This study is an attempt to review the theory and applications of autoregressive fractionally integrated moving average (ARFIMA) and fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) models, mainly for the purpose of the description of the observed...

The design of models for time series forecasting has found a solid foundation on statistics and mathematics. On this basis, in recent years, using intelligence-based techniques for forecasting has proved to be extremely successful and also is an appropriate choice as approximators to model and...

This paper advances a new analysis technology path of estimation and test for long memory time series. I propose the definitions of time scale series, strong variance scale exponent and weak variance scale exponent, and prove the strict mathematical equations that strong and weak variance scale...

The spurious regression phenomenon in Least Squares occurs for a wide range of Data Generating Processes, such as driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity. Indeed, spurious regressions have played a fundamental role in the building of modern...

The exponential model for the spectrum of a time series and its fractional extensions are based on the Fourier series expansion of the logarithm of the spectral density. The coefficients of the expansion form the cepstrum of the time series. After deriving the cepstrum of important classes of...

This research investigates the presence of structural breaks in the indices of the Egyptian stock market using the Bai-Perron strcutural breaks test. The indices used are the EGX 30, the EGX 70, the EGX 100, and the EGX 20. The presence of long memory is then investigated using the GPH test and...

This article examines the PPP hypothesis, i.e. the proposition that the real exchange rates are stationary, in the case of Europe. For that purpose, we study the statistical properties of 14 European bilateral real exchange rates against the Deutschmark, over the periods snake and EMS. These...

This paper examines persistence in the Ukrainian stock market during the recent financial crisis. Using two different long memory approaches (R/S analysis and fractional integration) we show that this market is inefficient and the degree of persistence is not the same in different stages of the...

The design of models for time series forecasting has found a solid foundation on statistics and mathematics. On this basis, in recent years, using intelligence-based techniques for forecasting has proved to be extremely successful and also is an appropriate choice as approximators to model and...

This study aims to introduce an ideal model for forecasting crude oil price volatility. For this purpose, the ‘predictability’ hypothesis was tested using the variance ratio test, BDS test and the chaos analysis. Structural analyses were also carried out to identify possible nonlinear...