Forecasting U.S.A Imports from China, Singapore, Indonesia, and Thailand. An Empirical Project Chittawan Chanagul UK 40186 (Econometric Forecasting): Prof. Robert M. Kunst
Introduction Times Series Data trend, seasonal, and cycles Thus, non-stationary
Transformations to achieve Stationarity Data differencing Fitting some type of curve to the data and then model the residuals from that fit.
Objective To evaluate the Deterministic and Stochastic trend models in Univariate times series data. Case study: US Imports from China, Indonesia, Singapore and Thailand.
Data U.S. imports (millions of U.S. dollars) from China, Indonesia, Singapore, and Thailand on monthly frequency basis.
Figure 1: U.S. imports from China, Singapore, Indonesia, and Thailand from 1990.01-2006.12 3 0 0 0 0 C H IN A 1 4 0 0 IN D O 2 5 0 0 0 1 2 0 0 2 0 0 0 0 1 0 0 0 1 5 0 0 0 8 0 0 6 0 0 1 0 0 0 0 4 0 0 5 0 0 0 2 0 0 0 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 0 1 9 9 0 1 9 9 2 1 99 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 0 S IN G A P O R E 2 4 0 0 TH A IL A N D 1 8 0 0 2 0 0 0 1 6 0 0 1 6 0 0 1 4 0 0 1 2 0 0 1 2 0 0 1 0 0 0 8 0 0 8 0 0 4 0 0 6 0 0 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 0 1 9 9 0 1 9 9 2 1 99 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6
Figure 2: First-difference of data 3000 DCHINA 200 DINDO 2000 1000 100 0-1000 0-2000 -100-3000 -4000 1990 1992 1994 1996 1998 2000 2002 2004 2006-200 1990 1992 1994 1996 1998 2000 2002 2004 2006 600 DSING 400 DTHAI 400 300 200 200 100 0 0-100 -200-200 -400 1990 1992 1994 1996 1998 2000 2002 2004 2006-300 1990 1992 1994 1996 1998 2000 2002 2004 2006
1 0.4 1 0.0 9.6 9.2 8.8 8.4 8.0 7.6 7.2 Figure 3: log of U.S imports from China, Singapore, Indonesia, and Thailand from 1990.01-2006.12 LOG C 8.0 7.6 7.2 6.8 6.4 6.0 L OG T 6.8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 5.6 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 7.2 LOGI ND O 7.6 L OGSING 6.8 7.4 6.4 7.2 7.0 6.0 6.8 5.6 6.6 5.2 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 6.4 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6
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 1990.01-2004.12 Reserve 2005.01-2006.12 for out-of-sample forecasting
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
Correlogram (log Singapore) Level and First Difference
Correlogram (log Thailand) Level and First Difference
Correlogram (log Indonesia) Level and First Difference
China picture : The Great Wall
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) 12 0.773-2.868-2.775 (0,1,0)x(1,0,1) 12 0.688-2.584-2.547 X (1,1,0)x(1,0,0) 12 0.575-2.270-2.232 X (2,1,0)x(1,0,1) 12 0.779-2.924-2.849 (0,1,1)x(1,0,1) 12 0.761-2.837-2.781 (1,0,1)x(0,1,1) 12 0.611-2.712-2.656 (0,1,1)x(0,1,1) 12 0.537-2.721-2.684
Best Stochastic Trend model and Out of Sample Forecast 10.6 10.4 10.2 10.0 9.8 9.6 9.4 2005M01 2005M07 2006M01 2006M07 LOGCF Forecast: LOGCF Actual: LOGC Forecast sample: 2005M01 2006M12 Included observations: 24 Root Mean Squared Error 0.044511 Mean Absolute Error 0.034383 Mean Abs. Percent Error 0.342447 Theil Inequality Coefficient 0.002229 Bias Proportion 0.171970 Variance Proportion 0.294227 Covariance Proportion 0.533803
