Abstract
Although many macroeconomic time series are assumed to follow nonlinear processes, nonlinear models often do not provide better predictions than their linear counterparts. Furthermore, nonlinear models easily become very complex and difficult to estimate. The aim of this study is to investigate whether simple nonlinear extensions of autoregressive processes are able to provide more accurate forecasting results than linear models. Therefore, simple autoregressive processes are extended by means of nonlinear transformations (quadratic, cubic, sine, exponential functions) of lagged time series observations and autoregression residuals. The proposed forecasting models are applied to a large set of macroeconomic and financial time series for 10 European countries. Findings suggest that these models, including nonlinear transformation of lagged autoregression residuals, are able to provide better forecasting results than simple linear models. Thus, it may be possible to improve the forecasting accuracy of linear models by including nonlinear components. This is especially true for time series that are positively tested for nonlinear characteristics and longer forecast horizons.
Acknowledgements
I thank two anonymous referees, the editor of this journal and Helmut Herwartz for very helpful comments and suggestions.
References
Balke, N., T. Fomby (1994), Large Shocks, Small Shocks, and Economic Fluctuations: Outliers in Macroeconomic Time Series. Journal of Applied Econometrics 9 (2): 181–200.Search in Google Scholar
Bleaney, M., P. Mizen (1996), Nonlinearities in Exchange-Rate Dynamics: Evidence from Five Currencies, 1973–94. The Economic Record 72 (216): 36–45.Search in Google Scholar
Boero, G., E. Marrocu (2002), The Performance of Non-Linear Exchange Rate Models: A Forecasting Comparison. Journal of Forecasting 21 (7): 513–542.Search in Google Scholar
Bollerslev, T. (1986), Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31 (3): 307–327.Search in Google Scholar
Brånnås, K., J. De Gooijer (1994), Autoregressive-asymmetric Moving Average Models for Business Cycle Data. Journal of Forecasting 13 (6): 529–544.Search in Google Scholar
Brock, W., W. Dechert, B. LeBaron, J. Scheinkman (1995), A Test for Independence Based on the Correlation Dimension. Working papers 9520, Wisconsin Madison – Social Systems.Search in Google Scholar
Chan, K., H. Tong (1986), On estimating Thresholds in Autoregressive Models. Journal of Time Series Analysis 7 (3): 179–190.Search in Google Scholar
Clements, M., P. Franses, N. Swanson (2004), Forecasting Economic and Financial Time-Series with Non-Linear Models. International Journal of Forecasting 20 (2): 169–183.Search in Google Scholar
Clements, M., J. Smith (2000), Evaluating the Forecast Densities of Linear and Non-Linear Models: Applications to Output Growth and Unemployment. Journal of Forecasting 19 (4): 255–276.Search in Google Scholar
Clements, M., J. Smith (2001), Evaluating Forecasts from SETAR Models of Exchange Rates. Journal of International Money and Finance 20 (1): 133–148.Search in Google Scholar
De Gooijer, J., K. Kumar (1992), Some Recent Developments in Non-linear Time Series Modelling, Testing, and Forecasting. International Journal of Forecasting 8 (2): 135–156.Search in Google Scholar
Diebold, F., J. Nason (1990), Nonparametric Exchange Rate Prediction? Journal of International Econometrics 28 (3–4): 315–332.Search in Google Scholar
Dijk, v. D., P. Franses, A. Lucas (1999), Testing for Smooth Transition Nonlinearity in the Presence of Outliers. Journal of Business and Economic Statistics 17 (2): 217–235.Search in Google Scholar
Franses, P., P. de Bruin (2002), On Data Transformations and Evidence of Nonlinearity. Computational Statistics and Data Analysis 40 (3): 621–632.Search in Google Scholar
Franses, P., R. Paap (1999), Does Seasonality Influence the Dating of Business Cycle Turning Points? Journal of Macroeconomics 21 (1): 79–92.Search in Google Scholar
Ghysels, E., C. Granger, P. Siklos (1996), Is Seasonal Adjustment A Linear or Nonlinear Data-Filtering Process? Journal of Business and Economic Statistics 14 (3): 374–386.Search in Google Scholar
Granger, C. (1993), Strategies for Modelling Nonlinear Time-Series Relationships. The Economic Record 69 (206): 233–238.Search in Google Scholar
