References
- Aknouche, A., H. Belbachir, and F. Hamdi. 2008. A note on calculating autocovariances of periodic ARMA models. Communications in Statistics—Simulation and Computation 37:924–7.
- Aknouche, A., and H. Guerbyenne. 2009a. On some probabilistic properties of double periodic AR models. Statistics & Probability Letters 79:407–13.
- Aknouche, A., and H. Guerbyenne. 2009b. Periodic stationarity of random coefficient periodic autoregressions. Statistics & Probability Letters 79:990–6.
- Anderson, P. L., and M. M. Meerschaert. 2005. Parameter estimation for periodically stationary time series. Journal of Time Series Analysis 26:489–518.
- Bentarzi, M., and M. Hallin. 1994. On the invertibility of periodic moving average models. Journal of Time Series Analysis 15:263–8.
- Bentarzi, M., H. Guerbyenne, and R. Hemis. 2008. Predictive density order selection of periodic AR models. Communications in Statistics—Simulation and Computation 37:1167–82.
- Boshnakov, G. N. 1996. Recursive computation of the parameters of periodic autoregressive moving-average processes. Journal of Time Series Analysis 17:333–49.
- Bougerol, P., and N. Picard. 1992. Strict stationarity of generalized autoregressive processes. Annals of Probability 20:1714–30.
- Cavicchioli, M. 2016. Third and fourth moments of vector autoregressions with regime switching. Communications in Statistics—Theory and Methods ( just-accepted).
- Chen, C. C., and W. J. Tsay. 2011. A Markov regime-switching ARMA approach for hedging stock indices. Journal of Futures Markets 31:165–91.
- Douc, R., Moulines E., and T. Ryden. 2004. Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime. Annals of Statistics 32:2254–304.
- Fiorentini, G., C. Planas, and A. Rossi. 2016. Marginal distribution of Markov-switching VAR processes. Communications in Statistics—Theory and Methods ( just-accepted).
- Francq, C., and J. M. Zakoïan. 2001. Stationarity of multivariate Markov-switching ARMA models. Journal of Econometrics 102:339–64.
- Francq, C., and J. M. Zakoïan. 2002. Autocovariance structure of powers of switching-regime ARMA processes. ESAIM: Probability and Statistics 6:259–70.
- Gray, S. F. 1996. Modeling the conditional distribution of interest rates as a regime-switching process. Journal of Financial Economics 42:27–62.
- Hamdi, F. 2012. Computing the exact Fisher information matrix of periodic state-space models. Communications in Statistics—Theory and Methods 41:4182–99.
- Hamilton, J. D. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57:357–84.
- Hamilton, J. D. 1994. Time series analysis. New Jersey: Princeton University Press.
- Krolzig, H. M. 1997. Markov-switching vector autoregressions: Modelling, statistical inference and application to business cycle analysis. Berlin-Heidelberg-New York: Springer Verlag.
- Lee, O. 2005. Probabilistic properties of a nonlinear ARMA process with Markov switching. Communications in Statistics—Theory and Methods 34:193–204.
- Lund, R., and I. V. Basawa. 2000. Recursive prediction and likelihood evaluation for periodic ARMA models. Journal of Time Series Analysis 21:75–93.
- Magnus, J. R., and H. Neudecker. 1999. Matrix differential calculus with applications in statistics and econometrics. Chichester: John Wiley & Sons Ltd.
- Newton, H. J. 1982. Using periodic autoregressions for multiple spectral estimation. Technometrics 24:109–16.
- Pagano, M. 1978. On periodic and multiple autoregression. Annals of Statistics 6:1310–17.
- Psaradakis, Z., and N. Spagnolo. 2003. On the determination of the number of regimes in Markov-switching autoregressive models. Journal of Time Series Analysis 24:237–52.
- Psaradakis, Z., and N. Spagnolo. 2006. Joint determination of the state dimension and autoregressive order for models with in Markov regime switching. Journal of Time Series Analysis 27:753–66.
- Shao, Q., and R. Lund. 2004. Computation and characterization of autocorrelations and partial autocorrelations in periodic ARMA models. Journal of Time Series Analysis 25:359–72.
- Ula, T. A., and A. A. Smadi. 1997. Periodic stationary conditions for periodic autoregressive moving average processes as eigenvalue problems. Water Resources Research 33:1929–34.
- Vecchia, A. V. 1985. Maximum likelihood estimation for periodic autoregressive moving average models. Technometrics 27:375–84.
- Zhang, J., and R. A. Stine. 2001. Autocovariance structure of Markov regime switching models and model selection. Journal of Time Series Analysis 22:107–24.