Sains Malaysiana 41(3)(2012): 371–377

Markov Switching Models for Time Series Data with Dramatic Jumps

(Model Peralihan Markov untuk Data Siri Masa dengan Lompatan Drastik)

Masoud Yarmohammadi*, Hamidreza Mostafaei

& Maryam Safaei

Department of Statistics, Tehran North Branch, Islamic Azal University, Tehran Iran

Diserahkan: 10 Jun 2011 / Diterima: 19 September 2011

ABSTRACT

In this research, the Markov switching autoregressive (MS-AR) model and six different time series modeling approaches are considered. These models are compared according to their performance for capturing the Iranian exchange rate series. The series has dramatic jump in early 2002 which coincides with the change in policy of the exchange rate regime. Our criteria are based on the AIC and BIC values. The results indicate that the MS-AR model can be considered as useful model, with the best fit, to evaluate the behaviors of Iran’s exchange rate.

Keywords: Fluctuations of exchange rate; Markov Switching Autoregressive model; nonlinear times series models

ABSTRAK

Dalam penyelidikan ini model autoregresi Markov (MS-AR) dan enam pendekatan model siri masa dipertimbangkan.  Model-model ini dibandingkan mengikut  keupayaan mendapatkan siri kadar pertukaran wang  Iran. Siri ini mempunyai lompatan drastik pada awal 2002 yang berlaku serentak dengan perubahan polisi kadar regim pertukaran wang.  Kriteria yang telah kami gunakan adalah berasaskan kepada nilai AIC dan BIC.  Keputusan menujukkan bahawa model MS-AR boleh dikatakan berguna.

Kata kunci: Model autoregrasi peralihan Markov; model siri masa tak linear; naik-turun kadar pertukaran

RUJUKAN

Akaike, H. 1974. A new look at statistical model identification, IEEE Transactions on Automatic Control 19: 716-723.

Akaike, H. 1979. A Bayesian extension of the minimum AIC procedure. Biometrika 66: 237-242.

Bollen, NP. B., Gray, S.F. & Whaley, R.E. 2000. Regime switching inforeign exchange rates: Evidence from currency option prices. Journal of Econometrics 94: 239-276.

Cologni, A. & Manera, M. 2009. The asymmetric effects of oil shocks on output growth: A Markov–Switching analysis for the G-7 countries. Economic Modelling 26: 1-29.

Engle, R.F. 1982. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of U.K. In_ation, Econometrica 50: 987-1007.

Engel, C. & Hamilton, J.D. 1990. Long switching in the dollar: are they the data and do Markets know it? American Economic Review 80: 689-713.

Franses, P.H. & Dijk, D.V. 2000. Non-linear time series models in empirical_nance, Cambridge: Cambridge University Press.

Hamilton, J.D. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 57: 357-384.

Hamilton, J.D. & Susmel, R. 1994. Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics 64: 307-333.

Hansen, B. 1999. Testing for linearity. Journal of Economic Surveys 13(5): 551-576.

Hassani, H. & Thomakos, D. 2010. A Review on Singular Spectrum Analysis for Economic and Financial Time Series, Statistics and its Interface 3(3): 377-397.

Hassani, H., Heravi, H. & Zhigljavsky, A. 2009. Forecasting European Industrial Production with Singular Spectrum Analysis, International Journal of Forecasting 25(1): 103-118.

Hassani, H. 2007. Singular Spectrum Analysis: Methodology and Comparison. Journal of Data Science 5(2): 239-257.

Hassani, H., Dionisio, A. & Ghodsi, M. 2010. The effect of noise reduction in measuring the linear and nonlinear dependency of financial markets, Nonlinear Analysis: Real World Applications 11(1): 492-502.

Ismail, M.T. & Isa, Z. 2006. Modelling Exchange Rates Using Regime Switching Models. Sains Malaysiana 35(2): 55-62.

Kang, I.B. 1999. International foreign exchange agreements and nominal exchange rate volatility: a GARCH application.The North American Journal of Economics and Finance, 10(2): 453-472.

Kroner, K.F. & Lastrapes, W.D. 1993. The impact of exchange rate volatility on international trade:Reduced form estimates using the GARCH-in-mean model. Journal of International Money and Finance 12(3): 298-318.

Lee, Y.H. & Chen, L.S. 2006. Why use Markov-switching models in exchange rate prediction? Economic Modelling, 23: 662-668.

Mills, C.T. & Markellos, N. R. 2008. The Econometric Modelling of Financial Time Series. Cambridge University Press. Priestley, M.B. 1988. Non-linear and Non-stationary Time Series Analysis. NY: Academic Press INC.

Psaradakis, Z. & Spagnolo, N. 2003. On the determination of the number of regimes in Markov–Switching autoregressive models, Journal of Time Series Analysis 24: 237-252.

Teräsvirta, T. 1994. Specification, estimation, and evaluation of smooth transition autoregressive models, Journal of the American Statistical Association 89: 208-18.

Tong, H. 1990. Non-Linear Time Series: A Dynamical Systems Approach. Oxford: Oxford University Press. Wang, J.X. & Wong, H.I. 1997. The predictability of Asian exchange rates: evidence from Kalman filter and ARCH estimations. Journal of Multinational Financial Management, 7(3): 231-252.

Wood, S.N. 2004. Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Amer. Statist. 99:673-686.

Wood, S.N. 2006. Generalized Additive Models: An Introduction with R, NY: CRC: Press.

Wood, S.N. 2011. Fast stable restricted maximum likelihood and marginal likelihood estimation of semi parametric generalized linear models. Journal of the Royal Statistical Society (B) 73(1): 3-36.

*Pengarang untuk surat-menyurat; email: h_mostafaei@iau-tnb.ac.ir