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Pdf Unit Roots And Cointegrating Matrix Estimation Using Subspace Meth

Leo Migdal
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pdf unit roots and cointegrating matrix estimation using subspace meth

Academia.edu no longer supports Internet Explorer. To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. We propose a new procedure to detect unit roots based on subspace methods. It has three main original features. First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, which loss functions can be adapted to the statistical properties of the data.

Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties. An example illustrates its application to real time series. By pointing out the spurious regression problem, Granger and Newbold~1974! have shown the importance of stochastic trends in time series data in the context of linear regression models+ At the time, removing trends by differencing was already common practice in univariate time series modeling...

unit roots and motivated the development of statistical procedures for their detection+ Dickey and Fuller~1979! and Fuller~1976! were pioneers in developing tests for unit roots that became widely used+ The foundation of asymptotic theory for regressions involving stochastic trends was led by Phillips~1986, 1987! with the introduction of the functional limit theory, weak convergence methods, convergence to stochastic integrals, nonparametric unit root testing, and continuous record asymptotics+ Phillips and Durlauf~1986! extended some of these results to the multivariate setting by presenting the multivariate invariance principles and the asymptotic theory of multivariate nonstationary and cointegrating regressions+ These contributions provided the asymptotic tools that have served... tests We are grateful to Peter Phillips for proposing a special issue of Econometric Theory for papers from our conference Unit Root and Cointegration Testing+ We thank all participants of the conference who contributed...

The problem of detecting unit roots in time series data is treated as a problem of multiple decisions instead of a testing problem, as is otherwise common in the econometric and statistical literature. The multiple decision design is based on a distinction between continuous primary and discrete secondary parameters. Four examples for such multiple decision designs are considered: first-and second-order integrated univariate processes; cointegration in a bivariate model; seasonal integration for semester data; seasonal integration for quarterly data. In all cases, restricted optimum decision rules are established based on Monte Carlo simulation. Zusammenfassung: Die Bestimmung von Einheitswurzeln in Zeitreihendaten wird als multiples Entscheidungsproblem behandelt und nicht als Hypothesentest-Problem, wie es sonst in derökonometrischen und statistischen Literaturüblich ist. Der verwendete entscheidungstheoretische Ansatz benützt eine Unterscheidung zwischen stetigen Primärparametern und diskreten Sekundärparametern.

Vier Beispiele für die Anwendung des Ansatzes werden im Detail behandelt: univariate Prozesse mit unbekannter Integrationsordnung; Kointegration in bivariaten Modellen; saisonale Integration bei Halbjahresdaten; saisonale Integration bei Quartalsdaten. In allen Fällen werden optimale Entscheidungsregeln mittels Monte-Carlo-Simulation gefunden. Academia.edu no longer supports Internet Explorer. To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. We propose a new procedure to detect unit roots based on subspace methods. It has three main original features.

First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, which loss functions can be adapted to the statistical properties of the data. Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties. An example illustrates its application to real time series.

By pointing out the spurious regression problem, Granger and Newbold~1974! have shown the importance of stochastic trends in time series data in the context of linear regression models+ At the time, removing trends by differencing was already common practice in univariate time series modeling... unit roots and motivated the development of statistical procedures for their detection+ Dickey and Fuller~1979! and Fuller~1976! were pioneers in developing tests for unit roots that became widely used+ The foundation of asymptotic theory for regressions involving stochastic trends was led by Phillips~1986, 1987! with the introduction of the functional limit theory, weak convergence methods, convergence to stochastic integrals, nonparametric unit root testing, and continuous record asymptotics+ Phillips and Durlauf~1986!

extended some of these results to the multivariate setting by presenting the multivariate invariance principles and the asymptotic theory of multivariate nonstationary and cointegrating regressions+ These contributions provided the asymptotic tools that have served... tests We are grateful to Peter Phillips for proposing a special issue of Econometric Theory for papers from our conference Unit Root and Cointegration Testing+ We thank all participants of the conference who contributed... The problem of detecting unit roots in time series data is treated as a problem of multiple decisions instead of a testing problem, as is otherwise common in the econometric and statistical literature. The multiple decision design is based on a distinction between continuous primary and discrete secondary parameters. Four examples for such multiple decision designs are considered: first-and second-order integrated univariate processes; cointegration in a bivariate model; seasonal integration for semester data; seasonal integration for quarterly data. In all cases, restricted optimum decision rules are established based on Monte Carlo simulation.

Zusammenfassung: Die Bestimmung von Einheitswurzeln in Zeitreihendaten wird als multiples Entscheidungsproblem behandelt und nicht als Hypothesentest-Problem, wie es sonst in derökonometrischen und statistischen Literaturüblich ist. Der verwendete entscheidungstheoretische Ansatz benützt eine Unterscheidung zwischen stetigen Primärparametern und diskreten Sekundärparametern. Vier Beispiele für die Anwendung des Ansatzes werden im Detail behandelt: univariate Prozesse mit unbekannter Integrationsordnung; Kointegration in bivariaten Modellen; saisonale Integration bei Halbjahresdaten; saisonale Integration bei Quartalsdaten. In allen Fällen werden optimale Entscheidungsregeln mittels Monte-Carlo-Simulation gefunden. More publications in: Documentos de Trabajo (ICAE) We propose a new procedure to detect unit roots based on subspace methods.

It has three main original features. First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, which loss functions can be adapted to the statistical properties of the data. Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties.

An example illustrates its application to real time series.

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Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties. An example illustrates its application to real time series. By pointing out the spurious regression problem, Granger and Newbold~19...

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