Valderio A. Reisen

Some simulations and applications of forecasting long-memory time-series models

In this paper, we show some results of forecasting based on the ARFIMA(p,d,q) and ARIMA(p,d,q) models. We show, by simulation, that the technique of forecasting of the ARIMA(p,d,q) model can also be used when d is fractional, i.e., for the ARFIMA(p,d,q) model. We also conduct a simulation study to compare the two estimators of d obtained through regression methods. They are used in the hypothesis test to decide whether or not the series has long memory property and are compared on the basis of their k-step ahead forecast errors. The properties of long-memory models are also investigated using an actual set of data.

Estimation of seasonal fractionally integrated processes

This paper discusses the estimation of fractionally integrated processes with seasonal components. In order to estimate the fractional parameters, we propose several estimators obtained from the regression of the log-periodogram on different bandwidths selected around and/or between the seasonal frequencies. For comparison purposes, the semi-parametric method introduced in Geweke and Porter-Hudak (1983) and Porter-Hudak (1990) and the maximum-likelihood estimates (ML) are also considered. As indicated by the Monte Carlo simulations, the performance of the estimators proposed is good even for small sample sizes.

Robust Estimation of the Scale and of the Autocovariance Function of Gaussian Short- and Long-Range Dependent Processes

A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an autocovariance estimator which is robust to additive outliers can be very useful for time-series modeling. In this paper, the asymptotic properties of the robust scale and autocovariance estimators proposed by Rousseeuw and Croux (1993) and Genton and Ma (2000) are established for Gaussian processes, with either short-range or long-range dependence. It is shown in the short-range dependence setting that this robust estimator is asymptotically normal at the rate

ESTIMATION OF PARAMETERS IN ARFIMA PROCESSES: A SIMULATION STUDY

\sqrt{n}

Asymptotic properties of U-processes under long-range dependence

, where

Robust estimation of periodic autoregressive processes in the presence of additive outliers

n

A comparison of estimation methods in non-stationary ARFIMA processes

is the number of observations. An explicit expression of the asymptotic variance is also given and compared to the asymptotic variance of the classical autocovariance estimator. In the long-range dependence setting, the limiting distribution displays the same behavior than that of the classical autocovariance estimator, with a Gaussian limit and rate

Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models

\sqrt{n}

Modeling and forecasting daily average PM10 concentrations by a seasonal long-memory model with volatility

when the Hurst parameter

Estimating seasonal long-memory processes: a Monte Carlo study

H