Short memory or long memory: an empirical survey of daily rainfall data

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 semi parametric contexts proposed by Geweke and Porter-Hudak to analyze 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 with F-statistic for the break date were applied, break dates were detected in all data sets. The data sets were partitioned according to their respective break date and further test for long memory was applied for all subseries. Results show that all subseries follows the same pattern with the original series. The estimate of the fractional parameters d1 and d2 on the subseries obtained by splitting the original series at the break-date, confirms that there is a long memory in the DGP. Therefore this evidence shows a true long memory not due to structural break.