Application of Modified KPSS Test With Fourier Analysis in Stationarity Test of Hydrologic Time Series (Case Study: Lake Urmia Water Level)

Many researches on time series modeling have been carried out without investigation of data series stationarity. If series stationarity and its effective parameters on non-stationarity are ignored, the results will not be accurate and therefore, will lead to error in modeling time series. On the other hand, the decomposition of time series into their components can help to interpret the existing relationships among the hydrologic processes. In the present study, application of the modified KPSS test with the Fourier analysis in stationarity analysis of multiple frequency hydrologic time series was investigated. The Lake Urmia level time series had multiple frequencies. Therefore, data of the Lake Urmia water level in monthly time scale was used as a case study in the period 1965-2008. The trend component was investigated using the Mann-Kendal test and Şen innovative method. The frequency component and stationarity test were studied using the Fourier analysis, traditional KPSS and the modified KPSS with Fourier analysis, respectively. The effect of periodicity on stationarity test was investigated. The results showed that the KPSS test had no ability for detecting the stationarity of the time series while of frequency and non-linear trend exist in data series. Differentiation of time series could not change it to a stationarity one. The Fourier analysis method was used as an alternative method and the results showed that the mentioned method could change the non-stationary time series into the stationarity time series.