1095.8 1024.0 906.2 1508.7 1408.1 1139.4
May-04 1063.6 1095.8 1024.0 1724.0 1508.7 1408.1
Jun-04 1248.6 1063.6 1095.8 1861.7 1724.0 1508.7Jul-04 1183.8 1248.6 1063.6 1457.7 1861.7 1724.0
Aug-04 1187.7 1183.8 1248.6 1475.2 1457.7 1861.7
Sep-04 1113.4 1187.7 1183.8 1377.7 1475.2 1457.7
Oct-04 997.7 1113.4 1187.7 1456.4 1377.7 1475.2
Nov-04 909.0 997.7 1113.4 1476.9 1456.4 1377.7
Dec-04 1130.0 909.0 997.7 1673.7 1476.9 1456.4
Jan-05 1148.2 1130.0 909.0 1610.3 1673.7 1476.9
Feb-05 1166.1 1148.2 1130.0 1783.0 1610.3 1673.7
Mar-05 1346.8 1166.1 1148.2 2135.2 1783.0 1610.3Apr-05 1297.9 1346.8 1166.1 1902.6 2135.2 1783.0
May-05 1378.2 1297.9 1346.8 2019.8 1902.6 2135.2
Jun-05 1532.2 1378.2 1297.9 2229.6 2019.8 1902.6
Jul-05 1269.3 1532.2 1378.2 1996.3 2229.6 2019.8
Aug-05 1400.7 1269.3 1532.2 2233.8 1996.3 2229.6
Sep-05 1483.3 1400.7 1269.3 2321.8 2233.8 1996.3
Oct-05 1325.0 1483.3 1400.7 2325.3 2321.8 2233.8
Nov-05 1113.5 1325.0 1483.3 2299.0 2325.3 2321.8
Dec-05 1455.3 1113.5 1325.0 2474.7 2299.0 2325.3
Jan-06 1224.7 1455.3 1113.5 2144.3 2474.7 2299.0Feb-06 1228.9 1224.7 1455.3 2210.4 2144.3 2474.7
Mar-06 1512.9 1228.9 1224.7 2681.9 2210.4 2144.3
Apr-06 1443.2 1512.9 1228.9 2258.6 2681.9 2210.4
May-06 1484.1 1443.2 1512.9 2648.5 2258.6 2681.9
Jun-06 1510.1 1484.1 1443.2 2986.4 2648.5 2258.6
Jul-06 1342.0 1510.1 1484.1 2459.9 2986.4 2648.5
Aug-06 1498.5 1342.0 1510.1 2523.6 2459.9 2986.4
Sep-06 1412.8 1498.5 1342.0 2442.3 2523.6 2459.9
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Oct-06 1262.6 1412.8 1498.5 2131.1 2442.3 2523.6
Nov-06 1374.9 1262.6 1412.8 2773.6 2131.1 2442.3
Dec-06 1516.6 1374.9 1262.6 2564.2 2773.6 2131.1
Jan-07 1175.6 1516.6 1374.9 2329.9 2564.2 2773.6
Feb-07 1271.9 1175.6 1516.6 2572.3 2329.9 2564.2
Mar-07 1523.1 1271.9 1175.6 2622.6 2572.3 2329.9
Apr-07 1469.3 1523.1 1271.9 2573.5 2622.6 2572.3May-07 1584.8 1469.3 1523.1 2750.3 2573.5 2622.6
Jun-07 1544.1 1584.8 1469.3 2796.5 2750.3 2573.5
Jul-07 1471.6 1544.1 1584.8 2573.8 2796.5 2750.3
Aug-07 1464.6 1471.6 1544.1 2747.4 2573.8 2796.5
Sep-07 1484.5 1464.6 1471.6 2734.9 2747.4 2573.8
Oct-07 1378.2 1484.5 1464.6 3384.7 2734.9 2747.4
Nov-07 1539.2 1378.2 1484.5 3161.3 3384.7 2734.9
Dec-07 1320.2 1539.2 1378.2 2348.8 3161.3 3384.7
Jan-08 1464.2 1320.2 1539.2 3529.1 2348.8 3161.3
Feb-08 1538.1 1464.2 1320.2 3657.9 3529.1 2348.8
Mar-08 1771.6 1538.1 1464.2 3821.6 3657.9 3529.1
Apr-08 1790.8 1771.6 1538.1 4099.9 3821.6 3657.9
May-08 1920.8 1790.8 1771.6 3882.3 4099.9 3821.6
Jun-08 1908.6 1920.8 1790.8 4023.8 3882.3 4099.9
Jul-08 1879.4 1908.6 1920.8 3548.9 4023.8 3882.3
Aug-08 1564.0 1879.4 1908.6 3459.5 3548.9 4023.8
Sep-08 1772.1 1564.0 1879.4 3806.1 3459.5 3548.9
Oct-08 1475.2 1772.1 1564.0 3460.3 3806.1 3459.5
Nov-08 1527.1 1475.2 1772.1 2716.9 3460.3 3806.1Dec-08 1256.5 1527.1 1475.2 2125.4 2716.9 3460.3
