From ages to ages there had been expectation of individuals on a specific predictions and future occurrences. So also in a game, different participant that involves in those specified game have their various expectations of the results or the output of the game they are involved in. That is why we need a mathematical theory that helps in prediction of the future expectations in our day to day activities. Therefore the Martingale Theory is a very good theory that explains and dissects the expectation of a gamer in a given game of chance. So in this thesis, we shall talk about the Martin-gale ...

The knowledge of whether a time series contains a unit root or not provides guidance to determine whether the series is stationary or not. This topic is one that covers vast amount of research given to its importance in the analysis of economic and other time series data. To understand the behavior, the properties of the series and the influence of any shock that occur to the series, stationary and unit root tests were constructed. In this thesis, we first present the Box and Jenkins ARMA models, discuss the conditions for station-arity. Then, we display different method to test autocorrelation. ...