Author : Muhammad Mohsin, Muhammad Anees, Shehzad Maqbool and Faliq Hussain

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 controls the variation on the Maximum Likelihood estimates.

Keywords: Discrete Time Markov Chains, Maximum likelihood, Laplace Smoothing methods, Equilibrium distribution, Inflation.