Jan-09 1346.0 1256.5 1527.1 2528.4 2125.4 2716.9
Feb-09 1249.6 1346.0 1256.5 2122.7 2528.4 2125.4
Mar-09 1311.8 1249.6 1346.0 2354.7 2122.7 2528.4
Apr-09 1321.5 1311.8 1249.6 2798.4 2354.7 2122.7
May-09 1462.7 1321.5 1311.8 2561.4 2798.4 2354.7
Jun-09 1522.0 1462.7 1321.5 3339.3 2561.4 2798.4
Jul-09 1467.6 1522.0 1462.7 2639.2 3339.3 2561.4
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Aug-09 1462.3 1467.6 1522.0 2528.2 2639.2 3339.3
Sep-09 1508.0 1462.3 1467.6 2419.3 2528.2 2639.2
Oct-09 1577.2 1508.0 1462.3 2971.6 2419.3 2528.2
Nov-09 1518.0 1577.2 1508.0 2528.4 2971.6 2419.3
Dec-09 1566.1 1518.0 1577.2 2907.6 2528.4 2971.6
Jan-10 1684.8 1566.1 1518.0 3320.9 2907.6 2528.4
Feb-10 1518.6 1684.8 1566.1 2504.6 3320.9 2907.6Mar-10 1769.6 1518.6 1684.8 3287.0 2504.6 3320.9
Apr-10 1700.8 1769.6 1518.6 3015.7 3287.0 2504.6
May-10 1753.6 1700.8 1769.6 3363.3 3015.7 3287.0
Jun-10 1780.6 1753.6 1700.8 3224.2 3363.3 3015.7
Jul-10 1726.2 1780.6 1753.6 3238.8 3224.2 3363.3
Aug-10 1738.4 1726.2 1780.6 3010.0 3238.8 3224.2
Sep-10 1593.0 1738.4 1726.2 2780.6 3010.0 3238.8
Oct-10 1938.1 1593.0 1738.4 3193.3 2780.6 3010.0
Nov-10 1776.7 1938.1 1593.0 3125.0 3193.3 2780.6
Dec-10 2126.6 1776.7 1938.1 3751.0 3125.0 3193.3
AR(1) Model
Export
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.877835685 Y=213.10+0.85Yt-1
R Square 0.77059549
Adjusted R Squar 0.768547235
Standard Error 161.8169512
Observations 114
ANOVA
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df SS MS F Significance F
Regression 1 9851232.338 9851232.338 376.2205667 1.33515E-37
Residual 112 2932689.277 26184.72569
Total 113 12783921.62
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 213.10 57.68 3.69 0.0003 98.81 327.39X Variable 1 0.85 0.04 19.40 0.0000 0.76 0.93
AR (2) Model
SUMMARY OUTPUT
Regression Statistics Y=187.02+0.49Yt-1+0.38Yt-2
Multiple R 0.898
R Square 0.806
Adjusted R Squar 0.803
Standard Error 149.428
Observations 114
ANOVA
df SS MS F Significance F
Regression 2 10305448.5 5152724.273 230.7680489 2.86659E-40
Residual 111 2478473.1 22328.58621
Total 113 12783921.6
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 187.02 53.58 3.49 0.00069 80.85 293.19
X Variable 1 0.49 0.09 5.48 0.00000 0.31 0.67
X Variable 2 0.38 0.09 4.51 0.00002 0.22 0.55
Result
Since the values of both X variable 1 and 2 is very small in AR 2 model, so we accept AR 1 Model for forecasting.
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Forecasting for following periods
Export Import W.Remittance
AR (1) AR (2) AR (1)
Jan-11 2020.7 3472.1 850.3
Feb-11 1930.7 3526.6 838.2
Mar-11 1854.2 3461.2 826.7
Apr-11 1789.2 3441.7 815.7
May-11 1733.9 3407.3 805.3
Jun-11 1686.9 3380.1 795.4
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remaining six months.
