The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic...

This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional Gaussian noise (FGN) with the Hurst parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="E2-0001.gif" display="inline"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math>. It is shown that the estimator is consistent for all...

The authors propose a family of tests for stationarity against a local unit root. It builds on the Karhunen–Loève (KL) expansions of the limiting CUSUM process under the null hypothesis and a local alternative. The variance ratio type statistic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="E3-0001.gif" display="inline"> <mml:mrow> <mml:mi mathvariant="script">V</mml:mi> <mml:msub> <mml:mi mathvariant="script">R</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:mrow> </mml:math>is a ratio of quadratic forms of q...

In this study, the authors investigate methods of sequential analysis to test prospectively for the existence of a unit root against stationary or explosive states in a p-th order autoregressive (AR) process monitored over time. Our sequential sampling schemes use stopping times based on the...

Joon Y. Park is one of the pioneers in developing nonlinear cointegrating regression. Since his initial work with Phillips (Park & Phillips, 2001) in the area, the past two decades have witnessed a surge of interest in modeling nonlinear nonstationarity in macroeconomic and financial time...

This chapter proposes a test for a parametric specification of the autoregressive function of a given stationary autoregressive time series. This test is based on the integrated square difference between the empirical distribution function estimate and a convolution-type distribution function...

This chapter develops an asymptotic theory for a general transformation model with a time trend, stationary regressors, and unit root nonstationary regressors. This model extends that of Han (1987) to incorporate time trend and nonstationary regressors. When the transformation is specified as an...

The authors derive a risk lower bound in estimating the threshold parameter without knowing whether the threshold regression model is continuous or not. The bound goes to zero as the sample size n grows only at the cube-root rate. Motivated by this finding, the authors develop a continuity test...

The authors propose a semiparametric approach for testing independence between two infinite-order cointegrated vector autoregressive series (IVAR(∞)). The procedures considered can be viewed as extensions of classical methods proposed by Haugh (1976, JASA ) and Hong (1996b, Biometrika ) for...

It is widely documented that while contemporaneous spot and forward financial prices trace each other extremely closely, their difference is often highly persistent and the conventional cointegration tests may suggest lack of cointegration. This chapter studies the possibility of having...