Purchasing power parity (PPP) is one of the most important, but empirically controversial theories in international macroeconomics. Although many researchers believe that some variant of PPP holds in the long run, there are diverse empirical results regarding the PPP hypothesis. We examine the...

This paper proposes two simple tests that are based on certain time domain properties of I(d) processes. First, if a time series follows an I(d) process, then each subsample of the time series also follows an I(d) process with the same value of d. Second, if a time series follows an I(d)...

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...

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...

This paper proposes two simple tests that are based on certain time domain properties of I(d) processes. First, if a time series follows an I(d) process, then each subsample of the time series also follows an I(d) process with the same value of d. Second, if a time series follows an I(d)...

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...

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.

A regime dependent VAR model is suggested that allows long memory (fractional integration) in each of the observed regime states as well as the possibility of fractional cointegration. The model is motivated by the dynamics of electricity prices where the transmission of power is subject to...

In this paper we compare through Monte Carlo simulations the finite sample properties of estimators of the fractional differencing parameter, d. This involves frequency domain, time domain, and wavelet based approaches and we consider both parametric and semiparametric estimation methods. The...

This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing Breitung's (2002) test as the special case d=1. It is shown that (i) each member of the family with d0 is consistent, (ii) the asymptotic distribution depends on d, and thus reflects...