Annual streamflow modelling with asymmetric distribution function

Abstract

Abstract:Classical autoregressive models (AR) have been used for forecasting streamflow data in spite of restrictive assumptions, such as the normality assumption for innovations. The main reason for making this assumption is the difficulties faced in finding model parameters for non-normal distribution functions. However, the modified maximum likelihood (MML) procedure used for estimating autoregressive model parameters assumes a non-normally distributed residual series. The aim in this study is to compare the performance of the AR(1) model with asymmetric innovations with that of the classical autoregressive model for hydrological annual data. The models considered are applied to annual streamflow data obtained from two streamflow gauging stations in Kızılırmak Basin, Turkey.

Disaggregation of Annual to daily Streamflows: A linear deterministic method

“…Station EIE 1501, located at the upstream of the dams was used as a reference to obtain the natural streamflow values (unaffected form) of the station by obtaining the correlation coefficient between observed data of these stations before the construction of the dams.The second selected pair of streamflow gauge stations, Sefaatli (EIE1517) and Cadirhoyuk (EIE 1541), are located at the biggest tributary (Delice river) of the main river. No diversions are constructed at the upstream of these stations, [17]. The detailed information, including latitude, longitude, elevation and observation period, are listed in Table 1.…”

Predictor Selection for Positive Autoregressive Processes

“…Over the past few decades, modeling and estimation for positive-valued time series have attracted great interest in fields such as reliability theory, economics, finance, hydrology and meteorology; see, e.g., Gaver and Lewis (1980), Lawrance and Lewis (1985), Bell and Smith (1986), Sim (1987), Lewis, Mckenzie and Hugus (1989), Hutton (1990), Barndorff-Nielsen and Shephard (2001), Nielsen and Shephard (2003) and Sarlak (2008). Among the many positive-valued time series models proposed in the literature, the stationary positive AR(1) model,…”

“…Model (1) has also found extensive applications in hydrological studies. For example, Bell and Smith (1986) analyzed two sets of pollution data from the Willamette River, Oregon, using model (1) with different positive errors, and Sarlak (2008) analyzed the annual streamflow data from Kizilirmak River, Turkey, showing that model…”

Nearly Unstable Processes: A Prediction Perspective

“…Model (1.1) with ε t satisfying (1.2) has found broad applications in hydrology, economics, finance, epidemiology and quality control; see, among others, Gaver and Lewis (1980), Bell and Smith (1986), Lawrance and Lewis (1985), Davis and McCormick (1989), Smith (1994), Barndorff-Nielsen and Shephard (2001), Nielsen and Shephard (2003), Sarlak (2008) and Ing and Yang (2014). In particular, Bell and Smith (1986) analyzed two sets of pollution data from the Willamette River, Oregon, using model (1.1) with ε t following the uniform distribution or exponential distribution; both are special cases of (1.2).…”

“…In addition, Sarlak (2008) adopted model (1.1) with a Weibull error to analyze the annual streamflow data from the Kizilirmak River in Turkey. On the other hand, model (1.1), focusing exclusively on the stationary case 0 ≤ ρ < 1, fails to accommodate data that may fluctuate around an upward trend with variance increasing over time.…”