Structural break or long memory: an empirical survey on daily rainfall data sets across Malaysia

Abstract

Abstract.A short memory process that encounters occasional structural breaks in mean can show a slower rate of decay in the autocorrelation function and other properties of fractional integrated I (d) processes. In this paper we employed a procedure for estimating the fractional differencing parameter in semiparametric contexts proposed by Geweke and Porter-Hudak (1983) to analyse nine daily rainfall data sets across Malaysia. The results indicate that all the data sets exhibit long memory. Furthermore, an empirical fluctuation process using the ordinary least square (OLS)-based cumulative sum (CUSUM) test for the break date was applied. Break dates were detected in all data sets. The data sets were partitioned according to their respective break date, and a further test for long memory was applied for all subseries. Results show that all subseries follows the same pattern as the original series. The estimate of the fractional parameters d 1 and d 2 on the subseries obtained by splitting the original series at the break date confirms that there is a long memory in the data generating process (DGP). Therefore this evidence shows a true long memory not due to structural break.

Assessment of Risk of Rainfall Events with a Hybrid of ARFIMA-GARCH

“…The value of the power factor  is the main determinant of the ordinates included in the regression, for more details see (Yusof et al, 2013).…”

“…Certainly, rainfall time series data usually have both linear and nonlinear patterns. To adequately fit these chaotic time series, other more complicated models that have the ability to capture the dynamics of the series more precisely have to be taken into account (Yusof & Kane, 2013). There are a number of studies on time series modelling and forecasting that argue that performance improves in hybrid models (Zhang, 2003).…”

“…Rainfall time series is often characterized by long memory behavior (Yusof et al, 2013) and are highly skewed with volatility clustering (Villarini et al, 2010). Long memory is an asymptotic property of a stochastic process, characterizing the decay of the correlation between observations separated by increasingly large time lags.…”

“…For 0.5 < d < l, the case is called non-stationary mean-reverting (Claude & Vivien, 2002). The testing of hydrological data with Long Memory models was done by number of authors (Koutsoyiannis, 2006;Koscielny-Bunde et al, 2006;Mudelsee, 2007;Wang et al, 2007;Gil-Alana, 2012;Yusof et al, 2013) and found it to be a common characteristic in hydrological data.…”

“…The results show that heteroskedasticity was present in all of the tested time series. Other application of hetereoskedastic models to hydrological data can be seen in (Chen et al, 2008;Laux et al, 2011;Yusof & Kane, 2013).…”