## Internal Stochastic Structure of Annual Discharge Time Series of Serbia’s Large Rivers - page 4

Results and Discussion

When time series are assessed, one of the questions that arises is whether the analyzed process is stationary. If the typical parameters of a time series (e.g. mathematical expectation, variance, probability density, etc.) do not change over time, then the time series is stationary. If they do, the time series is non-stationary. In the present research, the time series of annual discharges were subjected to a stationarity analysis with regard to the average value of the time series, i.e. first-order stationarity (Fig. 2).

Figure 2: Stationarity test of annual discharge time series based on average values:*Q* – average discharges, *m _{5}(Q), m_{15}(Q), m_{30}(Q)* – moving averages of annual discharges.

Moving averages *m(Q)* were defined for window widths of 5, 15 and 30 time steps. They exhibited a periodic nature and also demonstrated a trend in some of the time series (Fig. 2). The conclusion was that the time series of annual discharges were non-stationary.

The nonparametric Mann-Kendall test, via test statistic *Z _{s}*, was applied to assess the trend of the time series of average annual discharges. This trend test showed that a downward trend was registered at the stations of Bogojevo, Sremska Mitrovica, Lubičevski Most and Orsova, and that there was an upward trend at Senta. However, the annual discharge trends were not significant for the adopted confidence threshold of

*α*=0.05, so the alternative hypothesis

*H*was adopted (Table 2). When the variance of the time series was corrected, the test statistic

_{1}*Z*was obtained, showing a reduced trend intensity for the given time series.

_{S1}

Table 2: Results of Mann-Kendall's test of annual discharges