Threshold Autoregression with a Near Unit Root PDF Download
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Author: Mehmet Caner
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
Author: Mehmet Caner
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
Author: Mehmet Caner
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Myunghwan Seo
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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Book Description
There is a growing literature on unit root testing in threshold autoregressive models. This paper makes two contributions to the literature. First, an asymptotic theory is developed for unit root testing in a threshold autoregression, in which the errors are allowed to be dependent and heterogeneous, and the lagged level of the dependent variable is employed as the threshold variable. The asymptotic distribution of the proposed Wald test is non-standard and depends on nuisance parameters. Second, the consistency of the proposed residual-based block bootstrap is established based on a newly developed asymptotic theory for this bootstrap. It is demonstrated by a set of Monte Carlo simulations that the Wald test exhibits considerable power gains over the ADF test that neglects threshold effects. The law of one price hypothesis is investigated among used car markets in the US.
Author: Jiti Gao
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ISBN:
Category :
Languages : en
Pages : 0
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This paper treats estimation in a class of new nonlinear threshold autoregressive models with both a stationary and a unit root regime. Existing literature on nonstationary threshold models have basically focused on models where the nonstationarity can be removed by differencing and/or where the threshold variable is stationary. This is not the case for the process we consider, and nonstandard estimation problems are the result. This paper proposes a parameter estimation method for such nonlinear threshold autoregressive models using the theory of null recurrent Markov chains. Under certain assumptions, we show that the ordinary least squares (OLS) estimators of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary regime can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary regime has a nonstandard asymptotic distribution. In the limit, the rate of convergence in the stationary regime is much slower than that in the nonstationary regime. The proposed theory and estimation method are illustrated by both simulated and real data examples.
Author: Frederique Bec
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ISBN:
Category :
Languages : en
Pages : 0
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This paper proposes SupWald tests from a threshold autoregressive model computed with an adaptive set of thresholds. Simple examples of adaptive threshold sets are given. A second contribution of the paper is a general asymptotic null limit theory when the threshold variable is a level variable. We obtain a pivotal null limiting distribution under some simple conditions for bounded or asymptotically unbounded thresholds. Our general approach is flexible enough to allow a choice of the auxiliary threshold model or of the threshold set involved in the test specifically designed for nonlinear stationary alternatives relevant for macroeconomic and financial topics involving arbitrage in presence of transaction costs. A Monte-Carlo study and an application to the interest rates spread for French, German, New-Zealander and US post-1980 monthly data illustrate the ability of the adaptive SupWald tests to reject unit-root when the ADF does not.
Author: George Kapetanios
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ISBN:
Category :
Languages : en
Pages : 0
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This paper proposes a simple direct testing procedure to distinguish a linear unit root process from a globally stationary three-regime self-exciting threshold autoregressive process. We derive the asymptotic null distribution of the Wald statistic, and show that it does not depend on unknown fixed threshold values. Monte Carlo evidence clearly indicates that the exponential average of the Wald statistic is more powerful than the Dickey-Fuller test that ignores the threshold nature under the alternative.
Author: Jean-Yves Pitarakis
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Category :
Languages : en
Pages :
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Author: Frederique Bec
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Category :
Languages : en
Pages : 0
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We consider modeling the real exchange rate by a stationary three-regime self-exciting threshold autoregressive (SETAR) model with possibly a unit root in the middle regime. This representation is consistent with purchasing power parity in the presence of trading costs. Our main contribution is to provide statistical tools for testing unit root versus a SETAR. First, we show that a SETAR with a unit root in the middle regime is stationary and mixing under reasonable assumptions. Second, we derive analytically the asymptotic distribution of our unit-root test under the null. Using monthly real exchange rate data, our test rejects the null of unit-root against a threshold process for five European series.
Author: Penelope A. Smith
Publisher:
ISBN: 9780734032218
Category : Mathematical statistics
Languages : en
Pages : 37
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Author: Jiti Gao
Publisher:
ISBN:
Category : Autoregression (Statistics)
Languages : en
Pages :
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Book Description
This paper proposes a class of new nonlinear threshold autoregressive models with both stationary and nonstationary regimes. Existing literature basically focuses on testing for a unit-root structure in a threshold autoregressive model. Under the null hypothesis, the model reduces to a simple random walk. Parameter estimation then becomes standard under the null hypothesis. How to estimate parameters involved in an alternative nonstationary model, when the null hypothesis is not true, becomes a nonstandard estimation problem. This is mainly because models under such an alternative are normally null recurrent Markov chains. This paper thus proposes to establish a parameter estimation method for such nonlinear threshold autoregressive models with null recurrent structure. Under certain assumptions, we show that the ordinary least squares (OLS) estimates of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary regime can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary regime has a nonstandard asymptotic distribution. In the limit, the rate of convergence in the stationary regime is n-1 = 4, whereas it is n-1 in the nonstationary regime. The proposed theory and estimation method is illustrated by both simulated and real data examples.
