Case RT1: Regression on Time Series Data – Forecasting Demand for Gasoline Consumption (Data from CHS, p.191)

Variables:

G:Total Gas Consumption in tens of millions of 1967 gasoline-dollars

PG :Price Index for Gasoline in 1967 dollars

Range:1960 – 86 (T=27)

Freq.:Annual

Timeplots

1.Regression on Level - 1

Dependent Variable: LOG_G
Method: Least Squares
Sample: 1960 1986
Included observations: 27
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 5.169513 / 0.041273 / 125.2529 / 0.0000
LOG_PG / 0.291745 / 0.056046 / 5.205438 / 0.0000
R-squared / 0.520122 / Mean dependent var / 5.308616
Adjusted R-squared / 0.500927 / S.D. dependent var / 0.231351
S.E. of regression / 0.163438 / Akaike info criterion / -0.713579
Sum squared resid / 0.667799 / Schwarz criterion / -0.617591
Log likelihood / 11.63332 / F-statistic / 27.09659
Durbin-Watson stat / 0.200642 / Prob(F-statistic) / 0.000022

Problems of this regression?

2.Regression on Level – 2

Dependent Variable: LOG_G
Method: Least Squares
Sample (adjusted): 1961 1986
Included observations: 26 after adjustments
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 5.206072 / 0.040678 / 127.9820 / 0.0000
LOG_PG(-1) / 0.263485 / 0.056467 / 4.666145 / 0.0001
R-squared / 0.475672 / Mean dependent var / 5.325669
Adjusted R-squared / 0.453825 / S.D. dependent var / 0.217940
S.E. of regression / 0.161065 / Akaike info criterion / -0.740208
Sum squared resid / 0.622610 / Schwarz criterion / -0.643432
Log likelihood / 11.62271 / F-statistic / 21.77291
Durbin-Watson stat / 0.147453 / Prob(F-statistic) / 0.000097

Problems of this regression?

3.Regression on the Change - 1

Dependent Variable: D(LOG_G)
Sample (adjusted): 1961 1986
Included observations: 26 after adjustments
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 0.040973 / 0.004723 / 8.674663 / 0.0000
D(LOG_PG) / -0.290744 / 0.038451 / -7.561328 / 0.0000
R-squared / 0.704338 / Mean dependent var / 0.028114
Adjusted R-squared / 0.692018 / S.D. dependent var / 0.040487
S.E. of regression / 0.022469 / Akaike info criterion / -4.679559
Sum squared resid / 0.012117 / Schwarz criterion / -4.582782
Log likelihood / 62.83427 / F-statistic / 57.17369
Durbin-Watson stat / 0.944091 / Prob(F-statistic) / 0.000000

Problems of this regression?


4.Regression on the Change – 2

Dependent Variable: D(LOG_G)
Sample (adjusted): 1962 1986
Included observations: 25 after adjustments
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 0.040695 / 0.008139 / 5.000005 / 0.0000
D(LOG_PG(-1)) / -0.213861 / 0.070681 / -3.025730 / 0.0060
R-squared / 0.284716 / Mean dependent var / 0.028748
Adjusted R-squared / 0.253616 / S.D. dependent var / 0.041190
S.E. of regression / 0.035586 / Akaike info criterion / -3.757121
Sum squared resid / 0.029126 / Schwarz criterion / -3.659611
Log likelihood / 48.96401 / F-statistic / 9.155041
Durbin-Watson stat / 1.937500 / Prob(F-statistic) / 0.006015

Problems of this regression?

5.Regression on level –lagged X and AR(1) error

Dependent Variable: LOG_G
Sample (adjusted): 1962 1986
Included observations: 25 after adjustments
Convergence achieved after 7 iterations
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 6.485475 / 0.900991 / 7.198158 / 0.0000
LOG_PG(-1) / -0.184498 / 0.073119 / -2.523267 / 0.0194
AR(1) / 0.964277 / 0.026505 / 36.38131 / 0.0000
R-squared / 0.972702 / Mean dependent var / 5.343597
Adjusted R-squared / 0.970221 / S.D. dependent var / 0.201922
S.E. of regression / 0.034845 / Akaike info criterion / -3.763646
Sum squared resid / 0.026712 / Schwarz criterion / -3.617381
Log likelihood / 50.04557 / F-statistic / 391.9648
Durbin-Watson stat / 1.958591 / Prob(F-statistic) / 0.000000
Inverted AR Roots / .96


Sample: 1962 1986
Included observations: 25
Q-statistic probabilities adjusted for 1 ARMA term(s)
Autocorrelation / Partial Correlation / AC / PAC / Q-Stat / Prob
. | . | / . | . | / 1 / -0.006 / -0.006 / 0.0011
. *| . | / . *| . | / 2 / -0.097 / -0.098 / 0.2798 / 0.597
. | . | / . | . | / 3 / -0.044 / -0.046 / 0.3388 / 0.844
.**| . | / .**| . | / 4 / -0.256 / -0.269 / 2.4416 / 0.486
. |* . | / . | . | / 5 / 0.066 / 0.052 / 2.5879 / 0.629

Problems of this regression?

6.Regression on Level – lagged X with lagged dependent variable

Dependent Variable: LOG_G
Sample (adjusted): 1961 1986
Included observations: 26 after adjustments
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 0.309612 / 0.253258 / 1.222517 / 0.2339
LOG_G(-1) / 0.947263 / 0.048957 / 19.34895 / 0.0000
LOG_PG(-1) / -0.004675 / 0.019613 / -0.238380 / 0.8137
R-squared / 0.969653 / Mean dependent var / 5.325669
Adjusted R-squared / 0.967014 / S.D. dependent var / 0.217940
S.E. of regression / 0.039583 / Akaike info criterion / -3.512689
Sum squared resid / 0.036036 / Schwarz criterion / -3.367524
Log likelihood / 48.66495 / F-statistic / 367.4444
Durbin-Watson stat / 1.316961 / Prob(F-statistic) / 0.000000

Problems of this regression?

8. Error Correction Model

Dependent Variable: LOG_G
Sample (adjusted): 1961 1986
Included observations: 26 after adjustments
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / -0.277369 / 0.108268 / -2.561870 / 0.0178
LOG_G(-1) / 1.064305 / 0.021071 / 50.50973 / 0.0000
LOG_PG / -0.343739 / 0.029268 / -11.74442 / 0.0000
LOG_PG(-1) / 0.299736 / 0.026966 / 11.11548 / 0.0000
R-squared / 0.995825 / Mean dependent var / 5.325669
Adjusted R-squared / 0.995256 / S.D. dependent var / 0.217940
S.E. of regression / 0.015011 / Akaike info criterion / -5.419469
Sum squared resid / 0.004957 / Schwarz criterion / -5.225915
Log likelihood / 74.45309 / F-statistic / 1749.337
Durbin-Watson stat / 2.072316 / Prob(F-statistic) / 0.000000

Problem of this regression?

1