Conditional Heteroscedasticity in Streamflow Process: Paradox or Reality?

Abstract

The various physical mechanisms governing the dynamics of streamflow processes act on a seemingly wide range of temporal and spatial scales; almost all the mechanisms involved present some degree of nonlinearity. Against the backdrop of these issues, in this paper, attempt was made to critically look at the subject of Autoregressive Conditional Heteroscedasticity (ARCH) or volatility of streamflow processes, a form of nonlinear phenomena. Towards this end, streamflow data (both daily and monthly) of the River Benue, Nigeria were used for the study. Results obtained from the analyses indicate that the existence of conditional heteroscedasticity in streamflow processes is no paradox. Too, ARCH effect is caused by seasonal variation in the variance for monthly flows and could partly explain same in the daily streamflow. It was also evident that the traditional seasonal Autoregressive Moving Average (ARMA) models are inadequate in describing ARCH effect in daily streamflow process though, robust for monthly streamflow; and can be removed if proper deseasonalisation pre-processing was done. Considering the findings, the potential for a hybrid Autoregressive Moving Average (ARMA) and Generalised Autoregressive Conditional Heteroscedasticity (GARCH)type models should be further explored and probably embraced for modelling daily streamflow regime in view of the relevance of statistical modelling in hydrology

Hybrid Forecasting of Daily River Discharges Considering Autoregressive Heteroscedasticity

“…Elek and Márkus (2008) analysed a conditionally heteroscedastic GARCH-type model, which is different from the more commonly used autoregressive moving average-generalized autoregressive conditionally heteroscedastic (ARMA-GARCH) processes, with a daily water discharge series observed along the Rivers Danube and Tisza in Hungary. Otache et al, (2012) used streamflow data (both daily and monthly) of the River Benue, Nigeria, to critically look at the subject of Autoregressive Conditional Heteroscedasticity (ARCH) and the volatility of streamflow processes. Modarres and Ouarda (2013) studied the advantages of a GARCH model against a linear ARIMA model by investigating three classes of the GARCH approach, namely the Power GARCH, Threshold GARCH and Exponential GARCH models, which use daily streamflow time series of the Matapedia River, Quebec, Canada.…”

Understanding the Impact of Observation Data Uncertainty on Probabilistic Streamflow Forecasts Using a Dynamic Hierarchical Model

“…In reality, the measurement error variance is often reported or assumed to be heteroscedastic; that is, the measurement error variance changes with time. Further, the measurement error variance could also change depending on the season (season-variant), it could be correlated with the previous measurement error variances, and the correlation among the measurement error variances becomes stronger as the number of measurements in a day (or within a 10.1029/2019WR025463 time-window) increases (Otache et al, 2012;Sorooshian & Dracup, 1980). Since our objective was to evaluate the performance of the BDHM, with a basic set of parameters and predictors as inputs to the model, we did not consider a time-variant measurement error during the model validation.…”

“…Water Resources Research DAS BHOWMIK ET AL. time-window) increases (Otache et al, 2012;Sorooshian & Dracup, 1980). Since our objective was to evaluate the performance of the BDHM, with a basic set of parameters and predictors as inputs to the model, we did not consider a time-variant measurement error during the model validation.…”