model selection econometrics
DESCRIPTION
Model Selection of various AR ProcessesTRANSCRIPT
2. Linear Trend
Dependent Variable: INDUSTRIAL
Method: Least Squares
Date: 02/19/15 Time: 12:03
Sample: 1999M01 2012M01
Included observations: 157
INDUSTRIAL=C(1)+C(2)*T
CoefficientStd. Errort-StatisticProb.
C(1)90.303330.643535140.32390.0000
C(2)0.0255890.0071343.5870050.0004
R-squared0.076648Mean dependent var92.29924
Adjusted R-squared0.070691S.D. dependent var4.202261
S.E. of regression4.051009Akaike info criterion5.648466
Sum squared resid2543.654Schwarz criterion5.687399
Log likelihood-441.4046Hannan-Quinn criter.5.664278
F-statistic12.86661Durbin-Watson stat0.027890
Prob(F-statistic)0.000448
Quadratic Trend
Dependent Variable: INDUSTRIAL
Method: Least Squares
Date: 02/19/15 Time: 12:05
Sample: 1999M01 2012M01
Included observations: 157
INDUSTRIAL= C(1)+ C(2)*T+C(3)*T2
CoefficientStd. Errort-StatisticProb.
C(1)86.833190.88349298.284020.0000
C(2)0.1599170.0261696.1109810.0000
C(3)-0.0008610.000162-5.3036010.0000
R-squared0.219252Mean dependent var92.29924
Adjusted R-squared0.209112S.D. dependent var4.202261
S.E. of regression3.737149Akaike info criterion5.493447
Sum squared resid2150.808Schwarz criterion5.551846
Log likelihood-428.2356Hannan-Quinn criter.5.517165
F-statistic21.62336Durbin-Watson stat0.033174
Prob(F-statistic)0.000000
Exponential Trend
Dependent Variable: INDUSTRIAL
Method: Least Squares
Date: 02/19/15 Time: 12:06
Sample: 1999M01 2012M01
Included observations: 157
Convergence achieved after 7 iterations
INDUSTRIAL= C(1)*EXP(C(2)*T)
CoefficientStd. Errort-StatisticProb.
C(1)90.347550.637150141.79950.0000
C(2)0.0002737.73E-053.5300570.0005
R-squared0.075487Mean dependent var92.29924
Adjusted R-squared0.069522S.D. dependent var4.202261
S.E. of regression4.053554Akaike info criterion5.649722
Sum squared resid2546.852Schwarz criterion5.688655
Log likelihood-441.5032Hannan-Quinn criter.5.665534
Durbin-Watson stat0.027857
SummarySIC CriteriaAIC CriteriaR squared
Linear5.6873995.6484660.076648
Quadratic5.5518465.4934470.219252
Exponential5.6886555.6497220.075487
Model selection of Question 2Based on SIC Criteria SelectQuadratic TrendBased on AIC Criteria SelectQuadratic TrendBased on R Squared SelectQuadratic Trend
3. Exponential Trend with AR(1)
Dependent Variable: INDUSTRIAL
Method: Least Squares
Date: 02/19/15 Time: 12:45
Sample (adjusted): 1999M02 2012M01
Included observations: 156 after adjustments
Convergence achieved after 6 iterations
INDUSTRIAL=C(1)*(EXP(C(2)*T))+C(3)*INDUSTRIAL(-1)
CoefficientStd. Errort-StatisticProb.
C(1)1.5370711.2171581.2628360.2086
C(2)-5.64E-050.000830-0.0679470.9459
C(3)0.9840530.01342773.289770.0000
R-squared0.974282Mean dependent var92.33489
Adjusted R-squared0.973945S.D. dependent var4.191897
S.E. of regression0.676633Akaike info criterion2.075667
Sum squared resid70.04825Schwarz criterion2.134318
Log likelihood-158.9020Hannan-Quinn criter.2.099488
Durbin-Watson stat1.465829
Quadratic Equation with AR(1)
Dependent Variable: INDUSTRIAL
Method: Least Squares
Date: 02/19/15 Time: 12:48
Sample (adjusted): 1999M02 2012M01
Included observations: 156 after adjustments
Convergence achieved after 12 iterations
VariableCoefficientStd. Errort-StatisticProb.
C230.9885544.89070.4239170.6722
T-1.1836143.377477-0.3504430.7265
T20.0032690.0068130.4797720.6321
AR(1)0.9899990.01468367.422660.0000
R-squared0.974450Mean dependent var92.33489
Adjusted R-squared0.973946S.D. dependent var4.191897
S.E. of regression0.676631Akaike info criterion2.081925
Sum squared resid69.59007Schwarz criterion2.160126
Log likelihood-158.3902Hannan-Quinn criter.2.113687
F-statistic1932.357Durbin-Watson stat1.484230
Prob(F-statistic)0.000000
Inverted AR Roots.99
Linear Model with AR(1)
Dependent Variable: INDUSTRIAL
Method: Least Squares
Date: 02/19/15 Time: 12:53
Sample (adjusted): 1999M02 2012M01
Included observations: 156 after adjustments
Convergence achieved after 4 iterations
VariableCoefficientStd. Errort-StatisticProb.
C96.6943113.103777.3791230.0000
T-0.0052400.079623-0.0658150.9476
AR(1)0.9840440.01342373.310010.0000
R-squared0.974282Mean dependent var92.33489
Adjusted R-squared0.973945S.D. dependent var4.191897
S.E. of regression0.676633Akaike info criterion2.075668
Sum squared resid70.04832Schwarz criterion2.134319
Log likelihood-158.9021Hannan-Quinn criter.2.099489
F-statistic2898.018Durbin-Watson stat1.465814
Prob(F-statistic)0.000000
Inverted AR Roots.98
Model selection of Question 3Based on BIC Criteria, we choose exponential trend ( . Though BIC criteria is almost same with Linear Model.