oru.sePublikationer
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Common features in vector nonlinear time series models
Örebro University, Orebro University School of Business, Örebro University, Sweden. School of Technology and Business Studies, Dalarna University, Borlänge, Sweden.
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. , 27 p.
Series
Örebro Studies in Statistics, ISSN 1651-8608 ; 6
Keyword [en]
nonliearity, time series, econometrics, smooth transition, common features, cointegration, forecasting, residual-based, ppp
National Category
Mathematics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:oru:diva-32233ISBN: 978-91-7668-952-3 (print)OAI: oai:DiVA.org:oru-32233DiVA: diva2:664475
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: 2016-09-22Bibliographically approved
List of papers
1. Testing linear cointegration against smooth-transition cointegration
Open this publication in new window or tab >>Testing linear cointegration against smooth-transition cointegration
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This study studies a smooth-transition (ST) type of cointegration. The proposed ST cointegration allows for regime switching structure in a cointegrated system and incorporates the linear cointegration developed by Engle and Granger (1987) and the threshold cointegration studied by Balke and Fomby (1997). We developed F-type tests to examine linear cointegration against ST cointegration in a class of vector ST cointegrating regression models. The null asymptotic distributions of the tests are derived when stationary transition variables are involved. Finite-sample distributions and the small-sample performances of these tests are studied using Monte Carlo simulations. Our F-type tests have better power when the system contains ST cointegration than when the system is linearly cointegrated. The testing procedure in this study is applied to purchasing power parity (PPP) data as an example, where we observe that there is no linear cointegration, but an ST cointegration exists in the system.

Keyword
nonlinear cointegration; threshold cointegration; smooth transition; F test
National Category
Mathematics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-32407 (URN)
Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2016-11-21Bibliographically approved
2. Testing common nonlinear features in vector nonlinear autoregressive models
Open this publication in new window or tab >>Testing common nonlinear features in vector nonlinear autoregressive models
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models, which contains common nonlinear features (CNFs). We proposed a triangular representation for these models and developed a procedure for testing CNFs in a VSTAR model. We first test a unit root against a stationary STAR process for each individual time series and subsequently examine whether CNFs exist in the system with the Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has a standard Chi-square asymptotic distribution. The critical values of our unit root tests and finite-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data for the United States (1985:1 to 2011:11). 

Keyword
Common features, Lagrange Multiplier test, Vector STAR models
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-32409 (URN)
Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2016-11-21Bibliographically approved
3. Forecasting with vector nonlinear time series models
Open this publication in new window or tab >>Forecasting with vector nonlinear time series models
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this study, vector nonlinear time series models are used for forecasting. Point forecasts are numerically obtained via bootstrapping. Our procedure is illustrated by two examples, each of which involves an application of macroeconomic data. Point forecast evaluation concentrates on forecast equality and encompassing. From these two applications, the forecasts from nonlinear models contribute useful information absent in the forecasts from linear models.

Keyword
point forecast, forecast evaluation, nonlinearity
National Category
Mathematics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-32410 (URN)
Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2016-11-21Bibliographically approved
4. Residual-based inference for common nonlinear features
Open this publication in new window or tab >>Residual-based inference for common nonlinear features
(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).

Keyword
common features, nonlinearity, residual-based test, bootstrap test, reduced-rank regression
National Category
Mathematics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-32411 (URN)
Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2016-11-21Bibliographically approved

Open Access in DiVA

sammanfattning(1714 kB)62 downloads
File information
File name SUMMARY01.pdfFile size 1714 kBChecksum SHA-512
64f049fab16449b330d2ac50b3dded682413ebb8812c917c05dc3146b57360c649d15b8e61d791efe2c4360162cf3850b2e63ad9260c2f7b7ab7db5727e86a0c
Type summaryMimetype application/pdf
omslag(94 kB)31 downloads
File information
File name COVER01.pdfFile size 94 kBChecksum SHA-512
a5e081a8b8493138526b9c35ea4e3d4428228f9f845697a2d388843b3a101c9f9874194d3e1f42c97358925696ba961f3f279f2d987abce5748060750fd49679
Type coverMimetype application/pdf
spikblad(100 kB)20 downloads
File information
File name SPIKBLAD01.pdfFile size 100 kBChecksum SHA-512
01fa42f230874a5b0e89c2dca178170abf762d915329cff2c153931015bbfe2e9288fe745e02d376e43f414fd1234a0079d6515f4ad58f1e0e12b87d354a55e4
Type spikbladMimetype application/pdf
bokmärke/bookmark(22 kB)11 downloads
File information
File name ATTACHMENT01.pdfFile size 22 kBChecksum SHA-512
97cab002ca06ca9d5df84c7b83b093051a67ca597dbb659b2060e3e14f4231425ebf41a77a6653b018cbb8cceb398c3a5685c092265ea6e67fa3c08e7bdce945
Type attachmentMimetype application/pdf
fulltext(22 kB)79 downloads
File information
File name FULLTEXT02.pdfFile size 22 kBChecksum SHA-512
97cab002ca06ca9d5df84c7b83b093051a67ca597dbb659b2060e3e14f4231425ebf41a77a6653b018cbb8cceb398c3a5685c092265ea6e67fa3c08e7bdce945
Type fulltextMimetype application/pdf

By organisation
Orebro University School of Business, Örebro University, Sweden
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 79 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 197 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf