Model selection criteria in multivariate models with multiple structural changes. (English) Zbl 1441.62786
Summary: This paper considers the issue of selecting the number of regressors and the number of structural breaks in multivariate regression models in the possible presence of multiple structural changes. We develop a modified Akaike information criterion (AIC), a modified Mallows’ \(C_{p}\) criterion and a modified Bayesian information criterion (BIC). The penalty terms in these criteria are shown to be different from the usual terms. We prove that the modified BIC consistently selects the regressors and the number of breaks whereas the modified AIC and the modified \(C_{p}\) criterion tend to overfit with positive probability. The finite sample performance of these criteria is investigated through Monte Carlo simulations and it turns out that our modification is successful in comparison to the classical model selection criteria and the sequential testing procedure robust to heteroskedasticity and autocorrelation.
MSC:
| 62P20 | Applications of statistics to economics |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62J05 | Linear regression; mixed models |
| 62B10 | Statistical aspects of information-theoretic topics |
References:
| [1] | Akaike, H., (1973). Information Theory and an Extension of the Maximum Likelihood Principle, in: B.N. Petrov and F. Csáki (eds.), 2nd International Symposium on Information Theory, Akadémiai Kiadó. Budapest, pp. 267-281.; Akaike, H., (1973). Information Theory and an Extension of the Maximum Likelihood Principle, in: B.N. Petrov and F. Csáki (eds.), 2nd International Symposium on Information Theory, Akadémiai Kiadó. Budapest, pp. 267-281. · Zbl 0283.62006 |
| [2] | Andrews, D. W.K., Tests for parameter instability and structural change with unknown change point, Econometrica, 61, 821-856 (1993) · Zbl 0795.62012 |
| [3] | Andrews, D. W.K.; Lee, I.; Ploberger, W., Optimal changepoint tests for normal linear regression, Journal of Econometrics, 70, 9-38 (1996) · Zbl 0834.62066 |
| [4] | Bai, J., Estimation of a change point in multiple regression models, Review of Economics and Statistics, 79, 551-563 (1997) |
| [5] | Bai, J., Estimating multiple breaks one at a time, Econometric Theory, 13, 315-352 (1997) |
| [6] | Bai, J., Likelihood ratio tests for multiple structural changes, Journal of Econometrics, 91, 299-323 (1999) · Zbl 1041.62514 |
| [7] | Bai, J., Vector autoregressive models with structural changes in regression coefficients and in variance-covariance matrices, Annals of Economics and Finance, 1, 303-339 (2000) |
| [8] | Bai, J.; Perron, P., Estimating and testing linear models with multiple structural changes, Econometrica, 66, 47-78 (1998) · Zbl 1056.62523 |
| [9] | Bai, J.; Perron, P., Computation and analysis of multiple structural change models, Journal of Applied Econometrics, 18, 1-22 (2003) |
| [10] | Bai, J.; Perron, P., Estimating and testing linear models with multiple structural changes, (Corbae, D.; Durlauf, S. N.; Hansen, B. E., Econometric Theory and Practice (2006), Cambridge University Press: Cambridge University Press Cambridge) · Zbl 1056.62523 |
| [11] | Bhattacharya, P. K.; Brockwell, P. J., The minimum of an additive process with applications to signal estimation and storage theory, Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 37, 51-75 (1976) · Zbl 0326.60053 |
| [12] | Burnham, K. P.; Anderson, D. R., Model Selection and Multimodel Inference (2002), Springer: Springer New York · Zbl 1005.62007 |
| [13] | Davis, R. A.; Lee, T. C.M.; Rodriguez-Yam, G. A., Structural break estimation for nonstationary time series models, Journal of the American Statistical Association, 101, 223-239 (2006) · Zbl 1118.62359 |
| [14] | Hannan, E. J., The estimation of the order of an ARMA process, Annals of Statistics, 8, 1071-1081 (1980) · Zbl 0451.62068 |
| [15] | Hannan, E. J.; Deistler, M., The Statistical Theory of Linear Systems (1988), Wiley: Wiley New York · Zbl 0641.93002 |
| [16] | Hansen, B. E., Averaging estimators for regressions with a possible structural break, Econometric Theory, 25, 1498-1514 (2009) · Zbl 1179.62119 |
| [17] | Konishi, S.; Kitagawa, G., Information Criteria and Statistical Modeling (2008), Springer-Verlag: Springer-Verlag New-York · Zbl 1172.62003 |
| [18] | Liu, J.; Wu, S.; Zidek, J. V., On segmented multivariate regressions, Statistica Sinica, 7, 497-525 (1997) · Zbl 1003.62524 |
| [19] | Mallows, C. L., Some comments on \(C_p\), Technometrics, 15, 661-675 (1973) · Zbl 0269.62061 |
| [20] | Ninomiya, Y., Information criterion for Gaussian change-point model, Statistics and Probability Letters, 72, 237-247 (2005) · Zbl 1075.62003 |
| [21] | Ninomiya, Y., AIC for change-point models and its application, (Research Memorandum 1002 (2006), Institute of Statistical Mathematics) |
| [22] | Perron, P., Dealing with structural breaks, (Mills, T. C.; Patterson, K., Palgrave Handbook of Econometrics, Vol. 1: Econometric Theory (2006), Palgrave Macmillan: Palgrave Macmillan New York) |
| [23] | Qu, Z.; Perron, P., Estimating and testing structural changes in multivariate regressions, Econometrica, 75, 459-502 (2007) · Zbl 1132.91555 |
| [24] | Ross, S. M., Stochastic Processes (1996), Wiley: Wiley New York · Zbl 0888.60002 |
| [25] | Schwarz, G., Estimating the dimension of a model, Annals of Statistics, 6, 461-464 (1978) · Zbl 0379.62005 |
| [26] | Shibata, R., Selection of the order of an autoregressive model by Akaike’s information criterion, Biometrika, 63, 117-126 (1976) · Zbl 0358.62048 |
| [27] | Yao, Y. C., Estimating the number of change-points via Schwarz’ criterion, Statistics and Probability Letters, 6, 181-189 (1988) · Zbl 0642.62016 |
| [28] | Zhang, N. R.; Siegmund, D., Modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data, Biometrics, 63, 22-32 (2007) · Zbl 1206.62174 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
