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Residual-based inference for common nonlinear features
Örebro University, Örebro University School of Business. School of Technology and Business Studies, Dalarna University, Borlänge, Sweden.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper investigates common nonlinear features (CNFs) in multivariate nonlinear autoregressive models via testing the residuals. A Wald-type test is proposed, and it is asymptotically Chi-square distributed. Simulation evidence is given to examine the finite-sample properties of the proposed test and, furthermore, to provide a bootstrap version of the test. In addition to the empirical size and power, a specification of the reduced-rank matrix coefficient is studied to measure the departure from the null of CNFs. As the model moves further from containing CNFs, the power of the test increases substantially. Bootstrap critical values are used to improve the empirical size and power, especially when the test has size distortions. To perform a bootstrap version of the test, an algorithm is also provided for the estimation using nonlinear reduced-rank regression (NRRR).

Keywords [en]
common features, nonlinearity, residual-based test, bootstrap test, reduced-rank regression
National Category
Mathematics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:oru:diva-32411OAI: oai:DiVA.org:oru-32411DiVA, id: diva2:664456
Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2017-10-17Bibliographically approved
In thesis
1. Common features in vector nonlinear time series models
Open this publication in new window or tab >>Common features in vector nonlinear time series models
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four manuscripts in the area of nonlinear time series econometrics on topics of testing, modeling and forecasting nonlinear common features. The aim of this thesis is to develop new econometric contributions for hypothesis testing and forecasting in thesearea.

Both stationary and nonstationary time series are concerned. A definition of common features is proposed in an appropriate way to each class. Based on the definition, a vector nonlinear time series model with common features is set up for testing for common features. The proposed models are available for forecasting as well after being well specified.

The first paper addresses a testing procedure on nonstationary time series. A class of nonlinear cointegration, smooth-transition (ST) cointegration, is examined. The ST cointegration nests the previously developed linear and threshold cointegration. An F-type test for examining the ST cointegration is derived when stationary transition variables are imposed rather than nonstationary variables. Later ones drive the test standard, while the former ones make the test nonstandard. This has important implications for empirical work. It is crucial to distinguish between the cases with stationary and nonstationary transition variables so that the correct test can be used. The second and the fourth papers develop testing approaches for stationary time series. In particular, the vector ST autoregressive (VSTAR) model is extended to allow for common nonlinear features (CNFs). These two papers propose a modeling procedure and derive tests for the presence of CNFs. Including model specification using the testing contributions above, the third paper considers forecasting with vector nonlinear time series models and extends the procedures available for univariate nonlinear models. The VSTAR model with CNFs and the ST cointegration model in the previous papers are exemplified in detail, and thereafter illustrated within two corresponding macroeconomic data sets.

Place, publisher, year, edition, pages
Örebro: Örebro universitet, 2013. p. 27
Series
Örebro Studies in Statistics, ISSN 1651-8608 ; 6
Keywords
nonliearity, time series, econometrics, smooth transition, common features, cointegration, forecasting, residual-based, ppp
National Category
Mathematics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-32233 (URN)978-91-7668-952-3 (ISBN)
Public defence
2013-10-01, Hörsal 3, Långhuset, Örebro universitet, Fakultetsgatan 1, 701 82 Örebro, 13:15 (English)
Opponent
Supervisors
Available from: 2013-11-15 Created: 2013-11-04 Last updated: 2017-10-17Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
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Language
  • de-DE
  • en-GB
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Output format
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