Estimation Fractional Integration Parameter and an Application to Major Turkish Financial Time Series

In this study, integration degrees of monthly logarithmic return series of ISE100 Index, interest rate, and exchange rate basket, are estimated for last 60 months by using monthly time series of 2002-2012. According to the results of the analysis, FI degrees at 24 month period between 2008-2009 years, when USA based global mortgage crises was effected, the average of FI degrees in the following 36 months period, their statistical significance prominently increased in all series. In spite of the improvement in integration degrees, average value of last 36 month FI degrees of ISE100 series are even at low values and weak in terms of statistically significance. Even if estimated FI values of ISE100 Index and interest rate are weak in terms of statistically significance, these series sometimes have the long memory properties. Then, it cannot be wrong to accept interest rate and especially ISE100 Index behave with respect to short term dynamics. However, exchange rate series for the same period has the evident properties of medium memory FI degree with -0.23117.