6th AssignmentAdvanced Methods of Data AnalysisFORECASTING METODS FAC!"T#$ D% &%ahlad Mish%aG%o'()*+#AS SING CA!AN !M,-,+*A"ISA MOANT# !M,-,+.CINMA#EE SA! !M,-,./SA!RA0 1AD1A!M,-,62SR!TI !M,-,6.3A"A3 &ATA4 !M,-+.6&RI#AM0ADA CO!D!R# !M,-+52S!DISNA "EN4A !M,-+627avie% Instit'te of Management8 0h'9anes:a%,; Fo%ecasting$ Fo%ecastingt%a(olativeSim(le &%o?ectionMoving Ave%age MethodsExponential smoothing methodsAdjusted for trend (Holts Method)Adjusted for trend , seasonal variations (WintersMethod)Adjusted for trend, seasonal and cyclic variation.Autoregressive time series Models (A, AMA, A!MA)E>(lanato%ySingle E='ation ModelsSim'ltaneo's E='ation ModelsIn('t@O't('t ModelsFo%ecasting is the process of making predictions of the future based on past and present data and analysis of trends. A commonplace example might be estimation of some variable of interest at some specifed future date. In forecasting we usually work with historical data in an attempt to predict, or forecast, the uncertain future.Forecast error - the dierence between the actual value and the forecast value for the corresponding period - is given as follows! "here # is the forecast error at period t, $ is the actual value at period t, and F is the forecast for period t.Fo%ecasting (%oced'%es may 9e classiAed as follo:s$a; %hort &erm and 'ong &erm wrt &ime9; (acro 'evel and (icro 'evel wrt )ositionc;*uantitative and *ualitative wrt +ature of ,ataA fo%ecasting model is as accurate as the data on which it is based. &he data should be!+ B ) a g e -eliable and accurate -elevant and representative of the circumstances for which they arebeing used. .onsistent &imelyThe fo%ecasting (%ocess consists of the follo:ing . ste(s$ ,ata collection! /ere we collect proper data and make sure that they are correct. *uality of data points is one of the important aspects of forecasting. ,ata reduction or condensation! It is necessary because there may be some data points which may not be relevant to the problem and may reduce forecasting accuracy. &here may be other data points that are suitable in certain historical periods only. %o we may need to remove those data points.(odel 0uilding and #valuation! &his step involves ftting the collected data into a forecasting model that is appropriate in terms of minimi1ing the forecasting error. &he simpler the model, the better it is. (odel #xtrapolation! It consists of the actual model forecasts that are generated once the appropriate data have been collected and possibly reduced and an appropriate forecasting model has been chosen. 