چكيده به لاتين
In this thesis, Integer-valued ARCH and threshold Integer-valued autoregressive models, with some characteristics of time series of counts such as over-dispersion, structural change, asymmetry, and a large proportion of zeros are considered. For this purpose, a class of generalized Poisson autoregressive models in the form of both linear and nonlinear models, were used to properly capture flexible asymmetric and nonlinear responses in the real data examples through a switching mechanism. Considering the weaknesses of the traditional estimation methods like MLE, a Bayesian approach based on an adaptive Monte Carlo Markov Chain (adaptive MCMC) sampling scheme was used to efficiently locate the structural break (structural change) and to estimate the model parameters. Also, to draw MCMC samples from posterior distributions regarding each parameter in this study, Metropolis and Metropolis-Hastings (MH) algorithms were applied.
In the simulation study, to reach more accurate results than that of parameter estimation used in the prior works, in the parameter estimation procedure, a number of 30,000 values were sampled from the posterior distribution and 8,000 samples were withdrawed as Burn-In iteration. Trace plots and histogram plots are provided for each of these parameters to appropriately show the Burn-in iteration and the convergence in the procedure.
Keywords: Integer-Valued Time Series, Threshold Poisson Autoregressive Models, Zero-Inflated Generalized Poisson, Structural Break, Monte-Carlo Markov Chain, Metropolis-Hastings.