AR(1) Model
WR Workers' Remittance
y x z
84.74 0 0 SUMMARY OUTPUT
96.89 84.74 0.0158.42 96.89 84.74 Regression Statistics
188.93 158.42 96.89 Multiple R 0.96 Y=30.37+0.95Yt-1
260.12 188.93 158.42 R Square 0.91
193.22 260.12 188.93 Adjusted R Squ 0.91
180.80 193.22 260.12 Standard Error 56.74
236.33 180.80 193.22 Observations 114
227.17 236.33 180.80
238.79 227.17 236.33
255.10 238.79 227.17 ANOVA
268.54 255.10 238.79 df SS MS
307.41 268.54 255.10 Regression 1 3870474.668 3870474.668
392.44 307.41 268.54 Residual 112 360576.0095 3219.428657
353.04 392.44 307.41 Total 113 4231050.678
377.77 353.04 392.44
353.83 377.77 353.04 Coefficients Standard Error t Stat
363.19 353.83 377.77 Intercept 30.37 13.66 2.22
383.22 363.19 353.83 X Variable 1 0.95 0.03 34.67
342.77 383.22 363.19
356.41 342.77 383.22 AR (2) Model306.85 356.41 342.77
336.42 306.85 356.41 SUMMARY OUTPUT
363.50 336.42 306.85
307.23 363.50 336.42 Regression Statistics Y=25.47+0.57Yt-1+
280.87 307.23 363.50 Multiple R 0.963
318.38 280.87 307.23 R Square 0.928
328.52 318.38 280.87 Adjusted R Squ 0.927
253.08 328.52 318.38 Standard Error 52.319
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385.71 253.08 328.52 Observations 114
382.31 385.71 253.08
289.49 382.31 385.71 ANOVA
329.67 289.49 382.31 df SS MS
335.31 329.67 289.49 Regression 2 3927212 1963606
306.00 335.31 329.67 Residual 111 303838 2737
355.01 306.00 335.31 Total 113 4231051330.51 355.01 306.00
339.70 330.51 355.01 Coefficients Standard Error t Stat
312.94 339.70 330.51 Intercept 25.47 12.645 2.014
334.80 312.94 339.70 X Variable 1 0.57 0.087 6.524
291.81 334.80 312.94 X Variable 2 0.40 0.087 4.553
336.38 291.81 334.80
321.38 336.38 291.81 Result
339.29 321.38 336.38 Since the values of both X variable 1 and 2 is very small in AR 2 model,
443.70 339.29 321.38
401.00 443.70 339.29
358.30 401.00 443.70
358.98 358.30 401.00
313.14 358.98 358.30
348.41 313.14 358.98
341.10 348.41 313.14
372.50 341.10 348.41
308.81 372.50 341.10
371.24 308.81 372.50
391.32 371.24 308.81358.13 391.32 371.24
423.56 358.13 391.32
401.47 423.56 358.13
506.57 401.47 423.56
463.87 506.57 401.47
377.01 463.87 506.57
434.84 377.01 463.87
421.74 434.84 377.01
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410.61 421.74 434.84
448.61 410.61 421.74
475.21 448.61 410.61
391.33 475.21 448.61
457.18 391.33 475.21
520.24 457.18 391.33
513.35 520.24 457.18537.98 513.35 520.24
505.55 537.98 513.35
495.69 505.55 537.98
489.51 495.69 505.55
516.05 489.51 495.69
580.24 516.05 489.51
505.58 580.24 516.05
479.26 505.58 580.24
557.07 479.26 505.58
502.76 557.07 479.26
602.21 502.76 557.07
590.71 602.21 502.76
584.75 590.71 602.21
547.41 584.75 590.71
627.21 547.41 584.75
592.30 627.21 547.41
660.35 592.30 627.21
466.13 660.35 592.30
620.52 466.13 660.35673.50 620.52 466.13
637.30 673.50 620.52
641.32 637.30 673.50
739.43 641.32 637.30
697.52 739.43 641.32
720.68 697.52 739.43
735.17 720.68 697.52
744.85 735.17 720.68
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780.53 744.85 735.17
806.12 780.53 744.85
758.29 806.12 780.53
742.79 758.29 806.12
697.60 742.79 758.29
667.90 697.60 742.79
589.03 667.90 697.60763.72 589.03 667.90
755.77 763.72 589.03
757.86 755.77 763.72
841.44 757.86 755.77
791.18 841.44 757.86
933.06 791.18 841.44
922.06 933.06 791.18
855.11 922.06 933.06
926.89 855.11 922.06
863.13 926.89 855.11
AR(1) Model
Import
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.936 Y=188.5+0.9Yt-1
R Square 0.877
Adjusted R Squa 0.876
Standard Error 328.912
Observations 114
ANOVA
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df SS MS F Significance F
Regression 1 86278300.56 86278300.56 797.5204184 9.26991E-53
Residual 112 12116516.94 108183.187
Total 113 98394817.5
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 188.5 76.4 2.5 0.0151 37.2X Variable 1 0.9 0.0 28.2 0.0000 0.9
AR (2) Model
SUMMARY OUTPUT
Regression Statistics Y=165.23+0.59Yt-1+0.35Yt-2
Multiple R 0.944
R Square 0.892
Adjusted R Squa 0.890
Standard Error 309.402
Observations 114
ANOVA
df SS MS F Significance F
Regression 2 87768852 43884425.9 458.422 2.25677E-54
Residual 111 10625966 95729.4
Total 113 98394818
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 165.23 72.08 2.29 0.024 22.40
X Variable 1 0.59 0.09 6.54 0.000 0.41
X Variable 2 0.35 0.09 3.95 0.000 0.17
Result
Since the value of X variable 1 is very small in AR 1 model, so we accept AR 2 model for forecasting
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F Significance F
1202.224084 1.01408E-61
P-value Lower 95% Upper 95%
0.03 3.30 57.45
0.00 0.90 1.00
0.40Yt-2
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F Significance F
717.3557196 3.30216E-64
P-value Lower 95% Upper 95%
0.046 0.414 50.528
0.000 0.397 0.743
0.000 0.225 0.572
so we accept AR 1 Model for forecasting.
