A Discrete Time Markov Chain Model for the Assessment of Inflation Rate in Pakistan

Markov chains epitomize a class of stochastic process for a wide range of applications. Specifically, discrete time Markov chains (DTMC) is employed to model the transition probabilities between discrete states with the help of the matrices. To examine and forecast the time series the Markov chain model is applied. The most important indicator in macroeconomics is inflation, which persisted in double digits in 1970s and also in last several years. Different states are checked with the model by using inflation rate data form July 2000 to April 2015. A simulation technique used for random sequences of inflation predefine states for one year and take 1st quarter data from it and then model the estimates by maximum likelihood and maximum likelihood with Laplace smoothing methods and check the equilibrium distribution using both techniques. Estimates obtained by Laplace Smoothing technique are reliable because it control the variation on the Maximum Likelihood estimates. Keywords: Discrete Time Markov Chains, Maximum likelihood, Laplace Smoothing methods, Equilibrium distribution, Inflation DOI: 10.7176/MTM/9-5-03 Publication date:May 31st 201

A higher-order Markov model for the Newsboy's problem

Markov models are commonly used in modelling many practical systems such as telecommunication systems, manufacturing systems and inventory systems. However, higher-order Markov models are not commonly used in practice because of their huge number of states and parameters that lead to computational difficulties. In this paper, we propose a higher-order Markov model whose number of states and parameters are linear with respect to the order of the model. We also develop efficient estimation methods for the model parameters. We then apply the model and method to solve the generalised Newsboy's problem. Numerical examples with applications to production planning are given to illustrate the power of our proposed model.link_to_subscribed_fulltex