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Issues of multicollinearity and conditional heteroscedasticy in time series econometrics
Jönköping University, Jönköping International Business School, JIBS, Statistics.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This doctoral thesis consists of four chapters all related to the field of time series econometrics. The main contribution is firstly the development of robust methods when testing for Granger causality in the presence of generalized autoregressive conditional heteroscedasticity (GARCH) and causality-in-variance (i.e. spillover) effects. The second contribution is the development of different shrinkage estimators for count data models which may be used when the explanatory variables are highly inter-correlated.

The first essay investigated the effect of spillover on some tests for causality in a Granger sense. As a remedy to the problem of over-rejection caused by the spillover effects White’s heteroscedasticity consistent covariance matrix is proposed. In the second essay the effect of GARCH errors on the statistical tests for Granger causality is investigated. Here some wavelet denoising methods are proposed and by means of Monte Carlo simulations it is shown that the size properties of the tests based on wavelet filtered data is better than the ones based on raw data.

In the third and fourth essays ridge regression estimators for the Poisson and negative binomial (NB) regression models are investigated respectively. Then finally in the fifth essaya Liu type of estimator is proposed for the NB regression model. By using Monte Carlo simulations it is shown that the estimated MSE is lower for the ridge and Liu type of estimators than maximum likelihood (ML).

Place, publisher, year, edition, pages
Jönköping: Jönköping University, Jönköping International Business School , 2012. , 15 p.
Series
JIBS Dissertation Series, ISSN 1403-0470 ; 075
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hj:diva-31977ISBN: 978-91-86345-27-3 (print)OAI: oai:DiVA.org:hj-31977DiVA: diva2:1037086
Supervisors
Available from: 2016-10-13 Created: 2016-10-13 Last updated: 2016-10-13Bibliographically approved
List of papers
1. Granger Causality Test in the Presence of Spillover Effects
Open this publication in new window or tab >>Granger Causality Test in the Presence of Spillover Effects
2009 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 38, no 10, 2039-2059 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we investigate the effect of spillover (i.e., causality in variance) on the reliability of Granger causality test based on ordinary least square estimates. We studied eight different versions of the test both, with and without Whites heteroskedasticity consistent covariance matrix (HCCME). The properties of the tests are investigated by means of a Monte Carlo experiment where 21 different data generating processes (DGP) are used and a number of factors that might affect the test are varied. The result shows that the best choice to test for Granger causality under the presence of spillover is the Lagrange Multiplier test with HCCME.

Keyword
GARCH, Granger causality test, Power, Size, Spillover
National Category
Economics
Identifiers
urn:nbn:se:hj:diva-13400 (URN)10.1080/03610910903243695 (DOI)
Available from: 2010-10-01 Created: 2010-10-01 Last updated: 2017-12-12Bibliographically approved
2. A Wavelet-Based Approach of Testing for Granger Causality in the Presence of GARCH Effects
Open this publication in new window or tab >>A Wavelet-Based Approach of Testing for Granger Causality in the Presence of GARCH Effects
2012 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, no 4, 717-728 p.Article in journal (Refereed) Published
Abstract [en]

The size and power of the most commonly used tests and a new wavelet-based approach of testing for Granger causality is evaluated in this paper by means of a Monte Carlo study in which the error term follows a generalized autoregressive conditional heteroscedasticity consistent (GARCH) process. In the simulation study it is shown that the commonly used causality tests tends to over-reject the true null hypothesis in the presence of GARCH errors and that the new wavelet-based approach improves the size properties of the Granger causality test for all of the different situations evaluated.

