1 New Single Family Houses Sold South QMB 5303 EMBA11 Team 7 Time Series Regression Mark Caulfield...

1

New Single Family Houses SoldSouth

QMB 5303 EMBA11 Team 7

Time Series Regression

•Mark Caulfield

•Robert Daum

•Tom Donegan

•Michael Rowley

•Rick Shafer

2

Graph of Raw Data

403020100

175

150

125

100

75

50

Months

New

Hom

es

Sold

South


Thousands

Time Period – Q4 1999 to Q3 2008

3

Initial Regression

The regression equation is

New Homes Sold South = 117 + 0.108 Months

Predictor Coef SE Coef T P

Constant 116.940 9.144 12.79 0.000

Months 0.1084 0.4310 0.25 0.803

S = 26.8625 R-Sq = 0.2% R-Sq(adj) = 0.0%

4

Preliminary Adjustments• Adjustments Considered

– First Time Home Buyer Tax Credit• Not applicable during analysis time period (could impact

forecast).

– Inflation• Series not in monetary terms so no need to adjust for

inflation.

– Seasonality• Adjusted for seasonality as home sales may be seasonal

in nature.

5

Seasonally Adjusted

• Seasonality doesn’t appear to be a significant factor (R2 only .0012).

• Some quarterly seasonality is evident.

• Q4 of each year appears to have the most seasonality until around Q1-2005.

Seasonal AdjustmentTime Period 4Q-1999 to 3Q-2008

y = 0.0835x + 117.4

R2 = 0.001260.00

80.00

100.00

120.00

140.00

160.00

180.00

0 4 8 12 16 20 24 28 32 36

Quarter

Ne

w H

om

es

So

ld S

ou

th

New Homes Sold South Deseasonalized Linear (Deseasonalized)

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Potential Predictors

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2750

2500

2250

2000

1750

1500

1250

1000

Months

Housi

ng S

tart

s


Thousands

403020100

2750

2500

2250

2000

1750

1500

1250

1000

Months

Build

ing P

erm

its


Thousands

403020100

6.0

5.5

5.0

4.5

4.0

Months

Unem

plo

ym

ent

Rate

s


Thousands

403020100

175

150

125

100

75

50

Months

New

Hom

es

Sold

South


Thousands

7

Potential Predictors (Cont’d)

403020100

450

400

350

300

250

200

Months

House

Price

Index:

South

Atlant


Thousands

403020100

450

400

350

300

250

200

Months

Consu

mer

Confidence


Thousands

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12000

11000

10000

9000

8000

Months

Pers

onal I

nco

me


Thousands

403020100

8.5

8.0

7.5

7.0

6.5

6.0

5.5

Months

FHA

30 m

ort

gage R

ate

s


Thousands

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Correlation TableNewHome Starts Permits Income Credit FHA Rates Un Rates HPI Cons Conf CPI R Completions

New Home Sales 1.000 Housing Starts .903 1.000 Building Permits .914 .991 1.000 Personal Income -.062 -.154 -.174 1.000 Consumer Credit .070 -.026 -.035 .968 1.000 FHA Rates -.424 -.349 -.373 -.508 -.695 1.000 Unem Rates .172 .131 .165 .051 .268 -.694 1.000 House Price Indx .130 .063 .040 .972 .958 -.558 .029 1.000 Consumer Conf .049 .132 .108 -.481 -.628 .776 -.800 -.415 1.000 CPI Rental -.088 -.187 -.201 .987 .983 -.586 .190 .947 -.595 1.000 Completions .631 .792 .774 .118 .182 -.276 -.043 .317 .152 .066 1.000

36 sample size

± .329 critical value .05 (two-tail)± .424 critical value .01 (two-tail)

• Correlation Table • Evans’/Doane’s Rules• Stepwise Regression/Selection

Which Predictors do we keep?

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Regression OutputThe regression equation isNew Homes Sold South = 313 + 0.0534 Building Permits + 0.000098 Consumer Credit Outstanding (Millions) + 0.272 House Price Index: South Atlantic - 0.938 CPI Rental

- 0.322 Housing Completions

Predictor Coef SE Coef T PConstant 313.4 208.5 1.50 0.143Building Permits 0.053 0.014 3.68 0.001Consumer Credit Out 0.00009767 0.00008051 1.21 0.235House Price Index 0.2724 0.1452 1.88 0.070CPI Rental -0.9383 0.6664 -1.41 0.169Housing Completions -0.3219 0.1062 -3.03 0.005

S = 9.67709 R-Sq = 88.6% R-Sq(adj) = 86.7%

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Residual Plot

35302520151051

20

10

0

-10

-20

Observation Order

Resi

dual

Versus Order(response is New Homes Sold South)

Time Period – Q4 1999 to Q3 2008

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Alternate Prediction Strategies

Forecasting Predictors

• Winters Method

• Decomposition

• Exponential Smoothing

12

Forecasted Predictors Q4 - 2008Bldg Permits

Forecast/MAPE

Consumer Credit

Forecast/MAPE

HPI

Forecast/MAPE

CPI Rental

Forecast/MAPE

Housing Comp

Forecast/MAPE

Actual 659/NA 2566197.24/NA 389.74/NA 665.12/NA 103/NA

Winters* 919/13.4 2602607/1 425.586/3.194 664.565/.7669 129.322/10.903

Decomp. 1802.62/21 2630507/1 441.133/4.151 651.468/.9973 185.415/13.331

Exponential

Smoothing

808.717/4.34 2580126/1 384.225/1.2060 663.301/.42354 105.538/11.712

* Selected Winters method to maximize accuracy with smoothing and trending parameters.

13

True Forecast Analysis

Y Y-hat Error

(Y-Y-hat)

|Error| APE

Q4-2008 46 67.93 -21.93 21.93 440425079.87

Q1-2009 49 68.48 -19.48 19.48 391418942.10

Q2-2009 56 56.80 -0.80 0.80 16165539.25

Q3-2009 53 47.82 5.18 5.18 104023201.75

The regression equation isNew Homes Sold South = 313 + 0.0534 Building Permits + 0.000098 Consumer Credit Outstanding (Millions) + 0.272 House Price Index: South Atlantic - 0.938 CPI Rental


MAD: 11.8475

MAPE: 0.929216

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Estimation Output

Predictor Coef SE Coef T PConstant 313.4 208.5 1.50 0.143Building Permits 0.053 0.014 3.68 0.001Consumer Credit Out0.00009767 0.00008051 1.21 0.235House Price Index 0.2724 0.1452 1.88 0.070CPI Rental -0.9383 0.6664 -1.41 0.169Housing Completions -0.3219 0.1062 -3.03 0.005

S = 9.67709 R-Sq = 88.6% R-Sq(adj) = 86.7%

15

Holdout Sample Prediction Analysis

Y Y-hat Error

(Y-Y-hat)

|Error| APE

Q4-2008 46 48.64 -2.64 2.64 12155.05

Q1-2009 49 55.07 -6.07 6.07 29740.00

Q2-2009 56 45.71 10.29 10.29 57646.87

Q3-2009 53 47.40 5.60 5.60 29702.69

The regression equation isNew Homes Sold South = 313 + 0.0534 Building Permits + 0.000098 Consumer Credit Outstanding (Millions) + 0.272 House Price Index: South Atlantic - 0.938 CPI Rental


MAD: 6.15

MAPE: 0.482353

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