Estimation and Inference for Varying-coefficient Models with Nonstationary Regressors using Penalized Splines
AbstractThis paper considers estimation and inference for varying-coefficient models with nonstationary regressors. We propose a nonparametric estimation method using penalized splines, which achieves the same optimal convergence rate as kernel-based methods, but enjoys computation advantages. Utilizing the mixed model representation of penalized splines, we develop a likelihood ratio test statistic for checking the stability of the regression coefficients. We derive both the exact and the asymptotic null distributions of this test statistic. We also demonstrate its optimality by examining its local power performance. These theoretical findings are well supported by simulation studies.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2013-033.
Length: 47 pages
Date of creation: Jul 2013
Date of revision:
Nonstationary Time Series; Varying-coe±cient Model; Likelihood Ratio Test; Penalized Splines;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-07-28 (All new papers)
- NEP-ECM-2013-07-28 (Econometrics)
- NEP-ETS-2013-07-28 (Econometric Time Series)
- NEP-ORE-2013-07-28 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- In Choi & Pentti Saikkonen, 2004. "Testing linearity in cointegrating smooth transition regressions," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 341-365, December.
- Lettau, Martin & Ludvigson, Sydney, 1999.
"Consumption, Aggregate Wealth and Expected Stock Returns,"
CEPR Discussion Papers
2223, C.E.P.R. Discussion Papers.
- Martin Lettau, 2001. "Consumption, Aggregate Wealth, and Expected Stock Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 815-849, 06.
- Sydney Ludvigson & Martin Lettau, 1999. "Consumption, aggregate wealth and expected stock returns," Staff Reports 77, Federal Reserve Bank of New York.
- Amit Goyal & Ivo Welch, 2002.
"Predicting the Equity Premium With Dividend Ratios,"
NBER Working Papers
8788, National Bureau of Economic Research, Inc.
- Amit Goyal & Ivo Welch, 2003. "Predicting the Equity Premium with Dividend Ratios," Management Science, INFORMS, vol. 49(5), pages 639-654, May.
- Amit Goyal & Ivo Welch, 1999. "Predicting the Equity Premium with Dividend Ratios," Yale School of Management Working Papers amz2437, Yale School of Management, revised 01 Nov 2002.
- Kuo, Biing-Shen, 1998. "Test for partial parameter instability in regressions with I(1) processes," Journal of Econometrics, Elsevier, vol. 86(2), pages 337-368, June.
- Hao, K., 1996. "Testing for Structural Change in Cointegrated Regression Models: Some Comparisons and Generalizations," Monash Econometrics and Business Statistics Working Papers 3/96, Monash University, Department of Econometrics and Business Statistics.
- Hong, Seung Hyun & Phillips, Peter C. B., 2010.
"Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 28(1), pages 96-114.
- Seung Hyun Hong & Peter C. B. Phillips, 2005. "Testing Linearity in Cointegrating Relations with an Application to Purchasing Power Parity," Cowles Foundation Discussion Papers 1541, Cowles Foundation for Research in Economics, Yale University.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, December.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Bent Nielsen & Soren Johansen and Rocco Mosconi, 2000.
"Cointegration analysis in the presence of structural breaks in the deterministic trend,"
Economics Series Working Papers
2000-W22, University of Oxford, Department of Economics.
- Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
- Bent Nielsen, 2000. "Cointegration Analysis in the Presence of Structural Breaks in the Deterministic Trend," Econometric Society World Congress 2000 Contributed Papers 1494, Econometric Society.
- Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
- Henrik Hansen & Søren Johansen, 1999. "Some tests for parameter constancy in cointegrated VAR-models," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 306-333.
- Bierens, Herman J. & Martins, Luis F., 2010. "Time-Varying Cointegration," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1453-1490, October.
- Ciprian Crainiceanu & David Ruppert & Gerda Claeskens & M. P. Wand, 2005. "Exact likelihood ratio tests for penalised splines," Biometrika, Biometrika Trust, vol. 92(1), pages 91-103, March.
- Hansen, Bruce E, 1992.
"Tests for Parameter Instability in Regressions with I(1) Processes,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 10(3), pages 321-35, July.
- Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
- Yingxing Li & David Ruppert, 2008. "On the asymptotics of penalized splines," Biometrika, Biometrika Trust, vol. 95(2), pages 415-436.
- Paye, Bradley S. & Timmermann, Allan, 2006. "Instability of return prediction models," Journal of Empirical Finance, Elsevier, vol. 13(3), pages 274-315, June.
- Joon Y. Park & Peter C. B. Phillips, 1999.
"Nonlinear Regressions with Integrated Time Series,"
Working Paper Series
no6, Institute of Economic Research, Seoul National University.
- Peter Hall & J. D. Opsomer, 2005. "Theory for penalised spline regression," Biometrika, Biometrika Trust, vol. 92(1), pages 105-118, March.
- Harris, David & McCabe, Brendan & Leybourne, Stephen, 2002. "Stochastic cointegration: estimation and inference," Journal of Econometrics, Elsevier, vol. 111(2), pages 363-384, December.
- Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, December.
- Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April.
- Friedrich Poeschel, 2013.
"Assortative matching through signals,"
ppo178, Job Market Papers.
- Poeschel, Friedrich, 2012. "Assortative matching through signals," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.
- Poeschel, Friedrich, 2012. "Assortative matching through signals," IAB Discussion Paper 201215, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
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