ASYMPTOTICS FOR GENERAL FRACTIONALLY INTEGRATED PROCESSES WITH APPLICATIONS TO UNIT ROOT TESTS

Qiying Wang · Yan‐Xia Lin · Chandra M. Gulati

66 citations0/0 files storedEconometric Theory

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Complex Systems and Time Series Analysis Monetary Policy and Economic Impact Time Series Analysis and Forecasting

Abstract

In this paper, functional limit theorems for general fractional processes are established under quite weak conditions. The results are then used to derive weak convergence of general nonstationary fractionally integrated processes and to characterize unit root distribution in a model with error being a fractional autoregressive moving average process or a nonstationary fractionally integrated process.The authors thank three referees and an associate editor for their detailed reading of this paper and valuable comments, which have led to this much improved version of the paper.

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References

1979Distribution of the Estimators for Autoregressive Time Series with a Unit Root 1992Testing the null hypothesis of stationarity against the alternative of a unit root 1979Distribution of the Estimators for Autoregressive Time Series With a Unit Root 1968Fractional Brownian Motions, Fractional Noises and Applications 1984Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order 1980AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING 1987Time Series Regression with a Unit Root 1981Fractional Differencing

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2011A simple test of changes in mean in the possible presence of long-range dependence 2015WEAK CONVERGENCE TO STOCHASTIC INTEGRALS FOR ECONOMETRIC APPLICATIONS

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