Testing for the cointegration rank between Periodically Integrated processes

del Barrio Castro, Tomás (2021): Testing for the cointegration rank between Periodically Integrated processes.

Abstract

Cointegration between periodically integrated (PI) processes has been analyzed by many, including Bladen-Hovell, Chui, Osborn, and Smith (1989), Boswijk and Franses (1995), Franses and Paap (2004), Kleibergen and Franses (1999) and del Barrio Castro and Osborn (2008), to name a few. However, there is currently no published method that allows us to determine the cointegration rank between P I processes. The present paper Ölls this gap in the literature with a method for determining the cointegration rank between a set of P I processes based on the idea of pseudo-demodulation, as proposed in the context of seasonal cointegration by del Barrio Castro, Cubadda, and Osborn (2020). Once a pseudodemodulated time series is obtained, the Johansen (1995) procedure can be applied to determine the cointegration rank. A Monte Carlo experiment shows that the proposed approach works satisfactorily for small samples.

• Item Type: MPRA Paper
• Language: English
• Keywords: Reduced Rank Regression,Periodic Cointegration, Periodically Integrated Processes.
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models

References

Ahn S.K. and Reinsel G.C. (1994) Estimation of partially nonstationary vector autoregressive models with seasonal behavior, Journal of Econometrics, Journal of Econometrics, 62, 317-350.

Birchenhall C.R., Bladen-Hovell R.C., Chui A.P.L., Osborn D.R. and Smith J.P. (1989) A Seasonal Model of Consumption, Economic Journal, 99, 837-843.

Boswijk H.P. and Franses P.H. (1995)Periodic cointegration: Representation and inference, The review of economics and statistics, 77, 436-454.

Boswijk H.P. and Franses P.H. (1996) Unit Roots In Periodic Autoregressions, Journal of Time Series Analysis, 17, 221-245.

Cubbada G. (2000) Complex Reduced Rank Models For Seasonally Cointegrated Time Series, Oxford Bulletin of Economics and Statistics, 63, 497-511.

del Barrio Castro T., Cubada G. and Osborn D. R. (2022) On cointegration for processes integrated at di§erent frequencies, Journal of Time Series Analysis, 43, 3, 412-435.

del Barrio Castro, T. and Osborn, D.R. (2008a) Cointegration For Periodically Integrated Processes, Econometric Theory, 24, 109-142.

del Barrio Castro, T. and Osborn, D.R. (2008a) Testing for Seasonal Unit Roots in Periodic Integrated Autoregressive Processes, Econometric Theory, 24, 1093-1112.

Engle R.F., Granger C.W.J., Hylleberg S. and Lee H.S. (1993) Seasonal Cointegration: The Japanese consumption function, 55, 1-357.

Franses P.H. and Paap R. (2004) Periodic Time Series Models, Oxford University Press.

Gersovitz M. and MacKinnon J.G. (1978) Seasonality in Regression: An Application of Smoothness Priors, Journal of the American Statistical Association, 73, 264-273.

Ghysels, E. and Osborn, D.R. (2001) The Econometric Analysis of Seasonal Time Series, Cambridge University Press.

Haldrup N., Hylleberg S., Pons G. and Sanso A. (2007) Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data, Journal of Business and Economic Statistics, 25, 21-32.

Hansen, L.P. and Sargent, T.J. (1993) Seasonality and Approximation errors in rational expectations models, Journal of Econometrics, 55, 21-55.

Hylleberg, S., Engle, R., Granger, C. and Yoo, B. (1990) Seasonal integration and cointegration. Journal of Econometrics 44, 215-238.

Johansen S. and Schaumburg E. (1998) Likelihood analysis of seasonal cointegration, Journal of Econometrics, 88, 301-339.

Johansen S. (1995) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press.

Kleibergen F.R. and Franses, P.H. (1999) Cointegration in a periodic vector autoregression, Econometric Institute Research Papers EI 9906-/A.

Lee H.S. (1992) 1992, Maximum likelihood inference on cointegration and seasonal cointegration, Journal of Econometrics 54, 1-47.

Lee H.S. and Siklos P.L. (1995) A note on the critical values for the maximum likelihood (seasonal) cointegration tests, Economics Letters, 49, 137-145.

Lutkepoht H. (2006) New introduction to Multiple Time Series Analysis, Springer.

Osborn, D.R. (1993) Seasonal cointegration, Journal of Econometrics, 55, 299-303.

Osborn, D.R. (1988) Seasonality and Habit Persistence in a Life Cycle Model of Consumption, Journal of Applied Econometrics, 3, 255-266.

Paap R. and Franses P.H. (1999) On trends and constants in periodic autoregressions, Econometric Reviews, 18, 271-286.

Pollock D.S.G. (1999) Handbook of Time-Series Analysis, Signal Processing and Dynamics, Academic Press.