Forecasting U.S.A Imports from China, Singapore, Indonesia, and Thailand.

Transcription

1 Forecasting U.S.A Imports from China, Singapore, Indonesia, and Thailand. An Empirical Project Chittawan Chanagul UK (Econometric Forecasting): Prof. Robert M. Kunst

2 Introduction Times Series Data trend, seasonal, and cycles Thus, non-stationary

3 Transformations to achieve Stationarity Data differencing Fitting some type of curve to the data and then model the residuals from that fit.

4 Objective To evaluate the Deterministic and Stochastic trend models in Univariate times series data. Case study: US Imports from China, Indonesia, Singapore and Thailand.

5 Data U.S. imports (millions of U.S. dollars) from China, Indonesia, Singapore, and Thailand on monthly frequency basis.

6 Figure 1: U.S. imports from China, Singapore, Indonesia, and Thailand from C H IN A IN D O S IN G A P O R E TH A IL A N D

7 Figure 2: First-difference of data 3000 DCHINA 200 DINDO DSING 400 DTHAI

8 Figure 3: log of U.S imports from China, Singapore, Indonesia, and Thailand from LOG C L OG T LOGI ND O 7.6 L OGSING

9 Data U.S. imports (millions of U.S. dollars) from China, Indonesia, Singapore, and Thailand on monthly frequency basis. Analysis and modeling on log of original data from Reserve for out-of-sample forecasting

10 Methodology Deterministic Trend Model working in levels and include deterministic trend component in the model. Stochastic Trend Model using strategy of differencing to achieve stationarity

11 Correlogram (log Singapore) Level and First Difference

12 Correlogram (log Thailand) Level and First Difference

13 Correlogram (log Indonesia) Level and First Difference

14 China picture : The Great Wall

15 Stochastic Trend Model (p,d,q)x(p,d,q) lag R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (0,1,3)x(1,0,1) (0,1,0)x(1,0,1) X (1,1,0)x(1,0,0) X (2,1,0)x(1,0,1) (0,1,1)x(1,0,1) (1,0,1)x(0,1,1) (0,1,1)x(0,1,1)

16 Best Stochastic Trend model and Out of Sample Forecast M M M M07 LOGCF Forecast: LOGCF Actual: LOGC Forecast sample: 2005M M12 Included observations: 24 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

17 Deterministic Trend Model China R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (1,1)x(1,1) (2,0)x(1,1) X

18 Best Deterministic Trend model and Out of Sample Forecast M M M M07 LOGCF Forecast: LOGCF Actual: LOGC Forecast sample: 2005M M12 Included observations: 24 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

19 Table comparing Deterministic and Stochastic trend models: China Deterministic trend model stochastic trend model AIC SIC RMSE MAE MAPE

20 Indonesia picture: Bali (Dreamland)

21 Stochastic Trend Model (p,d,q)x(p,d,q)lag R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (1,1,0)x(1,0,0) (2,1,0)x(1,0,0) (2,1,1)x(1,0,1) (0,1,1)x(1,1,1) (2,1,0)x(1,0,1) (1,0,1)x(0,1,1) X

22 Best Stochastic Trend model and Out of Sample Forecast M M M M07 LOGINDOF Forecast: LOGINDOF Actual: LOGINDO Forecast sample: 2005M M12 Included observations: 24 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

23 Deterministic Trend Model Indonesia R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (2,0)x(1,1)

24 Best Deterministic Trend model and Out of Sample Forecast M M M M07 LOGINDOF Forecast: LOGINDOF Actual: LOGINDO Forecast sample: 2005M M12 Included observations: 24 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

25 Table comparing Deterministic and Stochastic trend models: Indonesia Deterministic trend model stochastic trend model AIC SIC RMSE MAE MAPE

26 Singapore picture: The Merlion

27 Stochastic Trend Model Singapore R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (0,1,1)x(1,0,1) X (2,1,0)x(1,0,0) (2,1,0)x(1,0,1) (1,0,1)x(0,1,1) X (3,1,0)x(0,1,1)

28 Best Stochastic Trend model and Out of Sample Forecast M M M M07 LOGSINGF Forecast: LOGSINGF Actual: LOGSING Forecast sample: 2005M M12 Included observations: 24 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

29 Deterministic Trend Model Singapore R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (0,4)x(1,1) X (3,0)x(1,1) (1,1)x(1,1) X

30 Best Deterministic Trend model and Out of Sample Forecast M M M M07 LOGSINGF Forecast: LOGSINGF Actual: LOGSING Forecast sample: 2005M M12 Included observations: 24 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

31 Table comparing Deterministic and Stochastic trend models: Singapore AIC Deterministic trend model stochastic trend model SIC RMSE MAE MAPE

32 Thailand picture: Phi Phi, Phuket

33 Stochastic Trend Model (p,d,q)x(p,d,q)lag R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (0,1,1)x(1,0,1) (2,1,0)x(1,0,1) (3,0,0)x(0,1,1) (2,1,0)x(0,1,1)

34 Best Stochastic Trend model and Out of Sample Forecast M M M M07 LOGTF Forecast: LOGTF Actual: LOGT Forecast sample: 2005M M12 Included observations: 24 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

35 Deterministic Trend Model Thailand R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (1,1)x(1,1) (3,0)x(1,1)

36 Best Deterministic Trend model and Out of Sample Forecast M M M M07 LOGTF Forecast: LOGTF Actual: LOGT Forecast sample: 2005M M12 Included observations: 24 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

37 Table comparing Deterministic and Stochastic trend models: Thailand Deterministic trend model stochastic trend model AIC SIC RMSE MAE MAPE

38 Deterministic vs Stochastic trend model SIC Thailand Indonesia China Singapore Deterministic trend model Stochastic trend model AIC Thailand Indonesia China Singapore Deterministic trend model stochastic trend model

39 Deterministic trend model Stochastic trend model Thailand RMSE MAE MAPE Indonesia RMSE MAE MAPE China RMSE MAE MAPE Singapore RMSE MAE MAPE

40 Conclusion Stochastic trend model is superior to deterministic trend model Franses and Kleibergen (1996) out-of-sample forecasts based on modelling the first differences of economic data are generally better than those obtained by fitting a deterministic trend Chatfield (2001) it has been found out that a deterministic linear trend rarely provides a satisfactory model for real data