The main purpose of the present study was to investigate the capabilities of two generations of models such as those based on dynamic neural network (e.g., Nonlinear Neural network Auto Regressive or NNAR model) and a regressive (Auto Regressive Fractionally Integrated Moving Average model which...

In this paper the long memory and non-linear properties of share prices in the UK’s Stock Exchange and AIM are explored. The results suggest that the most commonly traded shares exhibit long memory thus raising interesting issues about the validity of normal assumptions of market efficiencies.

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...

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...

We develop an ordinary least squares estimator of the long memory parameter from a fractionally integrated process that is an alternative to the Geweke Porter-Hudak estimator. Using the wavelet transform from a fractionally integrated process, we establish a log-linear relationship between the...

Recently, with the development of financial markets and due to the importance of these markets and their close relationship with other macroeconomic variables, using advanced mathematical models with complicated structures for forecasting these markets has become very popular. Besides, neural...