In this article, a special type of orthogonalization is obtained to construct a multiple input transfer function model. By using this technique, construction of a transfer function model is divided to sequential construction of transfer function models with less input time series. Furthermore, based on real and simulated time series we provide an instruction to adequately perform the stages of ...

Overview In contrast to the classical linear regression model, in which the components of the dependent variable vector y are not identically distributed (because its mean vector varies with the regressors) but may be independently distributed, time series models have dependent variables which may be identically distributed, but are typically not independent across ovbservations. Such models ar...

Overview In contrast to the classical linear regression model, in which the components of the dependent variable vector y are not identically distributed (because its mean vector varies with the regressors) but may be independently distributed, time series models have dependent variables which may be identically distributed, but are typically not independent across ovbservations. Such models ar...

For a long time the most frequently used models in time series analysis were the AR, MA and ARMA processes. Their spectral densities are continuous and therefore bounded functions on [ — n, it]. If the periodogram of real data reached significantly high values, it was considered as an indication of the trend or of a periodic component. The bias arising after trend removal in the spectral densit...

Well-known Box-Jenkins Autoregressive integrated moving average (ARIMA) methodology has virtually dominated analysis of time-series data since 1930s. However, it is applicable to only those data that are either stationary or can be made so. Another limitation is that the resultant model is “Linear”. During the last two decades or so, the area of “Nonlinear time-series” is rapidly growing. Here,...

Three types of residuals in time series models (namely ”conditional residuals”, ”unconditional residuals” and ”innovations”) are considered with regard to (i) their precise definitions, (ii) their computation after model estimation, (iii) their approximate distributions in ?nite samples, and (iv) potential applications of their properties in model diagnostic checking. Both partially-known and n...

In this paper the class of BL-GARCH (Bilinear General AutoregRessive Conditional Heteroskedasticity) models is introduced. The proposed model is a modification to the BL-GARCH model proposed by Storti and Vitale (2003). Stationary conditions and autocorrelation structure for special cases of these new models are derived. Maximum likelihood estimation of the model is also considered. Some simula...

in this paper, we propose a new residual analysis method using fourier series transform into fuzzy time series model for improving the forecasting performance. this hybrid model takes advantage of the high predictable power of fuzzy time series model and fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...