Detecting Mean-Variance Shifts in a Financial Time Series: A Firm Level Case Analysis of Karachi Stock Exchange

Muhammad Ali Bhatti, Eatzaz Ahmad and Marium Iqbal

Abstract

This study aims at detecting the number, locations and size of deterministic shifts in a financial time series, using Inclan and Tiao (1994)’s algorithm. The algorithm, developed to address the violation of the assumption of constant unconditional variance of GARCH model in order to reduce the persistence of volatility over time, uses the cumulative sums of squares of partitioned series, and is iteratively applied to detect both mean- and variance-changes in the series, hence named Iterated Cumulative Sums of Squares (ICSS) algorithm. A properly normalized version of the maximum of CSS-statistic asymptotically follows normal distribution, the quantiles of which are used in the algorithm. Firm-level data from Karachi Stock Exchange is used to demonstrate the application of the algorithm. An improved form of the algorithm, by Bos and Hoontrakul (2002), is also applied as a sensitivity check to evaluate and rectify the cases where ICSS algorithm might have detected a mean-shift in the series as a variance-shift.