Investigating Structural break-GARCH-based Unit root test in US exchange rates

Yaya, OlaOluwa S and Akinlana, Damola M and Ogbonna, Ahamuefula E (2017): Investigating Structural break-GARCH-based Unit root test in US exchange rates. Forthcoming in: Journal of Science Research , Vol. 16, (2017)

Abstract

This paper applied a structural break-GARCH-based unit root test in studying the US exchange rates for twenty-two different currencies across America, Europe, Asia-Pacific and Southern Africa. The study employed three different data frequencies – daily, weekly and monthly with a view to understand the dynamics of a high frequency series that is characterized by alternating trend patterns and plausible presence of structural breaks. The chosen sample interval included periods of financial crisis or peculiar events. The exchange rates were found to exhibit ARCH effects at higher lags, thus informing the adaptation of the more parsimonious GARCH process in the residuals in contrast to the white noise disturbance assumption. The non-trended and trended structural break-GARCH-based unit root tests performances were adjudged with other existing tests. With significant break dates, between 2 and 5, the presence or otherwise of a unit root in foreign exchange rate series would be better captured when the inherent heteroscedasticity, trend and structural breaks in foreign exchange rate series are put into consideration

• Item Type: MPRA Paper
• Language: English
• Keywords: Exchange rate, Heteroscedasticity, Unit root, Structural break
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

[1]. Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. 1994. Time series analysis. New Jersey: Prentice Hall.

[2]. Dickey, D.A. and Fuller, W.A. 1979. Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. 74(366): 427-431.

[3]. Phillips, P.C.B. and Perron, P. 1988. Testing for a unit root in time series regression. Biometrika, 75: 335–346.

[4]. Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, Y. 1992. Testing the null hypothesis of stationarity against the alternative of unit root. Journal of Econometrics, 54: 159-178.

[5]. Ng, S. and Perron, P. 2001. Lag length selection and the construction of unit root tests with good size and power. Econometrica, 69: 1519-1554.

[6]. Kapetanios, G., Shin, Y. and Snell, A. 2003. Testing for a Unit Root in the Nonlinear STAR Framework. Journal of Econometrics 112, 359–379.

[7]. Hylleberg, S., Engle, R., Granger, C. W. J. and Yoo, B. S. 1990. Seasonal Integration and Cointegration. Journal of Econometrics, 44, 215-238.

[8]. Beaulieu, J.J. and Miron, J.A. 1993. Seasonal unit roots in aggregate US data. Journal of Econometrics, 55: 305–328.

[9]. Lumsdaine, R.L. and Papell, D.H. 1997. Multiple trend breaks and the unit-root hypothesis. Review of Economics and Statistics. 79, 212–218.

[10]. Lee, J. and Strazicich, M.C. 2003. Minimum Lagrange multiplier unit root test with two structural breaks. Review of Economics and Statistics 85, 1082–1089.

[11]. Perron, P. 2006. Dealing with Structural Breaks in Palgrave Handbook of Econometrics. Vol. 1: Econometric Theory, K. Patterson and T.C. Mills (eds.), Palgrave Macmillan, 278-352.

[12]. Narayan, P. K. and Popp, S. 2010. A new unit root test with two structural breaks in level and slope at unknown time. Journal of Applied Statistics, 37, 1425–38.

[13]. Smyth, R. 2013. Are fluctuations in energy variables permanent or transitory? A survey of the literature on the integration properties of energy consumption and production. Applied Energy. 104, 371-378.

[14]. Lean, H. H. and Smyth, R. 2013. Will policies to promote renewable electricity generation be effective? Evidence from panel stationarity and unit root tests for 115 countries. Renewable and Sustainable Energy Reviews. 22, 371-379.

[15]. Kim, K. and Schmidt, P. 1993. Unit root tests with conditional heteroskedasticity. Journal of Economics. 59, 287–300.

[16]. Haldrup, N. 1994. Heteroskedasticity in non-stationary time series: some Monte Carlo evidence. Statistical Papers. 35, 287-307.

[17]. Ling, S. and Li, W.K. 1998. Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroskedastic errors. Annals of Statistics. 26, 84–125.

[18]. Ling, S., Li, W.K. and McAleer, M. 2003. Estimation and testing for unit root process with GARCH (1, 1) errors: theory and Monte Carlo evidence. Econometric Reviews, 22, 179–202.

[19]. Cook, S. 2008. Joint maximum likelihood estimation of unit root testing equations and GARCH processes: some finite-sample issues. Mathematics and Computers in Simulation. 77, 109-116.

[20]. Narayan, P.K. and Liu, R. 2011. Are shocks to commodity prices persistent? Applied Energy, 88: 409-416.

[21]. Narayan, P. K. and Liu, R. 2015. A unit root model for trending time-series energy variables. Energy Economics. 50, 391-402.

[22]. Narayan, P. K., Liu, R. and Westerlund, J. 2016. A GARCH model for testing market efficiency. Journal of International Financial Markets Institutions and Money, 41, 121-138.

[23]. Salisu, A.A., Ndako, U.B., Oloko, T.F. and Akanni, L.O. 2016. Unit root modelling for trending stock market series. Borsa Istanbul Review, 16-2: 82-91.

[24]. Bai, J., and Perron, P. 2003. Computation and analysis of multiple structural change models. Journal of Applied Economics. 18, 1–22.