Abstract
The Mixture Transition Distribution (MTD) model used for the approximation of high-order Markov chains does not allow a simple calculation of confidence intervals, and computationnally intensive methods based on bootstrap are generally used. We show here how standard methods can be extended to the MTD model as well as other models such as the Hidden Markov Model. Starting from existing methods used for multinomial distributions, we describe how the quantities required for their application can be obtained directly from the data or from one run of the E-step of an EM algorithm. Simulation results indicate that when the MTD model is estimated reliably, the resulting confidence intervals are comparable to those obtained from more demanding methods.
Highlights
Markovian models such as homogeneous Markov chains, Mixture Transition Distribution (MTD)models and Hidden Markov Models (HMMs) are widely used for the analysis of time series
At least two reasons can explain this: (i) Markov chains were often used in a theoretical framework which does not require real data; (ii) even if models such as HMMs are of standard use today, they are often applied in fields where the number of available data is very large, limiting the need to worry about sample size and confidence intervals
The purpose of this paper is to show that existing methods can be applied to the MTD model and other advanced Markovian models, the only requirement being a way for correctly estimating the number of observations entering in the computation of each transition probability
Summary
Markovian models such as homogeneous Markov chains, Mixture Transition Distribution (MTD). Includes an implementation of this principle based on the work of Sison and Glaz [4] This approach works well, because in empirical situations, the number of data points used to estimate each element of the transition matrix is generally known. This is not the case for the MTD and the HMM models. The purpose of this paper is to show that existing methods can be applied to the MTD model and other advanced Markovian models, the only requirement being a way for correctly estimating the number of observations entering in the computation of each transition probability.
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