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Since the pension system reform in Poland, carried out in 1999, the open pension funds (OPFs) are in operation. They are forming the second pillar of the system and realize capital pension insurances. The main aim of pension funds activity is accumulation and investing contributions paying by the employees. The measure which indicates the growth of pension funds assets made by investments is an accounting unit. The paper presents the forecasting model for the accounting unit and the comparison of the accuracy of the forecasts estimated with use of it and two different methods: exponential smoothing methods and trend models. The proposed model (a mathematical expression is given), is referred to as the model of time series with the linear combination of increases because the forecast is the sum of the last observation and the combination of a number of last increases. The parameters are estimated with use of the criterion of the minimal middle ex post error. The accuracy of the forecasts of the accounting unit value, estimated with use of the model of time series with the linear combination of increases, is significantly higher than in case of the forecasts estimated with use of the exponential smoothing model and trend model. The assessment of the possible more universal application of proposed model to forecasting time series requires its testing on different variables which is the subject of authors investigations.
XX
In the article we first introduce asymmetric response of equity volatility to return shock and then the effect of good and bad news to volatility for empirical time series of EUR/USD (EUR currency against US dollar) exchange rates in the pre-crisis period, during the crisis and the post-crisis period. We found that GARCH-class models with normal errors are not capable to capture fully the leptokurtosis in empirical time series, while Student´s t and GED errors provide better description for the conditional volatility. Then, we alternatively develop forecasting models based on the ARIMA/GARCH methodology and on the neural approach. In the direct comparison between statistical and neural models, the experiment shows that the neural approach clearly improve the forecast accuracy.
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