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Upper 95%
339.81.0
Upper 95%
308.07
0.77
0.53
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Q7: Calculate 3 months, 5months, 7 months and 12 months moving average of the given series and forecast for the remaini
3 Months Moving Average 5 Months Moving Average
Exp Imp WR Exp Imp WR Exp Imp WR
Jul-01 951.9 791.6 84.74
Aug-01 683.9 938.0 96.89Sep-01 780.5 774.5 158.42 805.4 834.69 113.35
Oct-01 800.2 838.3 188.93 754.9 850.26 148.08
Nov-01 760.0 825.3 260.12 780.2 812.70 202.49 795.3 833.54 157.82
Dec-01 711.1 707.7 193.22 757.1 790.45 214.09 747.1 816.76 179.516
Jan-02 722.2 854.8 180.80 731.1 795.94 211.38 754.8 800.12 196.298
Feb-02 699.6 738.1 236.33 711.0 766.87 203.45 738.6 792.84 211.88
Mar-02 654.9 886.6 227.17 692.2 826.47 214.77 709.6 802.49 219.528
Apr-02 725.8 890.1 238.79 693.4 838.23 234.10 702.7 815.44 215.262
May-02 786.0 1119.3 255.10 722.2 965.31 240.35 717.7 897.76 227.638
Jun-02 846.1 975.3 268.54 785.9 994.90 254.14 742.5 921.87 245.186
Jul-02 816.7 927.2 307.41 816.2 1007.29 277.02 765.9 959.70 259.402
Aug-02 902.8 969.3 392.44 855.2 957.27 322.80 815.5 976.24 292.456
Sep-02 869.0 880.3 353.04 862.8 925.60 350.96 844.1 974.29 315.306
Oct-02 891.7 1018.0 377.77 887.8 955.86 374.42 865.3 954.02 339.84
Nov-02 854.1 960.2 353.83 871.6 952.84 361.55 866.9 951.00 356.898
Dec-02 863.2 1032.6 363.19 869.7 1003.60 364.93 876.2 972.08 368.054
Jan-03 946.5 1053.1 383.22 888.0 1015.30 366.75 884.9 988.84 366.21
Feb-03 776.4 918.7 342.77 862.1 1001.45 363.06 866.4 996.51 364.156
Mar-03 935.6 1270.5 356.41 886.2 1080.75 360.80 875.2 1047.01 359.884Apr-03 990.2 1068.0 306.85 900.7 1085.71 335.34 902.4 1068.56 350.488
May-03 1049.6 969.8 336.42 991.8 1102.77 333.23 939.7 1056.01 345.134
Jun-03 1264.4 1152.6 363.50 1101.4 1063.47 335.59 1003.2 1075.91 341.19
Jul-03 890.2 999.8 307.23 1068.1 1040.73 335.72 1026.0 1092.13 334.082
Aug-03 1038.7 1035.1 280.87 1064.4 1062.49 317.20 1046.6 1045.06 318.974
Sep-03 1038.8 1077.6 318.38 989.2 1037.49 302.16 1056.3 1046.98 321.28
Oct-03 1006.6 1176.5 328.52 1028.0 1096.41 309.26 1047.7 1088.32 319.7
Nov-03 861.6 991.6 253.08 969.0 1081.89 299.99 967.2 1056.11 297.616
Dec 03 1045 1 1323 8 385 71 971 1 1163 95 322 44 998 2 1120 91 313 312
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Dec-03 1045.1 1323.8 385.71 971.1 1163.95 322.44 998.2 1120.91 313.312
Jan-04 1094.0 1345.7 382.31 1000.3 1220.33 340.37 1009.2 1183.02 333.6
Feb-04 906.2 1139.4 289.49 1015.1 1269.61 352.50 982.7 1195.38 327.822
Mar-04 1024.0 1408.1 329.67 1008.1 1297.71 333.82 986.2 1241.69 328.052
Apr-04 1095.8 1508.7 335.31 1008.7 1352.04 318.16 1033.0 1345.11 344.498
May-04 1063.6 1724.0 306.00 1061.1 1546.90 323.66 1036.7 1425.15 328.556
Jun-04 1248.6 1861.7 355.01 1136.0 1698.11 332.11 1067.7 1528.36 323.096Jul-04 1183.8 1457.7 330.51 1165.3 1681.12 330.51 1123.2 1592.02 331.3
