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Comparing idiosyncratic unit root tests based on the residuals estimated from ML and PC methods in a static factor model
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics. (Time Series Econometrics)
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics Other Social Sciences not elsewhere specified
Identifiers
URN: urn:nbn:se:uu:diva-233090OAI: oai:DiVA.org:uu-233090DiVA: diva2:750586
Note

For static factor models or dynamic factor models with static representations, the idiosyncratic components can be estimated either from the method of principal components (PC) or from the method of (quasi) maximum likelihood (ML). In this paper, we compare the size and power properties of some commonly used unit root tests under the two sets of residuals. We also compare the estimation efficiency of the common factors, factor loadings and the idiosyncratic components across the two methods when the factor model is either stationary or non-stationary. The simulation results show that when the number of cross-section individuals (N) is small and the number of the observations (T) is large, the ML method is superior to the PC method. When $N$ and $T$ are both large, the difference between the methods is negligible.

Available from: 2014-09-29 Created: 2014-09-29 Last updated: 2015-01-23
In thesis
1. Likelihood-Based Panel Unit Root Tests for Factor Models
Open this publication in new window or tab >>Likelihood-Based Panel Unit Root Tests for Factor Models
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The thesis consists of four papers that address likelihood-based unit root tests for panel data with cross-sectional dependence arising from common factors.

In the first three papers, we derive Lagrange multiplier (LM)-type tests for common and idiosyncratic unit roots in the exact factor models based on the likelihood function of the differenced data. Also derived are the asymptotic distributions of these test statistics. The finite sample properties of these tests are compared by simulation with other commonly used unit root tests. The results show that our LM-type tests have better size and local power properties.

In the fourth paper, we estimate the spaces spanned by the common factors and the spaces spanned by the idiosyncratic components of the static factor model by using the quasi-maximum likelihood (ML) method and compare it with the widely used method of principal components (PC). Next, by simulation, we compare the size and power properties of established tests for idiosyncratic unit roots, using both the ML and PC methods. Simulation results show that the idiosyncratic unit root tests based on the likelihood-based residuals generally have better size and higher size-adjusted power, especially when the cross-sectional dimension is small and the time series dimension is large.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. 35 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 103
Keyword
Panel unit root, Exact factor model, Dynamic factor model, Maximum likelihood, Principal components, Lagrange multiplier
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-233094 (URN)978-91-554-9049-2 (ISBN)
Public defence
2014-11-14, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2014-10-24 Created: 2014-09-29 Last updated: 2015-01-23

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