Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an...

We consider a local Whittle analysis of a stationary fractionally cointegrated model. A two step estimator equivalent to the local Whittle QMLE is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The...

Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d < 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d = 1, the limit distribution is mixed normal. For d > 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.

An exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have...

This paper analyzes the semiparametric estimation of multivariate long-range dependent processes. The class of spectral densities considered is motivated by and includes those of multivariate fractionally integrated processes. The paper establishes the consistency of the multivariate Gaussian...

We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the...

In this paper we specify a multi-factor long-memory process that enables us to estimate the fractional differencing parameters at each frequency separately, and adopt this framework to model quarterly prices in three European countries (France, Italy and the UK). The empirical results suggest...

In this paper we specify a multi-factor long-memory process that enables us to estimate the fractional differencing parameters at each frequency separately, and adopt this framework to model quarterly prices in three European countries (France, Italy and the UK). The empirical results suggest...

This paper investigates the degree of persistence of market fear. Specifically, two different long-memory approaches (R/S analysis with the Hurst exponent method and fractional integration) are used to analyse persistence of the VIX index over the sample period 2004-2016, as well as some...

This paper investigates the degree of persistence of market fear. Specifically, two different long-memory approaches (R/S analysis with the Hurst exponent method and fractional integration) are used to analyse persistence of the VIX index over the sample period 2004-2016, as well as some...