Aug-04 1187.7 1475.2 339.70 1206.7 1598.21 341.74 1155.9 1605.45 333.306
Sep-04 1113.4 1377.7 312.94 1161.6 1436.86 327.72 1159.4 1579.25 328.832
Oct-04 997.7 1456.4 334.80 1099.6 1436.42 329.15 1146.2 1525.73 334.592
Nov-04 909.0 1476.9 291.81 1006.7 1436.98 313.18 1078.3 1448.77 321.952
Dec-04 1130.0 1673.7 336.38 1012.2 1535.66 321.00 1067.6 1491.97 323.126
Jan-05 1148.2 1610.3 321.38 1062.4 1586.97 316.52 1059.7 1518.99 319.462
Feb-05 1166.1 1783.0 339.29 1148.1 1689.00 332.35 1070.2 1600.05 324.732
Mar-05 1346.8 2135.2 443.70 1220.4 1842.82 368.12 1140.0 1735.82 346.512
Apr-05 1297.9 1902.6 401.00 1270.3 1940.26 394.66 1217.8 1820.95 368.35May-05 1378.2 2019.8 358.30 1341.0 2019.19 401.00 1267.5 1890.18 372.734
Jun-05 1532.2 2229.6 358.98 1402.8 2050.68 372.76 1344.3 2014.05 380.254
Jul-05 1269.3 1996.3 313.14 1393.3 2081.91 343.47 1364.9 2056.70 375.024
Aug-05 1400.7 2233.8 348.41 1400.8 2153.25 340.18 1375.7 2076.43 355.966
Sep-05 1483.3 2321.8 341.10 1384.5 2183.96 334.22 1412.8 2160.27 343.986
Oct-05 1325.0 2325.3 372.50 1403.0 2293.64 354.00 1402.1 2221.37 346.826
Nov-05 1113.5 2299.0 308.81 1307.3 2315.37 340.80 1318.4 2235.24 336.792
Dec-05 1455.3 2474.7 371.24 1297.9 2366.34 350.85 1355.6 2330.93 348.412
Jan-06 1224.7 2144.3 391.32 1264.5 2306.02 357.12 1320.4 2313.03 356.994
Feb-06 1228.9 2210.4 358.13 1303.0 2276.49 373.56 1269.5 2290.76 360.4
Mar-06 1512.9 2681.9 423.56 1322.2 2345.55 391.00 1307.1 2362.07 370.612
Apr-06 1443.2 2258.6 401.47 1395.0 2383.66 394.39 1373.0 2354.00 389.144
May-06 1484.1 2648.5 506.57 1480.1 2529.68 443.87 1378.8 2388.76 416.21
Jun-06 1510.1 2986.4 463.87 1479.1 2631.18 457.30 1435.9 2557.17 430.72
Jul-06 1342.0 2459.9 377.01 1445.4 2698.28 449.15 1458.5 2607.08 434.496
Aug-06 1498.5 2523.6 434.84 1450.2 2656.66 425.24 1455.6 2575.42 436.752
Sep-06 1412.8 2442.3 421.74 1417.8 2475.30 411.20 1449.5 2612.16 440.806
Oct-06 1262 6 2131 1 410 61 1391 3 2365 69 422 40 1405 2 2508 68 421 614
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Oct-06 1262.6 2131.1 410.61 1391.3 2365.69 422.40 1405.2 2508.68 421.614
Nov-06 1374.9 2773.6 448.61 1350.1 2449.00 426.99 1378.2 2466.11 418.562
Dec-06 1516.6 2564.2 475.21 1384.7 2489.61 444.81 1413.1 2486.96 438.202
Jan-07 1175.6 2329.9 391.33 1355.7 2555.89 438.38 1348.5 2448.22 429.5
Feb-07 1271.9 2572.3 457.18 1321.4 2488.79 441.24 1320.3 2474.21 436.588
Mar-07 1523.1 2622.6 520.24 1323.5 2508.27 456.25 1372.4 2572.50 458.514
Apr-07 1469.3 2573.5 513.35 1421.4 2589.44 496.92 1391.3 2532.48 471.462May-07 1584.8 2750.3 537.98 1525.7 2648.79 523.86 1404.9 2569.72 484.016
Jun-07 1544.1 2796.5 505.55 1532.7 2706.75 518.96 1478.7 2663.02 506.86
Jul-07 1471.6 2573.8 495.69 1533.5 2706.88 513.07 1518.6 2663.34 514.562
Aug-07 1464.6 2747.4 489.51 1493.4 2705.91 496.92 1506.9 2688.30 508.416
Sep-07 1484.5 2734.9 516.05 1473.5 2685.36 500.42 1509.9 2720.58 508.956