2ften forecasting for recent periods in which the actual historical values are known is used to check the accuracy of the process. Following which, the forecasting errors are observed and summari1ed. Forecast #valuation! &his step involves comparing forecast values with actual historical values. In this process, a few of the most recent data values are often held back from the data set being analy1ed. After the forecasting model is completed, forecast are made for these periods and compared with the known historical values. &he estimation of the error pattern helps us to modify the forecasting procedure so as to minimi1e the error./ere in this exercise we will be working with time series data. A time series consists of data that are collected, recorded or observed over successful increments of time.An important aspect to consider while selecting an appropriate forecasting method for time series data is to consider the dierent types of data patterns! /ori1ontal! "hen data observations 3uctuate around a constant level or mean. &rend! "hen data observations 3uctuate grow or decline over an extended period of time. .yclical! "hen data observations exhibit rise and falls that are not of a fxed period. 2 B ) a g e %easonal! "hen data observations are in3uenced by seasonal factors. It refers to a pattern of change that repeats itself year after year.+; Assignment)6$O9?ective$ &o examine the time series data pattern using time as an independent variable. &o determine whether there exists a structural change using the time series data. &o determine forecasting error by using the above given forecasting models to forecast the values for the test period and then comparing them with the actual values of the test period. &o determine the best forecasting model using (A)#.a;&%esent E>e%cise$&o implement the #xtrapolative (odels of forecasting and check the accuracy of outputs9;Ca%ia9les !sed in the %esea%ch 4. De(endent va%ia9le D %tock-%plit .ompensated .lose5. Inde(endent Ca%ia9le D &imec;A (%io%i Reasoning.d;y(othesis +ull /ypothesis!. 6789: Alternate /ypothesis!. 67;9: Data !sed$ Time Se%ies DataE ,/- data (oints F,ate .lose%plit Ad(ar>5999?@94.@A54 ?@94.@A54 BC@D@99B>Apr>5999 ?499 ?499 E44ED994>(ay>5999E@@9.94E4 E@@9.94E4 49?D99994>Fun>5999?B4?.?CDD ?B4?.?CDD 49?4?999- B ) a g eB>Ful>5999E?99.@E E?99.@E 4B5BED994>Aug>5999?BDB.4A5B ?BDB.4A5B 4?CAA?994>%ep>5999DBAD.BCC5 DBAD.BCC5 4AE99D995>2ct>5999D49C.ACB@ D49C.ACB@ 4DC554994>+ov>5999D4A?.E?? D4A?.E?? 4ABCCD994>,ec>5999AADA.99D? AADA.99D? 4959?@99@>Fan>5994E?EC.@@55 E?EC.@@55 ?BA99E>Feb>5994 AA99 AA99 4E@@995>(ar>5994 B@99 B@99 5B5D9945>Apr>5994B@B@.5@A@ B@B@.5@A@ B?9599B>(ay>5994BDDA.99?4 BDDA.99?4 CCAB99A>Fun>5994B5?@.@?B@ B5?@.@?B@ BBD9995>Ful>5994BDE4.B45 BDE4.B45 45CEE?994>Aug>5994BAB5.5??4 BAB5.5??4 D@EBB99B>%ep>59945BA5.EC@D 5BA5.EC@D 4EB9C9994>2ct>59945@4C.B99? 5@4C.B99? 4EA@?A994>+ov>5994B?@A.@BE B?@A.@BE 45A?D?99B>,ec>5994C9DB.E994 C9DB.E994 45D5B4994>Fan>5995B??@.BCC B??@.BCC 4AC@4A994>Feb>5995BAB9.5C BAB9.5C 499ECB994>(ar>5995BE?5.59? BE?5.59? 