This paper draws its motivation from applications in geophysics, agricultural, and environmental sciences where empirical evidence of slow decay correlations have been found for data observed on a regular lattice. Spatial ARFIMA models represent widely used class spatial analyzing such data. Here, we consider their generalization to conditional autoregressive fractional integrated moving averag...

In this work we present how to model an observed time series by a FOU(p) process. We will show that the processes can be used wide range of varying from short dependence long dependence, with performance similar ARMA or ARFIMA models and in several cases outperforming them. Also, extend theoretical results for any case which Hurst parameter is less than 1/2 theoretically simulations under some ...

In this paper we investigate the commonly used autoregressive filter method of adjusting appraisal-based real estate returns to correct for the perceived biases induced in the appraisal process. Since the early work by Geltner (1989), many papers have been written on this topic but remarkably few have considered the relationship between smoothing at the individual property level and the amount ...

We propose an estimator of change point in the long memory parameter d of an ARFIMA(p, d, q) process using the sup Wald test. We derive the consistency and the rate of convergence of the parameter. The convergence rate of our change point estimator depends on the magnitude of a shift. Furthermore, we obtain the limiting distribution of our change point estimator without depending on the distrib...

We propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility (LMSV) model. The LMSV model is constructed by incorporating an ARFIMA process in a standard stochastic volatility scheme. Strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the Gaussian likelihood. The ...

A major issue in nancial economics is the behaviour of stock returns over long horizons. This study provides empirical evidence of the long-range behaviour of various speculative returns. Using di erent techniques such as R=S and modi ed R=S analysis, detrended uctuation analysis (DFA), fractional di erencing test (GPH) and ARFIMA maximum likelihood estimation, we nd little evidence of long mem...

We develop forecasting methodology for the fractional exponential (FEXP) model. First, we devise algorithms for fast exact computation of the coefficients in the infinite order autoregressive and moving average representations of a FEXP process. We also describe an algorithm to accurately approximate the autocovariances and to simulate realizations of the process. Next, we present a fast freque...

This paper investigates the existence of long memory in the volatility of the Mexican stock market. We use a stochastic volatility (SV) model to derive statistical test for changes in volatility. In this case, estimation is carried out through the Kalman filter (KF) and the improved quasi-maximum likelihood (IQML). We also test for both persistence and long memory by using a long-memory stochas...