Oct-07 1378.2 3384.7 580.24 1442.4 2955.66 528.60 1468.6 2847.46 517.408
Nov-07 1539.2 3161.3 505.58 1467.3 3093.62 533.96 1467.6 2920.42 517.414
Dec-07 1320.2 2348.8 479.26 1412.5 2964.94 521.69 1437.3 2875.42 514.128
Jan-08 1464.2 3529.1 557.07 1441.2 3013.05 513.97 1437.3 3031.75 527.64
Feb-08 1538.1 3657.9 502.76 1440.9 3178.59 513.03 1448.0 3216.36 524.982Mar-08 1771.6 3821.6 602.21 1591.3 3669.52 554.01 1526.7 3303.73 529.376
Apr-08 1790.8 4099.9 590.71 1700.2 3859.79 565.23 1577.0 3491.45 546.402
May-08 1920.8 3882.3 584.75 1827.7 3934.60 592.56 1697.1 3798.16 567.5
Jun-08 1908.6 4023.8 547.41 1873.4 4002.02 574.29 1786.0 3897.11 565.568
Jul-08 1879.4 3548.9 627.21 1902.9 3818.34 586.46 1854.2 3875.30 590.458
Aug-08 1564.0 3459.5 592.30 1784.0 3677.38 588.97 1812.7 3802.87 588.476
Sep-08 1772.1 3806.1 660.35 1738.5 3604.82 626.62 1809.0 3744.13 602.404
Oct-08 1475.2 3460.3 466.13 1603.8 3575.31 572.93 1719.9 3659.72 578.68
Nov-08 1527.1 2716.9 620.52 1591.5 3327.80 582.33 1643.6 3398.34 593.302
Dec-08 1256.5 2125.4 673.50 1419.6 2767.56 586.72 1519.0 3113.65 602.56
Jan-09 1346.0 2528.4 637.30 1376.5 2456.93 643.77 1475.4 2927.45 611.56
Feb-09 1249.6 2122.7 641.32 1284.0 2258.86 650.71 1370.9 2590.77 607.754
Mar-09 1311.8 2354.7 739.43 1302.4 2335.28 672.68 1338.2 2369.64 662.414
Apr-09 1321.5 2798.4 697.52 1294.3 2425.26 692.76 1297.1 2385.93 677.814
May-09 1462.7 2561.4 720.68 1365.3 2571.48 719.21 1338.3 2473.12 687.25
Jun-09 1522.0 3339.3 735.17 1435.4 2899.69 717.79 1373.5 2635.30 706.824
Jul-09 1467.6 2639.2 744.85 1484.1 2846.64 733.57 1417.1 2738.59 727.53
Aug-09 1462 3 2528 2 780 53 1484 0 2835 58 753 52 1447 2 2773 30 735 75
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Aug 09 1462.3 2528.2 780.53 1484.0 2835.58 753.52 1447.2 2773.30 735.75
Sep-09 1508.0 2419.3 806.12 1479.3 2528.92 777.17 1484.5 2697.49 757.47
Oct-09 1577.2 2971.6 758.29 1515.9 2639.71 781.65 1507.4 2779.52 764.992
Nov-09 1518.0 2528.4 742.79 1534.4 2639.76 769.07 1506.6 2617.34 766.516
Dec-09 1566.1 2907.6 697.60 1553.8 2802.50 732.89 1526.3 2671.01 757.066
Jan-10 1684.8 3320.9 667.90 1589.7 2918.95 702.76 1570.8 2829.54 734.54
Feb-10 1518.6 2504.6 589.03 1589.8 2911.01 651.51 1573.0 2846.60 691.1221Mar-10 1769.6 3287.0 763.72 1657.7 3037.49 673.55 1611.4 2909.69 692.208
Apr-10 1700.8 3015.7 755.77 1663.0 2935.75 702.84 1648.0 3007.14 694.804
May-10 1753.6 3363.3 757.86 1741.3 3222.00 759.12 1685.5 3098.29 706.8566
Jun-10 1780.6 3224.2 841.44 1745.0 3201.08 785.02 1704.6 3078.96 741.5648
Jul-10 1726.2 3238.8 791.18 1753.5 3275.45 796.83 1746.1 3225.81 781.9946
Aug-10 1738.4 3010.0 933.06 1748.4 3157.69 855.23 1739.9 3170.41 815.8628
Sep-10 1593.0 2780.6 922.06 1685.9 3009.81 882.10 1718.4 3123.40 849.1208
Oct-10 1938.1 3193.3 855.11 1756.5 2994.65 903.41 1755.3 3089.40 868.5702
