The dataset, which have been chosen, contain 50 annually observations of the GDP China (constant 2000 US Dollar) for the period 1960 to 2009. To estimate this forecasting model, the period 1965 to 2004 is selected and the hold-out 2005 to 2009 is used to examine the out-of-sample forecasting performance.
To begin with, the GDP –China graph is plotted by using the STATA command in order to check overall the trend.
Next, it is necessary to tell the STATA that this dataset is the time series format by using “tsset time” command. Then, the autocorrelations and partial autocorrelation are used to examine that whether the series is non-stationary or ...view middle of the document...
Residual (Quadratic trend)
Log of GDP trend model
The estimation results show that the log linear trend seems to fit better than linear and quadratic trend. However, it is difficult to compare the log-linear trend with the linear and the quadratic trend because of levels of log.
Log Linear Trend
Exponential trend model
Due to the fact that it is difficult to comparable the log-linear trend with others as mentioned before, the exponential trend is used to estimate by using nonlinear least square so as to solve that problem. It can be seen that the exponential trend seems to fit well in the Exponential graph below.
Finally, we examine the AIC and the BIC for the three trend models, which are linear trend, quadratic trend and exponential trends, to set the final model. After executed the AIC and BIC for each model, the results show according to the table below. From this table, we can concluded that the exponential trend is fit model because the AIC and BIC are the lowest.
Linear Trend 1091.7812 1095.1589
Quadratic Trend 982.87408 986.25184
Exponential Trend 907.40865 909.09753
Moreover, comparing between the quadratic trend forecast and the exponential trend forecast for 2005 to 2009, the realization values , and a 95% forecast interval the results can show that the exponential forecast is good , as the realization hugs almost the forecast trend line quite closely. Most of the realizations, additionally, fall inside the 95% forecast interval whereas the quadratic trend fall outside that interval. To ensure that the exponential is fitted model, using the whole sample size to re-estimate and the result is satisfactory.
Quadratic trend forecast
Exponential trend forecast
Regression analysis the whole sample size for 1960 to 2009
To construct forecasts for the cyclical component of GDP that is deviations from trend, the ARMA approach is used to examine the results. As mentioned above, the Exponential trend provides the best fit for the trend as can be seen in the Exponential Trend graph. Moreover, the residual graph shows the deviations from trend that is cycles plus irregular components.