Buffered autoregressive models with conditional heteroscedasticity: An application to exchange rates

Zhu, Ke and Li, Wai Keung and Yu, Philip L.H. (2014): Buffered autoregressive models with conditional heteroscedasticity: An application to exchange rates.

Abstract

This paper introduces a new model called the buffered autoregressive model with generalized autoregressive conditional heteroskedasticity (BAR-GARCH). The proposed model, as an extension of the BAR model in Li et al. (2013), can capture the buffering phenomenon of time series in both conditional mean and conditional variance. Thus, it provides us a new way to study the nonlinearity of a time series. Compared with the existing AR-GARCH and threshold AR-GARCH models, an application to several exchange rates highlights an interesting interpretation of the buffer zone determined by the fitted BAR-GARCH models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Buffered AR model; Buffered AR-GARCH model; Exchange rate; GARCH model; Nonlinear time series; Threshold AR model.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; G - Financial Economics > G1 - General Financial Markets

References

ANDREWS, D.W.K. (1993). Tests for parameter instability and structural change with unknow change point. Econometrica 61, 821–856.

BOLLERSLEV, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–327.

BOLLERSLEV, T., CHOU, R.Y. & KRONER, K.F. (1992). ARCH modelling in finance: A review of the theory and empirical evidence. Journal of Econometrics 52, 5–59.

BOLLERSLEV, T. & WOOLDRIDGE, J.M. (1992). Quasi-maximum likelihood estimation of dynamic models with time varying covariance. Econometric Reviews 11, 143–172.

BROOKS, C. (2001). A double-threshold GARCH model for the French Franc/Deutschmark exchange rate. Journal of Forecasting 20, 135–143.

BUCKLEY, N. (2012). Economy: Nation avoided recession but risks persist. Financial Times, June 13, 2012.

CHAN, K.S. (1990). Testing for threshold autoregression. Annals of Statistics 18, 1886–1894.

CHAN, K.S. (1991). Percentage points of likelihood ratio tests for threshold autoregression. Journal of the Royal Statistical Society Series B 53, 691–696.

ENGLE, R.F. (1982). Autoregressive conditional heteroskedasticity with estimates of variance of U.K. inflation. Econometrica 50, 987–1008.

FRANCQ, C. & ZAKOIAN, J.M. (2010). GARCH Models: Structure, Statistical Inference and Financial Applications. Chichester, UK: John Wiley.

HANSEN, B.E. (2011). Threshold autoregression in economics. Statistics and Its Interface 4, 123–127.

LI, G.D., GUAN, B., LI, W.K. & YU, P.L.H. (2013). Buffered threshold autoregressive time series models. Working paper. University of Hong Kong.

LI, C.W. & LI, W.K. (1996). On a double-threshold autoregressive heteroscedastic time series model. Jounral of Applied Econometrics 11, 253–274.

LI, G.D. & LI, W.K. (2008). Testing for threshold moving average with conditional heteroscedasticity. Statistica Sinica 18, 647–665.

LI, G.D. & LI, W.K. (2011). Testing a linear time series models against its threshold extension. Biometrika 98, 243–250.

LI, D., LI, W.K. & LING, S. (2011). On the least squares estimation of threshold autoregressive and moving-average models. Statistics and Its Interface 4, 183–196.

LI, D. & LING, S. (2012). On the least squares estimation of multiple-regime threshold autoregressive models. Journal of Econometrics 167, 240–253.

LI, D., LING, S. & LI, W.K. (2013). Asymptotic theory on the least squares estimation of threshold moving-average models. Econometric Theory 29, 482–516.

LI, W.K. & LAM, K. (1995). Modelling asymmetry in stock returns by a threshold autoregressive conditional heteroscedastic model. Journal of the Royal Statistical Society. Series D (The Statistician) 44, 333–341

LING, S. & TONG, H. (2005). Testing a linear MA model against threshold MA models. Annals of Statistics 33, 2529–2552.

LIU, J., LI, W.K. & LI, C.W. (1997). On a threshold autoregression with conditional heteroscedastic variances. Journal of Statistical Planning and Inference 62, 279–300.

PESARAN, M.H. & POTTER, S.M. (1997). A floor and ceiling model of US output. Journal of Economic Dynamics and Control 21, 661–695.

RABEMANJARA, R. & ZAKOIAN, J.M. (1993). Threshold ARCH model and asymmetries in volatility. Journal of Applied Econometrics 8, 31–49.

TONG, H. (1978). On a threshold model. In Pattern Recognition and Signal Processing (C.H. Chen, ed.) 575-586. Amsterdam: Sijthoff and Noordhoff.

TONG, H. (1990). Non-linear Time Series. A Dynamical System Approach. Clarendon Press, Oxford.

TONG, H. (2011). Threshold models in time series analysis—30 years on (with discussions). Statistics and Its Interface 4, 107–135.

TSAY, R.S. (1989). Testing and modeling threshold autoregressive processes. Journal of American Statistical Association 84, 231–240.

TSAY, R.S. (1998). Testing and modeling multivariate threshold models. Journal of American Statistical Association 93, 1188–1202.

TSAY, R.S. (2005). Analysis of financial time series (2nd ed.). New York: John Wiley & Sons, Incorporated.

WONG, C.S. & LI, W.K. (1997). Testing for threshold autoregression with conditional heteroscedasticity. Biometrika 84, 407-418.

WONG, C.S. & LI, W.K. (2000). Testing for double threshold autoregressive conditional heteroscedastic model. Statistica Sinica 10, 173–189.

ZAKOIAN, J.M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control 18, 931–955.

ZHU, K. & LING, S. (2012). Likelihood ratio tests for the structural change of an AR(p) model to a threshold AR(p) model. Journal of Time Series Analysis 33, 223-232.

ZHU, K., YU, P.L.H. & LI, W.K. (2013). Testing for the buffered autoregressive processes. Statistica Sinica. forthcoming.