REGIME-SWITCHING AUTOREGRESSIVE COEFFICIENTS AND THE ASYMPTOTICS FOR UNIT ROOT TESTS

2008 ◽  
Vol 24 (4) ◽  
pp. 1137-1148
Author(s):  
Giuseppe Cavaliere ◽  
Iliyan Georgiev
Keyword(s):  
Sample Size ◽  
Unit Root ◽  
Regime Switching ◽  
Asymptotic Theory ◽  
Unit Roots ◽  
Stationary Regime ◽  
Unit Root Tests ◽  
Asymptotic Results ◽  
Switching Models ◽  
Root Model

Most of the asymptotic results for Markov regime-switching models with possible unit roots are based on specifications implying that the number of regime switches grows to infinity as the sample size increases. Conversely, in this note we derive some new asymptotic results for the case of Markov regime switches that are infrequent in the sense that their number is bounded in probability, even asymptotically. This is achieved by (inversely) relating the probability of regime switching to the sample size. The proposed asymptotic theory is applied to a well-known stochastic unit root model, where the dynamics of the observed variable switches between a unit root regime and a stationary regime.

LSTUR regression theory and the instability of the sample correlation coefficient between financial return indices

2020 ◽  
Author(s):  
Tim Ginker ◽  
Offer Lieberman
Keyword(s):  
Correlation Coefficient ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Financial Return ◽  
Spurious Regression ◽  
Root Model ◽  
Sampling Window ◽  
Sample Correlation ◽  
Underlying Processes ◽  
Regression Theory

Summary It is well known that the sample correlation coefficient between many financial return indices exhibits substantial variation on any reasonable sampling window. This stylised fact contradicts a unit root model for the underlying processes in levels, as the statistic converges in probability to a constant under this modeling scheme. In this paper, we establish asymptotic theory for regression in local stochastic unit root (LSTUR) variables. An empirical application reveals that the new theory explains very well the instability, in both sign and scale, of the sample correlation coefficient between gold, oil, and stock return price indices. In addition, we establish spurious regression theory for LSTUR variables, which generalises the results known hitherto, as well as a theory for balanced regression in this setting.

scholarly journals ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS

2012 ◽  
Vol 28 (5) ◽  
pp. 1121-1143 ◽  
Author(s):  
Tomás del Barrio Castro ◽  
Denise R. Osborn ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Linear Process ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
Martingale Difference ◽  
Linear Processes ◽  
Seasonal Unit Roots ◽  
Null Distributions ◽  
Augmented Dickey Fuller

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.

scholarly journals Spurious Regression

2009 ◽  
Vol 2009 ◽  
pp. 1-27 ◽  
Author(s):  
D. Ventosa-Santaulària
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Long Memory ◽  
Unit Roots ◽  
Unit Root Tests ◽  
Modern Time ◽  
Spurious Regression ◽  
Time Series Econometrics ◽  
Wide Range ◽  
Applied Macroeconomics

The spurious regression phenomenon in least squares occurs for a wide range of data generating processes, such as driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity. Indeed, spurious regressions have played a fundamental role in the building of modern time series econometrics and have revolutionized many of the procedures used in applied macroeconomics. Spin-offs from this research range from unit-root tests to cointegration and error-correction models. This paper provides an overview of results about spurious regression, pulled from disperse sources, and explains their implications.

Regime-switching purchasing power parity in Latin America: Monte Carlo unit root tests with dynamic conditional score

2016 ◽  
Vol 48 (29) ◽  
pp. 2675-2696
Author(s):  
Astrid Ayala ◽  
Szabolcs Blazsek ◽  
Juncal Cuñado ◽  
Luis Albériko Gil-Alana
Keyword(s):  
Monte Carlo ◽  
Latin America ◽  
Purchasing Power Parity ◽  
Unit Root ◽  
Regime Switching ◽  
Unit Root Tests ◽  
Purchasing Power ◽  
Power Parity

Testing for Unit Roots in Models with Structural Change

1994 ◽  
Vol 10 (5) ◽  
pp. 917-936 ◽  
Author(s):  
Joon Y. Park ◽  
Jaewhan Sung
Keyword(s):  
Structural Change ◽  
Least Squares ◽  
Unit Root ◽  
Unit Roots ◽  
Generalized Least Squares ◽  
Testing Procedure ◽  
Unit Root Tests ◽  
Limiting Distributions ◽  
Independent Unit ◽  
Unit Root Models

This paper considers the unit root tests in models with structural change. Particular attention is given to their dependency on the limiting ratios of the subsample sizes between breaks. The dependency is analyzed in detail, and the invariant testing procedure based on a transformed model is developed. The required transformation is essentially identical to the generalized least-squares correction for heteroskedasticity. The limiting distributions of the new tests do not depend on the relative sizes of the subsamples and are shown to be simple mixtures of the limiting distributions of the corresponding tests from the independent unit root models without structural change.

scholarly journals Markov Regime-Switching and Unit Root Tests

2000 ◽  
Vol 2000 (683) ◽  
pp. 1-31 ◽  
Author(s):  
Jeremy Max Piger ◽  
◽  
Eric Zivot ◽  
Charles Nelson
Keyword(s):  
Unit Root ◽  
Regime Switching ◽  
Unit Root Tests ◽  
Markov Regime Switching

Unit Root Tests of Structural Break with GARCH-Error Process

2012 ◽  
Vol 452-453 ◽  
pp. 986-990
Author(s):  
Jing Yong Wang ◽  
Li Da Xue
Keyword(s):  
Sample Size ◽  
Unit Root ◽  
Structural Breaks ◽  
Structural Break ◽  
Unit Roots ◽  
Test Statistic ◽  
Test Power ◽  
Nominal Size ◽  
Parameter Test ◽  
Garch Process

This paper studies the effect of GARCH process on the robustness and reliabilities of unit roots test with structural breaks. It gives that, as the GARCH process approaches integratedness, the test statistic’ the proportion of rejections reported actually increases as the sample size increases. Consequently, we can see that the standard asymptotic theory is inapplicable in this case. The statistic , their actual test size on the whole is accordant to nominal size in unit root and no break as the volatility parameter is small, =0 or approach to 0. The statistic exists a serious over sizing of null hypothesis as integratedness in all structural break type. The statistic test power increases as the sample size increases, but test power do not increases as the sample size increase under AR parameter. Test power increases as integratedness increases, and decreases as volatility parameter increases.

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