454C??994>Apr>5995BE?@.A9B@ BE?@.A9B@ D?@5A995>(ay>5995BB?5.9C?4 BB?5.9C?4 A?@B?99B>Fun>5995B9EA.DA9A B9EA.DA9A ?AB9@9945>Aug>5995BE4@.9C BE4@.9C 49BAD4995>%ep>5995BC99.5??4 BC99.5??4 ?@5C?994>2ct>599 BD?D.? BD?D.?9?4 44@E4C99. B ) a g e5 9?44>+ov>5995CAE?.DBA? CAE?.DBA? 4ACA59995>,ec>5995CDD4.4BE5 CDD4.4BE5 455??C994>Fan>599BCB94.9AE5 CB94.9AE5 45EA?599B>Feb>599BC5?C.4E95 C5?C.4E95 494A4@99B>(ar>599BC9C9.5??4 C9C9.5??4 @5DDA994>Apr>599B5D@9.EC@D 5D@9.EC@D 4AD5AA994>(ay>599B5ED5.B@@@ 5ED5.B@@@ 49D5C?995>Fun>599BB5EC.?EC B5EC.?EC ?E9A5994>Ful>599BBA@B.B45 BA@B.B45 449E5D994>Aug>599BB@49.B@@@ B@49.B@@@ ?ABEE994>%ep>599BCA5C.4@4@ CA5C.4@4@ 45BCB5994>2ct>599BCDC4.CB@@ CDC4.CB@@ ?959@99B>+ov>599BC@5C.A455 C@5C.A455 E5A?4994>,ec>599BAAEB.D44@ AAEB.D44@ C@AAC994>Fan>599CA4@A.4BE5 A4@A.4BE5 A?A?D995>Feb>599CA9D4.@9B? A9D4.@9B? DC@@4994>(ar>599CC@B?.4CC C@B?.4CC ?4?@D994>Apr>599CA4CE.@CB? A4CE.@CB? E?D@A99B>(ay>599CA59?.?@E A59?.?@E AAED9994>Fun>599CAA55.@454 AA55.@454 C@DBB994>Ful>599C4AAB.DA5 E54A.99? C54?C995>Aug>599C4ADC.@9C4 E5@@.E4EC B5?DE994>%ep>599C 4E@A.5 ED?9.? B?BEA994>2ct>599C 4@9E.C DE5A.E CBCA@994>+ov>599C54C?.BA54 ?A@B.C9?C 5?A@9994>,ec>599C 59?@ ?BAE 59@CA996 B ) a g eB>Fan>599A59ED.5C? ?5E?.@@5 BBE@5994>Feb>599A55BD.4A54 ?@C?.E9?C 5EABB994>(ar>599A55A5.AA5 @949.59? 4E@A5994>Apr>599A4??D.BA54 DAC@.C9?C 5A?@5995>(ay>599A55A9.E@E @995.D?C 5CAD?994>Fun>599A5BAD.ECD@ @CB9.A@4E 4??@B994>Ful>599A 55E@.5 @9DE.? 54@5E994>Aug>599A5BDE.5C? @A9C.@@5 45CC5994>%ep>599A 5A4D 499E? 45@ED99B>2ct>599A5A5B.?@E 499@A.A?C 5EAC?994>+ov>599A5E?C.49C 49DBE.C4E 4?5@B994>,ec>599A5@@E.DA5 44@?D.99? 54@AE995>Fan>599E5?D@.E@E 44A4?.D?C 5BCD@994>Feb>599E5?5?.E994 44B4C.C99C 5999C994>(ar>599E5@?9.?CD@ 44@5B.B@4E 4@@C?99B>Apr>599EB4BB.?@E 45ABA.A?C 5E5EE995>(ay>599E5@9?.9C?4 44EB5.4@5C 4E@EB994>Fun>599EB9DD.AA5 45B49.59? 4E?@B99B>Ful>599E 4EAB.@ 4B5B4.5 4@?DB994>Aug>599E 4?9?.? 4CCD9.C @E@?994>%ep>599E 4?CD.@ 4CD?B.5 D@DC995>2ct>599E 59@C.? 4EDA?.C 45AED994>+ov>599E54?9.CC? 4DCCB.A?C @EE5994>,ec>599E 55C9.A 4D@5C ?9C?994>Fan>599D55CC.CC? 4D@AA.A?C 495A@994>Feb>599D59D?.BA54 4EE5E.?4E? 495?C994>(ar>599D 5945.E 4E499.? 45B9@995 B ) a g e5>Apr>599D59C@.BA54 4EB@C.?4E? 4B5EE994>(ay>599D4@59.5C? 4ABE4.@?C 459?9994>Fun>599D 4@5@.5 4ACBB.E @@B4995>Ful>599D4@DD.5C? 4A?4D.@?C 4CD4A994>Aug>599D4?AA.9A5 4C?C9.C4E 44D5999B>%ep>599D4?@E.DA5 4A4DC.94E 445EB994>2ct>599D 4?B@.4 4CD45.? 4EAEA994>+ov>599D4E9C.9A5 45?B5.C4E 45AA599B>,ec>599D 4DE?.C 4C4CD.5 ?9A4994>Fan>599? 4A9B.@ 459B4.5 455B?994>Feb>599?4ACE.?C? 45BDC.D?C @CB999B>(ar>599?4CB9.4A5 44CC4.54E @?5D994>Apr>599?4DAB.DA5 4C9B9.94E 4@5EC994>(ay>599?4@AD.AA5 4AEE9.C4E 4A45@995>Fun>599?4DBC.DA5 4B?D?.94E 44?E?994>Ful>599? 4A?B.B 45EEE.C 4@5?A994>Aug>599? 4DC?.A 4B@?? 459E@994>%ep>599?4B@D.AA5 444?9.C4E 4BBD@994>2ct>599?4B?4.EA5 449AB.54E 45EBD99B>+ov>599? 