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Common Features in Vector Nonlinear Time Series Models
Dalarna University, School of Technology and Business Studies, Statistics. Handelshögskolan vid Örebro universitet, Statistik.
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 these area.

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 Ftypetest 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
Öerbro: Örebro University , 2013.
Series
Örebro Studies in Statistics, ISSN 1651-8608 ; 6
Keyword [en]
Nonlinearity, Time series, Econometrics, Smooth transition, Common features, Cointegration, Forecasting, Residual-based, PPP.
National Category
Probability Theory and Statistics
Research subject
Komplexa system - mikrodataanalys
Identifiers
URN: urn:nbn:se:du-13253ISBN: 978-91-7668-952-3 (print)OAI: oai:DiVA.org:du-13253DiVA: diva2:663260
Public defence
2013-10-01, Långhuset HSL 3, Örebro University, Örebro, 13:15 (English)
Opponent
Supervisors
Available from: 2013-11-11 Created: 2013-11-11 Last updated: 2015-03-18Bibliographically 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
2011 (English)Report (Other academic)
Abstract [en]

This paper studies a smooth-transition (ST) type cointegration. The proposed ST cointegration allows for regime switching structure in a cointegrated system. It nests the linear cointegration developed by Engle and Granger (1987) and the threshold cointegration studied by Balke and Fomby (1997). We develop F-type tests to examine linear cointegration against ST cointegration in ST-type cointegrating regression models with or without time trends. The null asymptotic distributions of the tests are derived with stationary transition variables in ST cointegrating regression models. And it is shown that our tests have nonstandard limiting distributions expressed in terms of standard Brownian motion when regressors are pure random walks, while have standard asymptotic distributions when regressors contain random walks with nonzero drift. Finite-sample distributions of those tests are studied by Monto Carlo simulations. The small-sample performance of the tests states that our F-type tests have a better power when the system contains ST cointegration than when the system is linearly cointegrated. An empirical example for the purchasing power parity (PPP) data (monthly US dollar, Italy lira and dollar-lira exchange rate from 1973:01 to 1989:10) is illustrated by applying the testing procedures in this paper. It is found that there is no linear cointegration in the system, but there exits the ST-type cointegration in the PPP data.

Place, publisher, year, edition, pages
Borlänge: Högskolan Dalarna, 2011
Series
Working papers in transport, tourism, information technology and microdata analysis, ISSN 1650-5581 ; 2011:01
Keyword
cointegration; smooth transition; F-type test; purchasing power parity.
National Category
Probability Theory and Statistics
Research subject
Komplexa system - mikrodataanalys, Nonlinear Cointegration i Nonlinear Vector autoregressive modeller: teori och tillämpningar
Identifiers
urn:nbn:se:du-6042 (URN)
Available from: 2011-11-04 Created: 2011-11-04 Last updated: 2013-11-12Bibliographically 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
2012 (English)Report (Other academic)
Abstract [en]

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-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 of United States (1985:1 to 2011:11).

Series
Working papers in transport, tourism, information technology and microdata analysis, ISSN 1650-5581 ; 2012:4
National Category
Probability Theory and Statistics
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-11114 (URN)
Available from: 2012-10-30 Created: 2012-10-25 Last updated: 2013-11-11Bibliographically approved
3. Forecasting with Vector Nonlinear Time Series Models
Open this publication in new window or tab >>Forecasting with Vector Nonlinear Time Series Models
2013 (English)Report (Other academic)
Abstract [en]

This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

Place, publisher, year, edition, pages
Borlänge: Högskolan Dalarna, 2013
Series
Working papers in transport, tourism, information technology and microdata analysis, ISSN 1650-5581 ; 2013:08
Keyword
forecasts, nonlinearity, evaluation, shocks
National Category
Probability Theory and Statistics
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-11873 (URN)
Available from: 2013-02-20 Created: 2013-02-20 Last updated: 2013-11-11
4. Residual-based Inference for Common Nonlinear Features
Open this publication in new window or tab >>Residual-based Inference for Common Nonlinear Features
2013 (English)Report (Other academic)
Abstract [en]

This paper investigates common nonlinear features in multivariate nonlinear autore-gressive models via testing the estimated residuals. A Wald-type test is proposed and itis asymptotically Chi-squared distributed. Simulation studies are given to examine thefinite-sample properties of the proposed test.

Place, publisher, year, edition, pages
Borlänge: Högskolan Dalarna, 2013
Series
Working papers in transport, tourism, information technology and microdata analysis, ISSN 1650-5581 ; 2013:09
Keyword
Common features, Nonlinearity, Residual-based test
National Category
Probability Theory and Statistics
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-11872 (URN)
Available from: 2013-02-20 Created: 2013-02-20 Last updated: 2013-11-11

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