ardl
Dependent Variable: LNGDP
Method: ARDL
Date: 11/18/24 Time: 20:32
Sample (adjusted): 2 23
Included observations: 22 after adjustments
Maximum dependent lags: 1 (Automatic selection)
Model selection method: Akaike info criterion (AIC)
Dynamic regressors (1 lag, automatic): LNRI LNI
Fixed regressors: C
Number of models evaluated: 4
Selected Model: ARDL(1, 0, 0)
Variable Coefficient Std. Error t-Statistic Prob.*
LNGDP(-1) 0.899525 0.029014 31.00354 0.0000
LNRI 0.466571 0.564923 0.825902 0.0197
LNI -0.241760 0.477820 -0.505964 0.0190
C 1.888280 1.074790 1.756883 0.0059
R-squared 0.993087 Mean dependent var 28.04774
Adjusted R-squared 0.991935 S.D. dependent var 0.602413
S.E. of regression 0.054101 Akaike info criterion -2.832975
Sum squared resid 0.052684 Schwarz criterion -2.634604
Log likelihood 35.16272 Hannan-Quinn criter. -2.786245
F-statistic 861.9237 Durbin-Watson stat 2.249605
Prob(F-statistic) 0.000000
*Note: p-values and any subsequent tests do not account for model
selection.
ARDL Long Run Form and Bounds Test
Dependent Variable: D(LNGDP)
Selected Model: ARDL(1, 0, 0)
Case 2: Restricted Constant and No Trend
Date: 11/18/24 Time: 20:39
Sample: 1 23
Included observations: 22
Conditional Error Correction Regression
Variable Coefficient Std. Error t-Statistic Prob.
C 1.888280 1.074790 1.756883 0.0959
LNGDP(-1)* -0.100475 0.029014 -3.463034 0.0028
LNRI** 0.466571 0.564923 0.825902 0.0197
LNI** -0.241760 0.477820 -0.505964 0.0190
* p-value incompatible with t-Bounds distribution.
** Variable interpreted as Z = Z(-1) + D(Z).
Levels Equation
Case 2: Restricted Constant and No Trend
Variable Coefficient Std. Error t-Statistic Prob.
LNRI 4.643646 6.452619 0.719653 0.0010
LNI -2.406167 5.189981 -0.463618 0.0485
C 18.79350 6.148067 3.056815 0.0068
EC = LNGDP - (4.6436*LNRI -2.4062*LNI + 18.7935)
F-Bounds Test Null Hypothesis: No levels relationship
Test Statistic Value Signif. I(0) I(1)
Asymptotic: n=1000
F-statistic 21.80736 10% 2.63 3.35
k 2 5% 3.1 3.87
2.5% 3.55 4.38
1% 4.13 5
Actual Sample Size 22 Finite Sample: n=35
10% 2.845 3.623
5% 3.478 4.335
1% 4.948 6.028
Finite Sample: n=30
10% 2.915 3.695
5% 3.538 4.428
1% 5.155 6.265
NORMALITY
8
Series: Residuals
7 Sample 2 23
Observations 22
6
5 Mean 1.35e-15
Median -0.009105
4 Maximum 0.074150
3 Minimum -0.115012
Std. Dev. 0.050087
2 Skewness -0.327564
Kurtosis 2.616855
1
0 Jarque-Bera 0.527994
-0.10 -0.05 0.00 0.05 Probability 0.767976
HETEROSKADICITY
Heteroskedasticity Test: Breusch-Pagan-Godfrey
Null hypothesis: Homoskedasticity
F-statistic 0.644378 Prob. F(3,18) 0.5965
Obs*R-squared 2.133581 Prob. Chi-Square(3) 0.5451
Scaled explained SS 1.154649 Prob. Chi-Square(3) 0.7639
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 11/18/24 Time: 20:46
Sample: 2 23
Included observations: 22
Variable Coefficient Std. Error t-Statistic Prob.
C -0.030169 0.063553 -0.474705 0.6407
LNGDP(-1) 0.001131 0.001716 0.659276 0.5181
LNRI -0.002344 0.033404 -0.070164 0.9448
LNI 0.002642 0.028254 0.093498 0.9265
R-squared 0.096981 Mean dependent var 0.002395
Adjusted R-squared -0.053522 S.D. dependent var 0.003117
S.E. of regression 0.003199 Akaike info criterion -8.488992
Sum squared resid 0.000184 Schwarz criterion -8.290620
Log likelihood 97.37891 Hannan-Quinn criter. -8.442261
F-statistic 0.644378 Durbin-Watson stat 2.114025
Prob(F-statistic) 0.596480
LM TEST
Breusch-Godfrey Serial Correlation LM Test:
Null hypothesis: No serial correlation at up to 2 lags
F-statistic 0.371111 Prob. F(2,16) 0.6958
Obs*R-squared 0.975312 Prob. Chi-Square(2) 0.6141
Test Equation:
Dependent Variable: RESID
Method: ARDL
Date: 11/18/24 Time: 20:46
Sample: 2 23
Included observations: 22
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
LNGDP(-1) 0.001625 0.030283 0.053650 0.9579
LNRI -0.129158 0.604913 -0.213516 0.8336
LNI 0.099108 0.508765 0.194802 0.8480
C 0.098136 1.121464 0.087507 0.9314
RESID(-1) -0.178727 0.264987 -0.674473 0.5096
RESID(-2) -0.176123 0.268856 -0.655081 0.5217
R-squared 0.044332 Mean dependent var 1.35E-15
Adjusted R-squared -0.254314 S.D. dependent var 0.050087
S.E. of regression 0.056096 Akaike info criterion -2.696502
Sum squared resid 0.050348 Schwarz criterion -2.398945
Log likelihood 35.66152 Hannan-Quinn criter. -2.626406
F-statistic 0.148445 Durbin-Watson stat 2.087771
Prob(F-statistic) 0.977603
CUSUM
15
10
-5
-10
-15
6 8 10 12 14 16 18 20 22
CUSUM 5% Significance
CUSUM SQAURE
1.6
1.2
0.8
0.4
0.0
-0.4
6 8 10 12 14 16 18 20 22
CUSUM of Squares 5% Significance