Keyword
GARCH, Granger causality, Wavelet, Size, Power
National Category
Social Sciences
Identifiers
urn:nbn:se:hj:diva-14419 (URN)10.1080/03610926.2010.529535 (DOI)
Available from: 2011-01-24 Created: 2011-01-24 Last updated: 2017-12-11Bibliographically approved
3. A poisson ridge regression estimator
Open this publication in new window or tab >>A poisson ridge regression estimator
2011 (English)In: Economic Modelling, ISSN 0264-9993, E-ISSN 1873-6122, Vol. 28, no 4, 1475-1481 p.Article in journal (Refereed) Published
Abstract [en]

The standard statistical method for analyzing count data is the Poisson regression model, which is usually estimated using maximum likelihood (ML) method. The ML method is very sensitive to multicollinearity. Therefore, we present a new Poisson ridge regression estimator (PRR) as a remedy to the problem of instability of the traditional ML method. To investigate the performance of the PRR and the traditional ML approaches for estimating the parameters of the Poisson regression model, we calculate the mean squared error (MSE) using Monte Carlo simulations. The result from the simulation study shows that the PRR method outperforms the traditional ML estimator in all of the different situations evaluated in this paper.

Keyword
poisson regression, maximum likelihood, ridge regression, MSE, Monte Carlo simulations, multicollinearity
National Category
Social Sciences
Identifiers
urn:nbn:se:hj:diva-17310 (URN)10.1016/j.econmod.2011.02.030 (DOI)
Available from: 2012-01-19 Created: 2012-01-19 Last updated: 2017-12-08Bibliographically approved
4. On ridge estimators for the negative binomial regression model
Open this publication in new window or tab >>On ridge estimators for the negative binomial regression model
2012 (English)In: Economic Modelling, ISSN 0264-9993, E-ISSN 1873-6122, Vol. 29, no 2, 178-184 p.Article in journal (Refereed) Published
Abstract [en]

The negative binomial (NB) regression model is very popular in applied research when analyzing count data. The commonly used maximum likelihood (ML) estimator is very sensitive to highly intercorrelated explanatory variables. Therefore, a NB ridge regression estimator (NBRR) is proposed as a robust option of estimating the parameters of the NB model in the presence of multicollinearity. To investigate the performance of the NBRR and the traditional ML approach the mean squared error (MSE) is calculated using Monte Carlo simulations. The simulated result indicated that some of the proposed NBRR methods should always be preferred to the ML method.

Keyword
Negative binomial regression; Maximum likelihood; Ridge regression; MSE; Monte Carlo simulations; Multicollinearity
National Category
Social Sciences
Identifiers
urn:nbn:se:hj:diva-17738 (URN)
Available from: 2012-03-01 Created: 2012-03-01 Last updated: 2017-12-07Bibliographically approved
5. Developing a Liu estimator for the negative binomial regression model: method and application
Open this publication in new window or tab >>Developing a Liu estimator for the negative binomial regression model: method and application
2013 (English)In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 83, no 9, 1773-1780 p.Article in journal (Refereed) Published
Abstract [en]

This paper introduces a new shrinkage estimator for the negative binomial regression model that is a generalization of the estimator proposed for the linear regression model by Liu [A new class of biased estimate in linear regression, Comm. Stat. Theor. Meth. 22 (1993), pp. 393–402]. This shrinkage estimator is proposed in order to solve the problem of an inflated mean squared error of the classical maximum likelihood (ML) method in the presence of multicollinearity. Furthermore, the paper presents some methods of estimating the shrinkage parameter. By means of Monte Carlo simulations, it is shown that if the Liu estimator is applied with these shrinkage parameters, it always outperforms ML. The benefit of the new estimation method is also illustrated in an empirical application. Finally, based on the results from the simulation study and the empirical application, a recommendation regarding which estimator of the shrinkage parameter that should be used is given.

Keyword
negative binomial regression, maximum likelihood, Liu, MSE, Monte Carlo simulations, multicollinearity, Primary 62J07, Secondary 62J02
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-29100 (URN)10.1080/00949655.2012.673127 (DOI)000324088300013 ()2-s2.0-84884258133 (Scopus ID)
Available from: 2016-01-15 Created: 2016-01-15 Last updated: 2017-11-30Bibliographically approved

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