Hiernaux, Alfredo G. and Jerez Méndez, Miguel and Casals Carro, José (2005) Unit roots and cointegrating matrix estimation using subspace methods. [Working Paper or Technical Report]
Official URL: http://eprints.ucm.es/7907/
We propose a new procedure to detect unit roots based on subspace methods. It has three main original features. First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, which loss functions can be adapted to the statistical properties of the data. Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties. An example illustrates its application to real time series.
|Item Type:||Working Paper or Technical Report|
|Uncontrolled Keywords:||State-space models, Subspace methods, Unit roots, Cointegration|
|Subjects:||Social sciences > Economics > Econometrics|
|Series Name:||Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)|
Abuaf, N. and Jorion, P. (1990). Purchasing power parity in the long run. The Journal of Finance, 45:157–174.
Akaike, H. (1975). Markovian representation of stochastic processes by canonical variables. SIAM Journal of Control, 13(1):162–173.
Akaike, H. (1976). Canonical Correlation Analysis of Time Series and the Use of an Information Criterion. Academic Press.
Bauer, D. and Wagner, M. (2002). Estimating cointegrated systems using subspace algorithms. Journal of Econometrics, 111: 47–84.
Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis, Forecasting and Control. Holden-Day, San Francisco, 2nd ed. edition.
Casals, J., Sotoca, S., and Jerez, M. (1999). A fast stable method to compute the likelihood of time invariant state space models. Economics Letters, 65(3):329–337.
Chui, C. K. and Chen, G. (1999). Kalman Filtering with Real-Time Applications. Berlin, Springer.
Chui, N. L. C. (1997). Subspace Methods and Informative Experiments for System Identiﬁcation. PhD thesis, Pembroke College Cambridge.
Dickey, D. A. and Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with unit root. Journal of the American Statistical Association, 74:427–431.
Eckart, C. and Young, G. (1936). The approximation of one matrix by another of lower rank. Psychometrika, 1:211–218.
Favoreel, W., De Moor, B., and Van Overschee, P. (2000). Subspace state space system identiﬁcation for industrial processes. Journal of Process Control, 10:149–155.
Flores, R. G., Jorion, P., Preumont, P. Y., and Szafarz, A. (1999). Multivariate unit roots test of ppp hypothesis. Journal of Empirical Finance, 6:335–353.
Ho, B. and Kalman, R. (1966). Eﬀective construction of linear state-variable models from input-output functions. Regelungstechnik, 14:545–548.
Jenkins, G. M. and Alavi, A. S. (1981). Somes aspects of modelling and forecasting multivariate time series. Journal of Time Series Analysis, 2(1):1–47.
Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12:231–254.
Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models. Econometrica, 59:1551–1580.
Knudsen, T. (2001). Consistency analysis of subspace identiﬁcation methods based on linear regression approach. Automatica, 37:81–89.
Larimore, W. E. (1983). System identiﬁcation, reduced-order ﬁltering and modeling via canonical variate analysis. Proceedings of the American Control Conference, ACC, San Francisco, pages 445–451.
Larimore, W. E. (1990). Canonical variate analysis in identiﬁcation, ﬁltering and adaptive control. Proceedings of the 29th Conference on Decision and Control, Hawaii, pages 596–604.
Lütkepohl, H. and Poskitt, D. S. (1998). Econometrics in Theory and Practice: Festchrift for Hans SchneeweiB, chapter Consistent Estimation of the Number of Cointegration Relations in a Vector Autorregresive Model, pages 87–100.
Martín Manjón, R. and Treadway, A. (1997). The fed controls only one of the two interest rates in the u.s. economy. Documento de Trabajo del ICAE, (9716).
Peternell, K., Scherrer, W., and Deistler, M. (1996). Statistical analysis of novel subspace identiﬁcation methods. Signal Processing, 52:161–177.
Phillips, P. B. C. and Durlauf, N. S. (1986). Multiple time series regression with integrated process. Review of Economic Studies, 53:473–495.
Poskitt, D. S. (2000). Strongly consistent determination of cointegrating rank via canonical correlations. Journal of Business and Economic Statistics, 18:77–90.
Riemers, H. E. (1992). Comparison of tests for multivariate cointegration. Statistical Papers, 33:335–359.
Sánchez, I. and Peña, D. (2001). Properties of predictors in overdiﬀerenced nearly nonstationary autoregression. Journal of Time Series Analysis, 22(1):45–66.
Tiao, G. C. and Box, G. E. P. (1981). Modeling multiple time series with applications. Journal of the American Statistical Association, 76:802–816.
Tiao, G. C. and Tsay, R. S. (1989). Model speciﬁcation in multivariate time series. Journal of the Royal Statistical Society, B Series, 51(2):157–213.
Toda, H. Y. (1995). Finite sample performance of likelihood ratio tests for cointegrating rank in vector autoregressions. Econometric Theory, 11:1015–1032.
Viberg, M. (1995). Subspace-based methods for the identiﬁcation of the linear time-invariant systems. Automatica, 31(12):1835–1852.
|Deposited On:||20 May 2008|
|Last Modified:||06 Feb 2014 07:56|
Repository Staff Only: item control page