Long memory process in hydrological time series based on three catchments in Malaysia / Norazyani Omar - Omar, Norazyani (2008)
The long memory process in a hydrological time series refers to considerable correlation and dependence between all data in a long time span of observations. Studies of long memory have been attempted in various fields of application such as in financial time series, meteorological time series and hydrological time series. This research is carried out to investigate the presence of long memory process in hydrological time series, and to estimate the parameter d that is the long memory parameter (or fractional differencing parameter), in order to generate the synthetic hydrological time series. The presence of long memory in hydrologic data as detected by Hurst (1951) has enhanced the various estimations and procedures of developing models until today. The presence of long memory process can be characterized in several ways: from autocorrelation structure plots (ACF) and the classical rescaled range (R/S) analysis (also known as the heuristic method); or by statistical tests of long memory such as Lo’s modified R/S Statistic and GPH (Geweke and Porter-Hudak) Test (also known as the statistical method). The long memory parameter d can be estimated by using R/S analysis and Periodogram method. The analysis of long memory process includes detrending, normalization, deseasonalizing of time series and transformation of data. In this study, some fundamental properties of long memory that are present in the hydrological time series are presented and have been applied to the daily streamflow time series using Autoregressive Fractional Integrated Moving Average models (ARFIMA) for the purpose of modelling. The class of ARFIMA models introduced by Granger and Joyeux (1980) and Hosking (1981) provides a convenient model for modelling long-term time series data. The synthetic hydrological time series are then generated by incorporating fractional differencing d. The comparison between the original and synthetic data is made where the statistical characteristics of the series are observed and compared. The streamflow series of Sungai Selangor, Sungai Linggi and Sungai Johor were chosen for the research. Several important aspects of stochasticity are discussed namely, trend analysis, normality, seasonality, autocorrelation and lastly long memory process. From R/S analysis and Periodogram method, the parameter of d obtained are 0.3601, 0.3597, 0.3605 and 0.3983, 0.3753, 0.3157 for each Sungai Selangor, Sungai Linggi and Sungai Johor. The parameter of d obtained is in the range of 0 < d < 0.5 for all streamflow and this shows that the long memory process is present. This statement is supported by the statistical evidence where the test statistics for each streamflow was significant at 1% level of confidence to reject null hypothesis of no long memory. The significance of the existence of long memory in the hydrological time series cannot be neglected. The model of long memory process in hydrology is useful for simulating a synthetic series of observations in order to study water resources management procedures and allows one to plan and test the water resources management with respect to many different hydrological scenarios.