Granger, C. (2001), Overview of Nonlinear Macroeconomtric Empirical Models. Macroeconomic Dynamics 5 (4): 466–481.Search in Google Scholar
Granger, C., A. Andersen (1978), An Introduction to Bilinear Time Series Model. Göttingen, Vandenhoeck and Ruprecht.Search in Google Scholar
Grillenzoni, C. (2001), Nonlinear Predictions of Financial Time Series. Statistica Applicata 13 (3): 257–279.Search in Google Scholar
Hamilton, J. (1989), A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica 57 (2): 357–384.Search in Google Scholar
Hansen, B.E. (2011), Threshold Autoregression in Economics. Statistics and Its Interface 4: 123–127.Search in Google Scholar
Hansen, P. (2010). A Winners Curse for Econometric Models: On the Joint Distribution of In-Sample Fit and Out-of-Sample Fit and Its Implications for Model Selection. Research Paper, 1–39.Search in Google Scholar
Herwartz, H. (2011), Forecast Accuracy and Uncertainty in Applied Econometrics: A Recommendation of Specific-to-General Predictor Selection. Empirical Economics 41 (2): 487–510.Search in Google Scholar
Herwartz, H. (2013), On the Predictive Content of Autoregression Residuals: A Semiparametric, Copula-Based Approach to Time Series Prediction. Journal of Forecasting 32 (4): 353–368.Search in Google Scholar
Keenan, D.M. (1985), A Tukey Nonadditivity-Type Test for Time Series Nonlinearity. Biometrika 72 (1): 39–44.Search in Google Scholar
Kräger, H., P. Kugler (1993), Non-Linearities in Foreign Exchange Markets: A Different Perspective. Journal of International Money and Finance 12 (2): 195–208.Search in Google Scholar
Maravall, A. (1983), An Application of Nonlinear Time Series Forecasting. Journal of Business and Economic Statistics 1 (1): 66–74.Search in Google Scholar
McLeod, A., W. Li (1983), Diagnostic Checking ARMA Time Series Models Using Squared-Residual Autocorrelations. Journal of Time Series Analysis 4 (4): 269–273.Search in Google Scholar
Neftci, S. (1984), Are Economic Time Series Asymmetric Over The Business Cycle? Journal of Political Economy 92 (2): 307–328.Search in Google Scholar
Peseran, M., A. Timmermann (2004), How Costly is It To Ignore Breaks When Forecasting the Direction of a Time Series? International Journal of Forecasting 20 (3): 411–425.Search in Google Scholar
Poskitt, D., A. Tremayne (1986), The Selection and Use of Linear and Bilinear Time Series Models. International Journal of Forecasting 2 (1): 101–114.Search in Google Scholar
Potter, S. (1995), A Nonlinear Approach to US GNP. Journal of Applied Econometrics 10 (2): 109–125.Search in Google Scholar
Ramsey, J. (1969), Tests for Specifications Errors in Classical Linear Least-Squares Regression Analysis. Journal of the Royal Statistical Society, Series B 31 (2): 350–371.Search in Google Scholar
Rao, T. (1981), On the Theory of Bilinear Time Series Models. Journal of the Royal Statistical Society, Series B 43 (2): 244–255.Search in Google Scholar
Stock, J.H., M.W. Watson (1998), A Comparison of Linear And Nonlinear Univariate Models for Forecasting Macroeconomic Time Series. NBER Working Paper Series 6607: 1–57.Search in Google Scholar
Teräsvirta, T. (1994), Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models. Journal of the American Statistical Association 89 (425): 208–218.Search in Google Scholar
Teräsvirta, T. (2005), Forecasting Economic Variables with Nonlinear Models. Handbook of Economic Forecasting 1: 413–457.Search in Google Scholar
Teräsvirta, T., H. Anderson (1992), Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models. Journal of Applied Econometrics 7 (S1): 119–136.Search in Google Scholar
Tong, H. (1990), On a Threshold Model. S. 101–141 in: C.H. Chen (ed.), Pattern Recognition and Signal Processing. NATO ASI Series E: Applied Sc. Sijtjoff & Noordhoff, Netherlands, 461–466.Search in Google Scholar
Tong, H. (1990), Non-Linear Time Series: A Dynamical System Approach. Oxford, Clarendon Press.Search in Google Scholar
Tsay, R.S. (1986), Nonlinearity Tests for Time Series. Biometrika 73 (2): 461–466.Search in Google Scholar
Zhou, S. (2011), Nonlinear Stationarity of real Interest Rates in the EMU Countries. Journal of Economic Studies 38 (6): 691–702.Search in Google Scholar
Supplemental Material
The online version of this article (DOI: 10.1515/jbnst-2015-1019) offers supplementary material, available to authorized users.
©2016 by De Gruyter Mouton
