Memory, periodicity and heteroscedasticity in hydrologic time series
Abstract
Three aspects of stochastic analysis and modeling of hydrologic time series are investigated in this study. These are, (1a) behavior of the Hurst exponent when short-term memory is considered, (1b) testing the null hypotheses for detection of long-term memory in annual and monthly hydrologic time series, (2) the identification of periodicities in annual and monthly hydrologic series by using data-driven methods, and (3) the ARCH model to characterize daily streamflow series. Mandelbrot's (1969) and Lo's (1991) versions of the rescaled range statistic are used to investigate the rescaled range characteristics of hydrologic time series. It is shown that, on using the modified rescaled range, the Hurst exponent is close to 0.5 for monthly series, indicating no long-term memory in these series. The short-term memory hypothesis is accepted and the long-term memory hypothesis is not accepted when the modified rescaled range statistic is used. The estimate of the Hurst exponent is robust when it is computed by rescaled range analysis compared to the estimates computed by using the Fractional Gaussian Noise (FGN) model. An empirical investigation of periodicities in hydrologic time series is carried out by using the Singular Spectral Analysis (SSA). The Multi-Taper Method (MTM) is used to test the statistical significance of periodicities. In the present study, very few significant periodicities were found by MTM and only weak periodicities which explain a small fraction of the variance of the series are identified. There is no consistency in the periodicities identified in the series located in the same geographical area. Coherence between PDSI and temperature and precipitation indicates that precipitation is a stronger indicator of droughts. Coherence between streamflow and precipitation is dependent on the proximity of the stations under consideration. Heteroskedasticity is identified in daily streamflow data using an ARCH model and a test suggested by Engle (1982). The variance of the residuals from the autoregressive-moving average models fitted to the log transformed daily flow series and its first difference shows variability.
Degree
Ph.D.
Advisors
Rao, Purdue University.
Subject Area
Civil engineering|Atmosphere|Statistics|Hydrology
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