Wykorzystanie metody moving block bootstrap w prognozowaniu szeregów czasowych z wahaniami okresowymi

The aim of the analysis of the time series is, among others, to facilitate the formulation of prognosis. The basis for the inference of the future variables are their future realizations. There are various methods used in time series forecasting, such as for example naïve method, Holt-Winters models, ARIMA models and various simulation methods. One of the most popular and widely used simulation method in statistical research is the bootstrap method proposed by B. Efron. It is usually applied in measuring the estimates of the variance and testing the hypotheses in cases when the distribution of the test statistic is unknown. This method does not require for the selected samples to be from the standard normal distribution population. Due to the construction of the random samples in this method, there is usually no possibility to directly apply it in the analysis of the periodic time series. In the literature written on this subject, there are the proposals to introduce some modifications to the bootstrap method that would provide the possibility to conduct such analyses. One of such methods is the moving block bootstrap. In the present essay, we will present the proposal to apply this method to create the confidential intervals for the periodic time series forecasts. The results gathered by applying that method are compared with the results obtained via the classic construction of the confidential intervals for the forecasts and on the confidential intervals based on ARIMA models.