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The SARIMA model-based monthly rainfall forecasting for the Turksvygbult Station at the Magoebaskloof Dam in South Africa

Tadesse Kassahun Birhanu, Dinka Megersa Olumana

Journal of Water and Land Development

2022

no. 53

100--107

Rainfall forecast information is important for the planning and management of water resources and agricultural activities. Turksvygbult rainfall near the Magoebaskloof Dam (South Africa) has never been modelled and forecasted. Hence, the objective of this study was to forecast its monthly rainfall using the SARIMA model. GReTL and automatic XLSTAT software were used for forecasting. The trend of the long-term rainfall time series (TS) was tested by Mann-Kendall and its stationarity was proved by various unit root tests. The TS data from Oct 1976 to Sept 2015 were used for model training and the remaining data (Oct 2015 to Sept 2018) for validation. Then, all TS (Oct 1976 to Sept 2018) were used for out of sample forecasting. Several SARIMA models were identified using correlograms that were derived from seasonally differentiated TS. Model parameters were derived by the maximum likelihood method. Residual correlogram and Ljung–Box Q tests were used to check the forecast accuracy. Based on minimum Akaike information criteria (AI) value of 5642.69, SARIMA (2, 0, 3) (3, 1, 3)12 model was developed using GReTL as the best of all models. SARIMA (1, 0, 1) (3, 1, 3)12, with minimum AI value of 5647.79, was the second-best model among GReTl models. This second model was also the first best automatically selected model by XLSTAT. In conclusion, these two best models can be used by managers for rainfall forecasting and management of water resources and agriculture, and thereby it can contribute to economic growth in the study area. Hence, the developed SARIMA forecasting procedure can be used for forecasting of rainfall and other time series in different areas.

Stationarity against integration in the autoregressive process with polynomial trend

Proïa F.

Probability and Mathematical Statistics

2018

Vol. 38, Fasc. 1

1--26

We tackle the stationarity issue of an autoregressive path with a polynomial trend, and generalize some aspects of the LMC test, the testing procedure of Leybourne and McCabe. First, we show that it is possible to get the asymptotic distribution of the test statistic under the null hypothesis of trend-stationarity as well as under the alternative of nonstationarity for any polynomial trend of order r. Then, we explain the reason why the LMC test, and by extension the KPSS test, does not reject the null hypothesis of trend-stationarity, mistakenly, when the random walk is generated by a unit root located at −1.We also observe it on simulated data and correct the procedure. Finally, we describe some useful stochastic processes that appear in our limiting distributions.