publication . Thesis

Generalized structural time series model

Djennad, Abdelmadjid;
Open Access English
  • Country: United Kingdom
Abstract
new class of univariate time series models is developed, the Generalized Structural (GEST) time series model. The GEST model extends Gaussian structural time series models by allowing the distribution of the dependent variable to come from any parametric distribution, including highly skew and=or kurtotic distributions. Furthermore, the GEST model expands the systematic part of time series models to allow the explicit modelling of any or all of the distribution parameters as structural terms and (smoothed) functions of independent variables. The proposed GEST model primarily addresses the difficulty in modelling time-varying skewness and kurtosis (beyond locatio...
Subjects
free text keywords: dewey510
39 references, page 1 of 3

1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Research motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Random e ect models 44 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2 Gaussian linear mixed models . . . . . . . . . . . . . . . . . . . . . . 47 4.3 Estimation of the xed parameters . . . . . . . . . . . . . . . . . . . 48 4.4 Estimation of the random e ects . . . . . . . . . . . . . . . . . . . . 49 4.5 Computing the hyperparameters via ^ and ^ . . . . . . . . . . . . . . 50 4.6 Estimation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.7 Several random e ects . . . . . . . . . . . . . . . . . . . . . . . . . . 52 7.2 The GEST process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.3 Properties of the GEST process . . . . . . . . . . . . . . . . . . . . . 111 7.3.1 Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.3.2 Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.4 Simulation of the GEST process . . . . . . . . . . . . . . . . . . . . . 113 7.4.1 GEST process with normal distribution . . . . . . . . . . . . . 114 7.4.2 GEST process with Poisson distribution . . . . . . . . . . . . 126 7.4.3 GEST process with negative binomial type I distribution . . . 130 7.4.4 GEST process with Student t distribution . . . . . . . . . . . 134 7.4.5 GEST process with skew Student t distribution . . . . . . . . 138

Anderson, B.D.O. and Moore, J.B. (1979). Optimal Filtering. Englewood Cli s: Prentice Hall.

Asai, M. and McAleer, M. (2005). Dynamic asymmetric leverage in stochastic volatility models. Econometric Reviews, 24, 317-332.

Baillie, R.T., Bollerslev, T., and Mikkelsen, H.O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74, 3-30. [OpenAIRE]

Benjamin, M., Rigby, R.A. and Stasinopoulos, D.M. (2003). Generalized autoregressive moving average models. J. Am. Statist. Ass., 98, 214-223. [OpenAIRE]

Bollerslev, T. (1986). Generalised autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327. [OpenAIRE]

Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994). Time Series Analysis: Forecasting and Control. Prentice Hall.

Breslow, N.E. and Clayton, D.G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25.

Briet, O.J.T., Amerasinghe, P.H. and Vounatsou, P. (2013). Generalized seasonal autoregressive integrated moving average models for count data with application to malaria time series with low case numbers. PLoS ONE 8(6): e65761. doi:10.1371/journal.pone.0065761. [OpenAIRE]

Brockwell, P.J. and Davis, R.A. (1996). Time Series: Theory and Methods. Springer-Verlag.

Broda, S.A, Haas, M., Krause, J., Paolella, M.S and Steude, S.C. (2013). Stable mixture GARCH models. Journal of Econometrics, 172, 292-306.

Brooks, C., Burke, S.P., Heravi, S. and Persand, G. (2005). Autoregressive conditional kurtosis. J. Fin. Econometrics, 3, 399-421.

Chib, S., Nardari, F. and Shephard, N. (2002). Markov chain Monte Carlo methods for stochastic volatility models. Journal of Econometrics, 108, 281- 316. [OpenAIRE]

Choy, S.T.B., Wan, W.Y. and Chan, C.M. (2008). Bayesian student-t stochastic volatility models via scale mixtures. Advances in Econometrics, 23, 595- 618. Special issue on Bayesian Econometrics Methods.

39 references, page 1 of 3
Abstract
new class of univariate time series models is developed, the Generalized Structural (GEST) time series model. The GEST model extends Gaussian structural time series models by allowing the distribution of the dependent variable to come from any parametric distribution, including highly skew and=or kurtotic distributions. Furthermore, the GEST model expands the systematic part of time series models to allow the explicit modelling of any or all of the distribution parameters as structural terms and (smoothed) functions of independent variables. The proposed GEST model primarily addresses the difficulty in modelling time-varying skewness and kurtosis (beyond locatio...
Subjects
free text keywords: dewey510
39 references, page 1 of 3

1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Research motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Random e ect models 44 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2 Gaussian linear mixed models . . . . . . . . . . . . . . . . . . . . . . 47 4.3 Estimation of the xed parameters . . . . . . . . . . . . . . . . . . . 48 4.4 Estimation of the random e ects . . . . . . . . . . . . . . . . . . . . 49 4.5 Computing the hyperparameters via ^ and ^ . . . . . . . . . . . . . . 50 4.6 Estimation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.7 Several random e ects . . . . . . . . . . . . . . . . . . . . . . . . . . 52 7.2 The GEST process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.3 Properties of the GEST process . . . . . . . . . . . . . . . . . . . . . 111 7.3.1 Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.3.2 Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.4 Simulation of the GEST process . . . . . . . . . . . . . . . . . . . . . 113 7.4.1 GEST process with normal distribution . . . . . . . . . . . . . 114 7.4.2 GEST process with Poisson distribution . . . . . . . . . . . . 126 7.4.3 GEST process with negative binomial type I distribution . . . 130 7.4.4 GEST process with Student t distribution . . . . . . . . . . . 134 7.4.5 GEST process with skew Student t distribution . . . . . . . . 138

Anderson, B.D.O. and Moore, J.B. (1979). Optimal Filtering. Englewood Cli s: Prentice Hall.

Asai, M. and McAleer, M. (2005). Dynamic asymmetric leverage in stochastic volatility models. Econometric Reviews, 24, 317-332.

Baillie, R.T., Bollerslev, T., and Mikkelsen, H.O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74, 3-30. [OpenAIRE]

Benjamin, M., Rigby, R.A. and Stasinopoulos, D.M. (2003). Generalized autoregressive moving average models. J. Am. Statist. Ass., 98, 214-223. [OpenAIRE]

Bollerslev, T. (1986). Generalised autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327. [OpenAIRE]

Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994). Time Series Analysis: Forecasting and Control. Prentice Hall.

Breslow, N.E. and Clayton, D.G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25.

Briet, O.J.T., Amerasinghe, P.H. and Vounatsou, P. (2013). Generalized seasonal autoregressive integrated moving average models for count data with application to malaria time series with low case numbers. PLoS ONE 8(6): e65761. doi:10.1371/journal.pone.0065761. [OpenAIRE]

Brockwell, P.J. and Davis, R.A. (1996). Time Series: Theory and Methods. Springer-Verlag.

Broda, S.A, Haas, M., Krause, J., Paolella, M.S and Steude, S.C. (2013). Stable mixture GARCH models. Journal of Econometrics, 172, 292-306.

Brooks, C., Burke, S.P., Heravi, S. and Persand, G. (2005). Autoregressive conditional kurtosis. J. Fin. Econometrics, 3, 399-421.

Chib, S., Nardari, F. and Shephard, N. (2002). Markov chain Monte Carlo methods for stochastic volatility models. Journal of Econometrics, 108, 281- 316. [OpenAIRE]

Choy, S.T.B., Wan, W.Y. and Chan, C.M. (2008). Bayesian student-t stochastic volatility models via scale mixtures. Advances in Econometrics, 23, 595- 618. Special issue on Bayesian Econometrics Methods.

39 references, page 1 of 3
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