Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

in this paper by using the data related to the monthly precipitation of 13 stations situated in west azerbaijan province of iran in a time period of 34 years, monitoring and forecasting the probability of a drought occurrence is evaluated in next coming months. in this process, first the monthly precipitation amounts for each rainfall station are used in order to calculate the standardized prec...

to evaluate and predict component-based software security, a two-dimensional model of software security is proposed by stochastic petri net in this paper. in this approach, the software security is modeled by graphical presentation ability of petri nets, and the quantitative prediction is provided by the evaluation capability of stochastic petri net and the computing power of markov chain. each...

We consider a hidden Markov model with multidimensional observations, and with misspecification, i.e. the assumed coefficients (transition probability matrix, and observation conditional densities) are possibly different from the true coefficients. Under mild assumptions on the coefficients of both the true and the assumed models, we prove that : (i) the prediction filter forgets almost surely ...

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

Since two decades, wavelet packet decompositions have been shown effective as a generic approach to feature extraction from time series and images for the prediction of a target variable. Redundancies exist between the wavelet coefficients and between the energy features that are derived from the wavelet coefficients. We assess these redundancies in wavelet packet decompositions by means of the...

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features at multiple scales and stores them persistence diagrams (PDs). In this paper, we propose random diagram generator (RPDG) generates sequence PDs from ones produced by RPDG underpinned model based on pairwise interacting point processes revers...

A Bayesian approach for calibrating a hidden Markov model (HMM) to long-term multi-site rainfall time series is presented. Using a HMM approach for simulating long-term persistence is attractive because it has an explicit mechanism to produce longterm wet and dry periods which are a feature of many long-term hydrological time series. The ability to fully evaluate parameter uncertainty for the m...

In this paper, we introduce a discrete-time higher-order Markov-switching (HMS) model for measuring the risk of a portfolio. We suppose that the logarithmic returns from a risky portfolio is governed by a HMS model with the drift and the volatility switch over time according to the states of a discrete-time higher-order hidden Markov model (HHMM). We interpret the states of the HHMM as unobserv...