Case 19: Two Alternative Formulations of Trend: Fixed vs
Case PT: Building a Fixed Trend Forecasting Model
1. Variable
gdp_real = Gross Domestic Product in Billions of Dollars, Seasonally Adjusted Annual Rate, Deflated by GDP Implicit Price Deflator Index 2000=100
Range: 1947-I to 2004-IV
Frequency Quarterly
# of obs. 232
2. Timeplot
3. Modeling
Y=log(gdp_real) will be chosen for modeling..
Data for analysis: 1947-I to 2002-IV, T = 224
Data for out-of-sample forecast, h=1,…,8
Y = Linear Trend + Cycle + Irregular
3-1: Estimating the Linear Trend
|Dependent Variable: Y | | |
|Sample: 1947:1 2002:4 | | |
|Included observations: 224 | | |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |7.402780 |0.005466 |1354.254 |0.0000 |
|QUARTER |0.008376 |4.21E-05 |198.8389 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.994416 | Mean dependent var |8.345125 |
|Adjusted R-squared |0.994391 | S.D. dependent var |0.544375 |
|S.E. of regression |0.040769 | Akaike info criterion |-3.552887 |
|Sum squared resid |0.368994 | Schwarz criterion |-3.522426 |
|Log likelihood |399.9234 | F-statistic |39536.91 |
|Durbin-Watson stat |0.061711 | Prob(F-statistic) |0.000000 |
| | | | | |
| | | | | |
3-2: Correlogram of the Residual
|Sample: 1947:1 2002:4 | | | | | | |
|Included observations: 224 | | | | | |
| | | | | | | | |
| | | | | | | | |
|Autocorrelation |Partial Correlation | |AC | PAC | Q-Stat | Prob | |
| | | | | | | | |
| | | | | | | | |
| .|*******| | .|*******| |1 |0.961 |0.961 |209.79 |0.000 | |
| .|*******| | **|. | |2 |0.902 |-0.295 |395.22 |0.000 | |
| .|****** | | *|. | |3 |0.830 |-0.131 |552.99 |0.000 | |
| .|****** | | .|. | |4 |0.761 |0.065 |686.08 |0.000 | |
| .|***** | | .|. | |5 |0.699 |0.065 |799.18 |0.000 | |
| .|***** | | .|* | |6 |0.651 |0.067 |897.45 |0.000 | |
| .|***** | | .|. | |7 |0.609 |-0.021 |983.85 |0.000 | |
| .|**** | | .|. | |8 |0.571 |-0.018 |1060.2 |0.000 | |
| .|**** | | .|. | |9 |0.532 |-0.051 |1126.9 |0.000 | |
| .|**** | | .|. | |10 |0.490 |-0.039 |1183.8 |0.000 | |
| .|*** | | .|. | |11 |0.444 |-0.049 |1230.7 |0.000 | |
| .|*** | | *|. | |12 |0.392 |-0.083 |1267.4 |0.000 | |
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3-3: AR(p) for p ................
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