Nov-10 1776.7 3125.0 926.89 1769.3 3032.98 901.35 1754.5 3069.55 885.66
Dec-10 2126.6 3751.0 863.13 1947.1 3356.44 881.71 1834.6 3171.99 900.05Jan-11 1189.9 1985.5 432.3 1206.8 2004.6 430.6
Feb-11 1186.1 1982.3 431.3 1182.2 2000.4 427.7
Mar-11 1222.7 2104.9 447.2 1207.4 2038.3 440.8
Apr-11 1260.8 2156.7 459.4 1238.0 2091.2 450.9
May-11 1339.6 2282.3 481.9 1274.0 2177.5 459.5
Jun-11 1388.0 2360.9 483.1 1326.2 2263.5 471.3
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g Six months.
7 Months Moving Average 12 Months Moving Average
Exp Imp WR Exp Imp WR
772.82 818.60 166.16
736.78 810.95 187.82
732.63 803.61 206.43
724.82 820.12 217.91
722.79 860.26 227.36
735.09 881.70 228.56 760.17 861.63 199.09
750.18 913.05 244.88 748.90 872.93 217.64
775.97 929.40 275.11 767.14 875.54 242.27
800.16 949.72 291.78 774.52 884.36 258.49
834.00 968.50 313.30 782.15 899.33 274.23
852.34 978.52 329.73 789.99 910.57 282.04
863.37 966.13 345.17 802.67 937.64 296.20
877.72 977.24 361.56 821.36 954.17 313.07
871.97 976.02 366.61 827.76 969.22 321.94
876.66 1019.05 361.46 851.16 1001.21 332.71893.98 1045.86 354.86 873.19 1016.04 338.38
916.52 1038.98 348.96 895.16 1003.58 345.16
975.14 1066.47 350.34 930.02 1018.35 353.07
978.99 1061.77 342.34 936.15 1024.40 353.06
992.15 1059.21 327.72 947.47 1029.89 343.76
1029.64 1081.91 324.24 961.62 1046.33 340.87
1039.78 1068.48 320.25 971.19 1059.54 336.77
1021.41 1057.57 312.57 971.82 1062.15 328.37
1020.78 1108.13 319.61 986.98 1086.41 330.25
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1020.78 1108.13 319.61 986.98 1086.41 330.25
996.43 1135.71 322.30 999.27 1110.80 330.17
998.72 1155.66 319.77 1010.09 1129.19 325.73
996.62 1208.94 326.74 1017.45 1140.65 323.50
1004.76 1270.52 329.16 1026.25 1177.38 325.87
1012.92 1348.73 325.94 1027.42 1240.22 323.34
1068.20 1473.03 340.50 1026.11 1299.31 322.631088.00 1492.16 332.61 1050.57 1337.48 324.57
1101.39 1510.67 326.53 1062.99 1374.15 329.47
1130.99 1544.71 329.88 1069.21 1399.16 329.02
1127.24 1551.61 330.61 1068.47 1422.48 329.54
1100.54 1547.08 324.40 1072.41 1462.92 332.77
1110.02 1539.90 328.74 1079.48 1492.08 328.66
1095.68 1503.98 323.93 1084.00 1514.14 323.58
1093.16 1550.45 325.19 1105.66 1567.77 327.73
1115.89 1644.73 340.04 1132.56 1628.36 337.24
1142.25 1719.72 352.62 1149.41 1661.19 342.711196.60 1800.21 355.98 1175.62 1685.85 347.07
1285.64 1907.74 365.58 1199.25 1716.51 347.40
1305.55 1953.83 362.26 1206.39 1761.39 345.95
1341.62 2042.91 366.12 1224.14 1824.61 346.68
1386.94 2119.87 366.38 1254.96 1903.28 349.02
1383.82 2147.03 356.20 1282.24 1975.69 352.17
1357.47 2203.67 343.03 1299.28 2044.20 353.58
1368.49 2268.65 344.88 1326.39 2110.95 356.49
1324.55 2256.46 349.50 1332.76 2155.46 362.32
1318.78 2287.06 355.93 1338.00 2191.07 363.89
1334.81 2351.07 366.67 1351.84 2236.63 362.21
1329.08 2342.05 375.29 1363.95 2266.31 362.25
1351.81 2388.21 394.44 1372.78 2318.69 374.60