Deterministic Trend Model China R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (1,1)x(1,1) 12 0.993-2.856-2.763 (2,0)x(1,1) 12 0.992-2.738-2.645 X
Best Deterministic Trend model and Out of Sample Forecast 11.0 10.8 10.6 10.4 10.2 10.0 9.8 9.6 9.4 2005M01 2005M07 2006M01 2006M07 LOGCF Forecast: LOGCF Actual: LOGC Forecast sample: 2005M01 2006M12 Included observations: 24 Root Mean Squared Error 0.074105 Mean Absolute Error 0.063165 Mean Abs. Percent Error 0.630606 Theil Inequality Coefficient 0.003696 Bias Proportion 0.726548 Variance Proportion 0.039278 Covariance Proportion 0.234174
Table comparing Deterministic and Stochastic trend models: China Deterministic trend model stochastic trend model AIC -2.856-2.924 SIC -2.763-2.894 RMSE 0.0741 0.0445 MAE 0.0631 0.0343 MAPE 0.6306 0.3424
Indonesia picture: Bali (Dreamland)
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) 12 0.371-1.938-1.900 (2,1,0)x(1,0,0) 12 0.389-1.948-1.891 (2,1,1)x(1,0,1) 12 0.437-2.019-1.944 (0,1,1)x(1,1,1) 12 0.586-2.309-2.250 (2,1,0)x(1,0,1) 12 0.505-2.148-2.073 (1,0,1)x(0,1,1) 12 0.693-2.188-2.132 X
Best Stochastic Trend model and Out of Sample Forecast 7.4 7.2 7.0 6.8 6.6 6.4 2005M01 2005M07 2006M01 2006M07 LOGINDOF Forecast: LOGINDOF Actual: LOGINDO Forecast sample: 2005M01 2006M12 Included observations: 24 Root Mean Squared Error 0.110582 Mean Absolute Error 0.097658 Mean Abs. Percent Error 1.398403 Theil Inequality Coefficient 0.007997 Bias Proportion 0.728224 Variance Proportion 0.006289 Covariance Proportion 0.265487
Deterministic Trend Model Indonesia R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (2,0)x(1,1) 12 0.947-2.142-2.048
Best Deterministic Trend model and Out of Sample Forecast 8.0 7.6 7.2 6.8 6.4 6.0 5.6 2005M01 2005M07 2006M01 2006M07 LOGINDOF Forecast: LOGINDOF Actual: LOGINDO Forecast sample: 2005M01 2006M12 Included observations: 24 Root Mean Squared Error 0.178288 Mean Absolute Error 0.169163 Mean Abs. Percent Error 2.422222 Theil Inequality Coefficient 0.012963 Bias Proportion 0.900251 Variance Proportion 0.027398 Covariance Proportion 0.072351
Table comparing Deterministic and Stochastic trend models: Indonesia Deterministic trend model stochastic trend model AIC -2.142-2.309 SIC -2.048-2.250 RMSE 0.178 0.110 MAE 0.169 0.097 MAPE 2.422 1.398
Singapore picture: The Merlion
Stochastic Trend Model Singapore R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (0,1,1)x(1,0,1) 12 0.629-2.449-2.393 X (2,1,0)x(1,0,0) 12 0.508-2.171-2.115 (2,1,0)x(1,0,1) 12 0.670-2.557-2.482 (1,0,1)x(0,1,1) 12 0.753-2.346-2.271 X (3,1,0)x(0,1,1) 12 0.572-2.441-2.365
Best Stochastic Trend model and Out of Sample Forecast 7.5 7.4 7.3 7.2 7.1 7.0 6.9 6.8 6.7 2005M01 2005M07 2006M01 2006M07 LOGSINGF Forecast: LOGSINGF Actual: LOGSING Forecast sample: 2005M01 2006M12 Included observations: 24 Root Mean Squared Error 0.137783 Mean Absolute Error 0.106786 Mean Abs. Percent Error 1.462638 Theil Inequality Coefficient 0.009613 Bias Proportion 0.526531 Variance Proportion 0.354857 Covariance Proportion 0.118612