45C9.E @@5C.? 4BE54994>,ec>599?444D.?C? ?@C5.D?C 49?4E994>Fan>599@ 4B9A.A 49CCC 4AEBC995>Feb>599@ 45B4.B @?A9.C ?E5A995>(ar>599@ 4B5C.4 49A@5.? D?EE994>Apr>599@ 4A9D.B 459A?.C DDCE994>(ay>599@ 4E95 45?4E ?A?A994>Fun>599@ 4DDE.@ 4C54A.5 E@AA99/ B ) a g e4>Ful>599@59EB.?@@@ 4EA44.4@@5 49ACC99B>Aug>599@ 54B5.B 4D9A?.C ADAD994>%ep>599@5B9?.B@@@ 4?CED.4@@5 A49E994>2ct>599@559A.B@@@ 4DECB.4@@5 EE?C995>+ov>599@5B?B.@C? 4@9D4.A?C @4?B994>,ec>599@5E9A.5C? 59?C4.@?C A9B@994>Fan>5949 5CDE.D 4@?4B.E EDAD994>Feb>59495E94.E994 59?45.?99? C5CC994>(ar>59495E4A.4994 59@59.?99? C4CA994>Apr>59495DBE.4CD@ 54??@.4?B5 D4B999B>(ay>59495EAD.ECD@ 545E4.4?B5 C94B994>Fun>59495D??.AA5 55B9?.C4E BCE?994>Ful>59495D??.?A54 55B49.?4E? A5BA995>Aug>59495D9D.4994 54EAE.?99? 5@5D994>%ep>5949 B9C4 5CB5? BEB@994>2ct>59495@E@.E994 5BDAE.?99? AD5B994>+ov>5949B9C@.CC? 5CB@A.A?C B95A994>,ec>5949 BCCA 5DAE9 BABC99B>Fan>5944 B44E.B 5C@B9.C CD@5994>Feb>5944B99B.9A5 5C95C.C4E BEED994>(ar>5944B5BE.DA5 5A?@C.94E CE9C994>Apr>59445@9A.@C? 5B5CD.A?C 4B@C9995>(ay>59445D@4.?A54 55BBC.?4E? BD@?994>Fun>59445@9D.B@@@ 5B5A@.4@@5 BB?5994>Ful>5944 5DEE.? 554BC.C A99C994>Aug>59445BAC.4994 4??B5.?99? D4D4995>%ep>5944 5ABB.? 595D9.C DC54996 B ) a g eB>2ct>5944 5?DA.5 5B994.E ?DAC994>+ov>59445E9D.AA5 59?E9.C4E AEDE994>,ec>59445DEA.9A5 55459.C4E CEEA995>Fan>59455DCB.BA54 54@CE.?4E? D5DA994>Feb>59455?DA.B@@@ 5B99B.4@@5 BA54994>(ar>59455?EC.@C? 55@4@.A?C B?AE995>Apr>59455CE5.E994 4@D99.?99? 44?4E994>(ay>59455CB@.?A54 4@A4?.?4E? CC9?994>Fun>59455A95.AA5 59959.C4E C9CE995>Ful>5945555D.B@@@ 4D?4@.4@@5 D4EB994>Aug>59455BDB.5C? 4?@?A.@?C 5EED99B>%ep>5945 5ABC 595D5 B44?994>2ct>5945 5BEB.A 4?@9? E?5B994>+ov>59455CBE.E994 4@C@5.?99? BAD?99B>,ec>5945 5B4?.A 4?AC? B9BB994>Fan>594B5D??.DA5 55B49.94E D5@C994>Feb>594B 5@9E 5B5C? B959994>(ar>594B5??@.?@@@ 5B44@.4@@5 5BDA994>Apr>594B55BC.CC? 4D?DA.A?C 49EAC994>(ay>594B5C9D.E994 4@5E9.?99? 5?ED99B>Fun>594B5C@B.5C? 4@@CA.@?C BCAD994>Ful>594B5@ED.4CD@ 5BDBD.4?B5 C??B994>Aug>594B B499.B 5C?95.C B5?D995>%ep>594BB94A.CC? 5C45B.A?C 5?@C994>2ct>594BBB9?.ECD@ 5ECE@.4?B5 A944994>+ov>594B BBAB.A 5E?5? BBAC995>,ec>594 BC?A.A 5D??C 5?DD99,* B ) a g eB4>Fan>594CBE@@.CC? 5@A@A.A?C BDAA99B>Feb>594C B?59.5 B9AE4.E 5B4B99B>(ar>594CB5D?.?A54 5E5B9.?4E? B4C@994>Apr>594C B4DD.5 5AC4D.E B5ED994>(ay>594C 5@C4.A 5BAB5 EAE4995>Fun>594CB5CE.CC? 5A@D4.A?C B?E?994>Ful>594C BBEA.D 5E@5A.E 55A9994>Aug>594C BA@C 5?DA5 4?BD994>%ep>594CBDCD.ECD@ 5@@?4.4?B5 5EA9994>2ct>594CC9A4.CB@@ B5C44.A4@5 BE4C99B>+ov>594C54D@.E594 BC?DB.@54E 5C5@994>,ec>594C 4@D4.5 B4AB@.5 D?B9994>Fan>594A54C5.DE BC5?C.4E CD@9995>Feb>594A55EE.BE94 BE5E4.DE4E 4?5D995>(ar>594A554E.E994 BACEA.E94E 54E5994>Apr>594A 4@C5.C B49D?.C C5?C994>(ay>594A 5955.C B5BA?.C C5D5994>Fun>594A @?A.BA B4AB4.5 5C9D994>Ful>594A 49EB.A BC9B5 5CEB99So'%ces GH