The application of correlation function in forecasting stochastic processes

Abstract

One of the most important applications of the correlation function is establishing a prediction model for stochastic process. Stationary property makes predicting the stochastic process entirely possible based on the correlation function. This predictive model is interested in cases, where the observation data are assumed to have no measurement errors. We provided some processing to make the forecasting model usable. It is proposed to calculate the value of the standardized correlation function in accordance with the actual observed sample and to estimate the necessary values of averaged correlation function that they cannot be calculated from the sample. We replaced the unknown values by their estimates, which we found using one of the predictive tools suitable for the time series. Theoretically, for the stationary stochastic processes, the correlation function and the standardized correlation function depend only on the time distance between two sections, without depending on the specific time value of each section. However, in this application, when we consider an observation process to be a stationary stochastic process, it means that we have approximated this observation process with a stationary stochastic process. Therefore, when calculating for a specific observation sample, the values of the sample correlation function and the sample standardized correlation function between two sections can fluctuate according to time values of each section, although time distance between two sections unchanged. The sample standardized correlation function of a section has been computed as the arithmetic mean of all values of the sample standardized correlation function between two sections. In this article, the prediction model is linear interpolation and extrapolation model and it is obtained by least squares method. The task for application of this model is to give the highest indexes of daily average temperature in July during last three years 2017-2019 in some localities in northern Vietnam using this forecasting model. The data has been compiled from the data source of the General Department of Meteorology and Hydrology of Vietnam. For processes occurring in the atmosphere and hydrosphere, their hypothesis of stationarity is relatively well satisfied in a time and distance that is not very large. Because of that, we selected the aforementioned data set to apply to the forecasting model. The calculation results are obtained by Matlab software.