Deterministic Trend Model Singapore R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (0,4)x(1,1) 12 0.905-2.346-2.197 X (3,0)x(1,1) 12 0.916-2.573-2.442 (1,1)x(1,1) 12 0.912-2.469-2.357 X
Best Deterministic Trend model and Out of Sample Forecast 7.3 7.2 7.1 7.0 6.9 6.8 6.7 6.6 6.5 2005M01 2005M07 2006M01 2006M07 LOGSINGF Forecast: LOGSINGF Actual: LOGSING Forecast sample: 2005M01 2006M12 Included observations: 24 Root Mean Squared Error 0.305652 Mean Absolute Error 0.256640 Mean Abs. Percent Error 3.523735 Theil Inequality Coefficient 0.021559 Bias Proportion 0.705008 Variance Proportion 0.018496 Covariance Proportion 0.276496
Table comparing Deterministic and Stochastic trend models: Singapore AIC Deterministic trend model -2.573 stochastic trend model -2.557 SIC -2.442-2.482 RMSE 0.3056 0.1377 MAE 0.2566 0.1067 MAPE 3.5237 1.4626
Thailand picture: Phi Phi, Phuket
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) 12 0.728-3.333-3.277 (2,1,0)x(1,0,1) 12 0.736-3.373-3.298 (3,0,0)x(0,1,1) 12 0.805-3.317-3.242 (2,1,0)x(0,1,1) 12 0.595-3.295-3.239
Best Stochastic Trend model and Out of Sample Forecast 7.9 7.8 7.7 7.6 7.5 7.4 7.3 7.2 7.1 2005M01 2005M07 2006M01 2006M07 LOGTF Forecast: LOGTF Actual: LOGT Forecast sample: 2005M01 2006M12 Included observations: 24 Root Mean Squared Error 0.051549 Mean Absolute Error 0.041234 Mean Abs. Percent Error 0.552044 Theil Inequality Coefficient 0.003452 Bias Proportion 0.022893 Variance Proportion 0.450576 Covariance Proportion 0.526531
Deterministic Trend Model Thailand R 2 AIC SIC Q-test (No significant ACFs or PACFs) Invertibility (1,1)x(1,1) 12 0.980-3.328-3.235 (3,0)x(1,1) 12 0.979-3.389-3.276
Best Deterministic Trend model and Out of Sample Forecast 8.2 8.0 7.8 7.6 7.4 7.2 7.0 6.8 2005M01 2005M07 2006M01 2006M07 LOGTF Forecast: LOGTF Actual: LOGT Forecast sample: 2005M01 2006M12 Included observations: 24 Root Mean Squared Error 0.049580 Mean Absolute Error 0.039950 Mean Abs. Percent Error 0.535213 Theil Inequality Coefficient 0.003320 Bias Proportion 0.019327 Variance Proportion 0.380412 Covariance Proportion 0.600262
Table comparing Deterministic and Stochastic trend models: Thailand Deterministic trend model stochastic trend model AIC SIC RMSE MAE MAPE -3.389-3.276 0.0495 0.0399 0.5352-3.373-3.298 0.0515 0.0412 0.5520
Deterministic vs Stochastic trend model SIC Thailand Indonesia China Singapore Deterministic trend model -3.276-2.048-2.763-2.442 Stochastic trend model -3.298-2.250-2.849-2.482 AIC Thailand Indonesia China Singapore Deterministic trend model -3.389-2.142-2.856-2.573 stochastic trend model -3.373-2.309-2.924-2.557
Deterministic trend model Stochastic trend model Thailand RMSE 0.049 0.051 MAE 0.039 0.041 MAPE 0.535 0.552 Indonesia RMSE 0.178 0.110 MAE 0.169 0.097 MAPE 2.422 1.398 China RMSE 0.074 0.044 MAE 0.063 0.034 MAPE 0.630 0.342 Singapore RMSE 0.305 0.137 MAE 0.252 0.106 MAPE 3.523 1.462
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