Unit Root Vector Autoregression with Volatility Induced Stationarity

Unit Root Quantile Autoregression Inference

We study statistical inference in quantile autoregression models when the largest autoregressive coefficient may be unity. The limiting distribution of a quantile autoregression estimator and its t-statistic is derived. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a linear combination of the Dickey-Fuller distribution and the standard normal, with the weig...

Unit Root Testing with Unstable Volatility

It is known that unit root test statistics may not have the usual asymptotic properties when the variance of innovations is unstable. In particular, persistent changes in volatility can cause the size of unit root tests to differ from the nominal level. In this paper we propose a class of modified unit root test statistics that are robust to the presence of unstable volatility. The modification...

Uniform Asymptotic Normality in Stationary and Unit Root Autoregression

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable ...

Testing for a Unit Root with Near-Integrated Volatility

This paper considers tests for a unit root when the innovations follow a near-integrated GARCH process. We compare the asymptotic properties of the likelihood ratio statistic with that of the leastsquares based Dickey-Fuller statistic. We first use asymptotics where the GARCH variance process is stationary with fixed parameters, and then consider parameter sequences such that the GARCH process ...

Lecture 6 : Vector Autoregression ∗