1408.47 2486.41 416.59 1370.93 2381.76 383.34
1392.28 2484.30 417.42 1376.98 2420.40 388.67
1431.40 2538.49 423.64 1385.14 2444.55 395.87
1457.67 2571.62 432.72 1379.26 2454.59 402.59
1421.91 2492.94 430.87 1374.06 2438.41 405.76
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1412.15 2566.49 437.61 1395.84 2477.95 417.41
1416.79 2554.45 433.13 1400.95 2485.41 426.08
1369.00 2460.67 422.76 1396.86 2500.88 426.08
1358.98 2476.71 434.22 1400.43 2531.03 434.33
1362.49 2490.85 446.42 1401.29 2526.09 442.39
1370.57 2509.58 459.50 1403.46 2552.32 451.711416.60 2598.04 477.70 1411.85 2560.81 454.33
1440.77 2601.32 485.83 1414.69 2544.98 457.80
1434.34 2602.70 488.76 1425.48 2554.47 467.69
1475.63 2662.34 502.79 1422.65 2573.12 472.25
1505.99 2685.56 511.20 1428.62 2597.50 480.11
1485.28 2794.44 519.77 1438.26 2701.97 494.25
1495.27 2878.41 518.66 1451.95 2734.28 498.99
1457.47 2821.06 510.27 1435.58 2716.33 499.33
1446.06 2925.71 517.63 1459.64 2816.26 513.14
1455.57 3080.58 518.64 1481.82 2906.73 516.941499.43 3234.03 534.74 1502.53 3006.64 523.77
1543.20 3429.04 545.40 1529.32 3133.85 530.22
1620.71 3500.12 546.05 1557.32 3228.18 534.12
1673.48 3623.35 552.02 1587.69 3330.46 537.60
1753.36 3794.78 573.16 1621.68 3411.71 548.56
1767.62 3784.83 578.19 1629.97 3471.05 557.13
1801.05 3806.01 600.71 1653.94 3560.32 569.15
1758.71 3754.40 581.27 1662.03 3566.62 559.65
1721.04 3556.84 585.52 1661.02 3529.59 569.22
1626.14 3305.85 598.20 1655.71 3510.98 585.41
1545.77 3092.22 611.04 1645.86 3427.59 592.10
1455.80 2888.49 613.06 1621.82 3299.66 603.64
1419.76 2730.67 634.08 1583.49 3177.42 615.08
1355.39 2586.70 639.39 1544.39 3068.96 623.98
1353.60 2458.28 675.75 1506.21 2958.88 635.31
1352.87 2547.19 692.13 1474.00 2901.84 650.95
1383.02 2620.59 702.32 1439.68 2826.03 660.76
1399.65 2620.56 722.79 1431.21 2748.43 676.44
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1436.56 2662.93 746.33 1409.20 2632.86 688.59
1474.49 2751.06 749.02 1417.70 2592.13 712.94
1502.56 2712.49 755.49 1416.94 2576.42 723.13
1517.33 2761.94 752.19 1442.74 2641.60 725.13
1540.59 2759.31 742.58 1470.98 2707.64 727.68
1547.87 2740.08 720.32 1493.39 2739.46 723.331591.76 2848.47 717.92 1531.54 2817.15 725.35
1619.30 2933.67 710.73 1563.15 2835.26 730.20
1644.49 2989.63 710.67 1587.39 2902.09 733.30
1682.00 3089.04 724.76 1608.93 2892.50 742.16
1704.87 3136.36 738.13 1630.49 2942.46 746.02
1712.53 3091.95 776.01 1653.49 2982.61 758.73
1723.17 3131.38 823.58 1660.58 3012.72 768.39
1747.24 3118.00 836.64 1690.65 3031.20 776.46
1758.09 3133.62 861.09 1712.20 3080.92 791.80
1811.37 3189.00 876.12 1758.91 3151.20 805.601218.7 1992.2 424.2 1276.3 2148.4 448.5
1204.2 1996.2 426.8 1284.9 2166.8 452.2
1214.5 2036.8 437.2 1296.5 2191.8 457.8
1220.4 2073.0 442.8 1306.6 2213.9 463.2
1248.5 2109.2 451.4 1316.7 2237.3 468.4
1291.3 2186.2 461.8 1263.5 2105.3 443.8