Intervention Analysis of Share Index Data for Banks and Other Financial Institutions in Bangladesh

IntroductionThe share index measures changes in the cost of earnings income at a certain level from investment to shares of joint stock companies and it changes very frequently as the reputation of the companies fluctuate. The changes may sometimes be very high due to some external events. Ordinary procedures to predict share index have no guidance of including such effect. One may use ARIMA model but fluctuation in the data may often affect the underlying ARIMA structure. Under this circumstance true ARIMA pattern will not be determined. In such a case, intervention analysis is a way to describe dynamic patterned distributed lag responses of the output series to the input series and the autocorrelation pattern of the disturbances. Thus, the purpose of our study is to apply intervention analysis to share index data for banks and other financial institutions and compare it with ARIMA model. Data has been collected from the Journal Index Numbers of Dhaka Stock Exchange Share Prices, published by Statistics Department, Bangladesh Bank.Methodology UsedIn intervention model, the input variable I( is a binary deterministic variable used to represent the possible intervention. Intervention may be of two types:* Pulse intervention* Step intervention.* Linear Transfer Function (LTF) MethodIn the LTF method, we estimate a free-form linear distributed lag regression (transfer function) which gives us a set of sample v-weights at the same time we specify a low-order AR proxy model for the disturbance ARIMA pattern: this is designed to give us more efficient estimates of the v-weights by accounting for most of the autocorrelation pattern in the disturbance.In this method, we first generate rather large number of statistics that gives clues about the patterns in the data. In the case of a DR model these statistics are :* a set of impulse response weights and* a set of sample autocorrelation and partial autocorrelation coefficients for the estimated disturbance series.Then we tentatively choose a parsimonious rational distributed lag model for the transfer function and a parsimonious ARIMA model for the disturbance series. We modify our tentative model as necessary based on the information produced at the estimation and checking stages.* Transfer Function Identification by Outlier DetectionIntervention models can also be constructed according to the nature of outliers present in the data series. Outliers can be classified in three types according as the nature of external events:* Additive Outliers (AO): It is similar as the oneperiod pulse intervention* Permanent Level Shift (LS): It similar as step intervention.* Innovational Outliers (10): These are additions to the random shock series e(: an 10 affects the output series P through th ARIMA structure of the disturbance series in the model for Pt.The critical value, C. for the likelihood ratio statistic L^sub A^, L^sub S^ and L^sub i^ are similar to a critical standard normal value or t value. However, it is not feasible to determine the exact repeated sampling distributions of the likelihood ratios in Equations 14,15 and 16. Therefore we don't know the exact significance level (a) associated with various values of Cd. Some simulation experiments are reported by Tsay, et. ai, for AO and 10 events. The common practice to choose Cd is between 3 to 4. If the estimated value of the Likelihood Statistic is greater than Cd we reject the null hypothesis of no intervention is present otherwise we accept the null hypothesis.Model BuildingAs the original data series produce higher residual standard error, we construct Model 3.1 using the transformed data, square root transformation of the original series.The autocorrelation function (ACF) (Figure. 3.1) and partial autocorrelation function (PACF) (Figure 3.2) of residuals and standardized residuals (Figure 3. …