講座題目：Threshold Stochastic Unit Root Models
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In this study, we introduce a new class of stochastic unit-root (STUR) processes, where a threshold variable drives the randomness of the autoregressive unit root, thereby allowing us to explain the existence of unit roots. This new model, namely the threshold autoregressive stochastic unit root (TARSUR) process, is strictly stationary, but if we do not consider the threshold effect, it can mislead to conclude that the process has a unit root. The TARSUR models are not only an alternative to fixed unit root models but present interpretation, estimation and testing advantages with respect to the existent STUR models.
This study analyzes the properties of the TARSUR models and proposes two simple tests to identify this type of processes. The first test will allow us to detect the presence of unit roots, which can be fixed or stochastic, and the asymptotic distribution (AD) of this test presents a distribution discontinuity depending if the unit root is fixed or stochastic. The second test we propose is a simple t-statistic (or the supremum of a sequence of t-statistics) for testing the null hypothesis of a fixed unit root versus a stochastic unit root hypothesis. It is shown that its asymptotic distribution (AD) depends if the threshold value is identified under the null hypothesis or not. When the threshold parameter is known, the AD is a standard normal distribution, while in the case of an unknown threshold value, the AD is a functional of Brownian Bridge. A Monte Carlo simulation shows that the proposed tests behave very well in finite sample, and the Dickey-Fuller test cannot easily distinguish between exact unit roots and threshold stochastic unit roots. The study concludes with applications to U.S. stock prices, U.S. house prices, U.S. interest rates, and USD/Pound exchange rates.
Dr.Junyi PengZhou is an Assistant Professor at Dongbei University of Finance and Economics. He held a Ph.D Degree from Universidad Carlos III de Madrid, Spain. His research interests include Econometric Theory, Time Series Modelling, Finance and non-linear process. His current research studies threshold models with unit roots from two different perspectives, an univariate approach by the stochastic unit root models where the randomness of the unit root is driven by other economic variables. On the other hand, from a multivariate perspective by introducing threshold effects in the cointegration relation allowing for the presence of multiple equilibria.