A Survey on stochastic unit root process: Theory and application

Much of applied econometric analysis is predicated on the assumption that the data series concerned are nonstationary and that they may be satisfactorily represented by a fixed-coefficient model that contains a unit root. However, various macroeconomic and financial series may include stochastic unit root. The process which has a stochastic unit root may be stationary for some periods and mildly explosive for others. Leybourne, McCabe and Tremayne (1996) and Leybourne, McCabe and Mills (1996) proposed a test to check whether a serie embodies a fixed or stochastic unit root. Modeling a serie with stochastic unit root as a fixed-coefficient autoregressive model may lead to results that are statistically undependable. Furthermore forecasts made under these conditions will also be undependable. Therefore, such a serie must be represented as a time varying coefficient model and must be estimated with an appropriate estimation method. In this study, data related to Istanbul Stock Exchange (ISE) national 100 Index closing values were initialized. The data covered the period from 7 February 1 986 to 24 May 2002, There were altogether 851 observation. The data is tested through Random Walk process see if it is efficient under weak form. For this purpose initially the serie is analyzed to determine whether the unit root is deterministic. The analysis indicated that the series embodies a stochastic unit root and hence Kalman Filter method is used to estimate unit root values each time period. In other words, period in which ISE is weak efficient. 2002, 100 Pages KEY WORDS: Stochastic Unit Root, Kalman Filter, ISE, Weakly Efficient Market Hypothesis