The current research is preparing an economic statistical study on exchange rate fluctuations for the period from ( 1996 to mid-2005 ) according to the well-known phrase: (The present is the past and the future is the present ). It is a modest attempt to crystallize this type of price in a scientific-statistic method by adopting the matrix of transitional probabilities in Markov chains, as these chains are among the models that are relied upon in the process of forecasting when the data are in the present time and in three cases: - High - Low - Stability. Between the past, the present and the future, the researcher was able to reach in his research to the analysis by applying the method of the greatest places, and to achieve the main purpose of this research, the researcher dealt with four chapters as follows: The first chapter dealt with the problem of research, its importance, need, purpose and determination of its terms. The second chapter reviewed the previous studies published on the subject, as well as the theoretical aspect, in which the matrix of transitional and stable possibilities, the state of stability and independence of the Markov chains, and the estimation of transitional possibilities in the greatest possible way were presented. As for the third chapter, it included the practical aspect and the field application. The data related to the research procedures were collected from the date of (17/10/2003 to 30/6/2005), in which the Iraqi currency was exchanged from the old to the currency currently in circulation, and in which the situation of the Iraqi market suggested great relative stability at the time. Finally, the fourth chapter of this research included the conclusions reached by the researcher from which it came: The market was characterized by a state of stability after the rise in the exchange rate against the dollar, which confirmed the accuracy of the results of the matrix of transitional possibilities, which was reflected on the local stock exchange, as well as the development of recommendations that can be used by the relevant parties.
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