| Abstract [eng] |
On the ground of previous works and ideas a new class of models which describe long memory periodic behaviour in a time varying volatility of financial returns is introduced. Generalised periodic long-memory filters, based on Gegenbauer polynomials, are included into volatility equation of LARCH model and capture long memory periodic behaviour of the data. Thus, a new type of model called h-factor Gegenbauer-LARCH is presented. Moreover, a covariance stationarity condition is checked for one factor Gegenbauer-LARCH model. Also, generated processes are demonstrated. Furthermore, h-factor Gegenbauer-LARCH model is applied to Euro-Dollar hourly exchange rate returns. Identified model is estimated by means of LUDE algorithm which maximizes maximum likelihood function. The adequasy of the model is checked by reviewing residuals behaviour. Concerning empirical results the following conclusion is drawn: • Although model captures specific characteristics of the data such as slowly decaying periodic behaviour of autocorrelation function and pronounced peaks in periodogram but residuals analysis shows that model should be improved. Bordignon, Caporin, Lisi suggest that all possible frequencies were included to the model because higher frequencies might not be obvious from autocorrelation function or periodogram. However, we face computer capability problem. As a matter of fact, we cannot estimate a more complex model. Inclusion of autoregresive coefficients into the model did not provide better results. Finally, h-factor Gegenbauer-LARCH model should be interesting for practicians, however either theoretical characteristics and practical application possibilities should be investigated further. |
