| Abstract [eng] |
A time series is a collection of observations made sequentially in time. Forecasting the future values of an observed time series is an important problem in many areas, including economics, production planning, sales, weather forecasting, stock control and etc. A wide variety of different forecast procedures are available and it’s significant to realize that no single method is universally applicable. Rather the analyst must choose the procedure which is most appropriate for a given set of conditions. In this research paper were used household costs data of three major cities of Lithuania: Vilnius, Kaunas, Klaipėda. Various models were fitted to them: seasonal additive and multiplicative time series models, ARIMA – autoregressive integrated moving average process. In our case, every time series of household costs data was non-stationary, so we used simple and seasonally differentiation of time series for ARIMA models. To estimate the precision and correctness of each model there was calculated MAPE - the mean absolute percentage error. Off course, all forecasting models were checked if they really provide an adequate description of data. Generalized Autoregressive Conditional Heteroskedasticity models (GARCH) was fitted to volatility of residuals. In conclusion, the results have shown, that the most precise forecasting method for Vilnius data is ARIMA(5,1,4) time series model with ARCH(1) process for residuals, for Kaunas data - seasonal multiplicative time series model with AR(2) process for residuals and for Klaipėda - seasonal multiplicative time series model with AR(1) process for residuals. As it is common for ARIMA models, good predictions are gained for short – time forecasting and for those periods, which had more observations. |
