Time Series Modeling and Forecasting in Banking Sector of KSE-100 and Distribution Fitting on Stock Market Data

One of the main important issues of statistical analysis is forecasting. There are two important objectives of this article one is to developed time series modeling of stock market data of Karachi Stock Exchange (KSE-100). Second is to identify the probability distribution on banking sector of Karachi Stock Exchange (KSE-100).In this work, statistical relation between prices and corresponding turnovers is introduced. Different probability distributions have been fitted on the closing price, turnover and their ratio (closing price and turnover).The theory of statistical distribution and time series modeling is applied on each Bank of Karachi Stock Exchange (KSE-100).Autoregressive Integrated Moving Average (ARIMA), the Autoregressive conditional Hetroscedasticity (ARCH) were fitted on each variable of Karachi Stock Exchange (KSE-100).We have found that mostly for closing price, best fitted distribution and their ratio(closing price/turnover) are Gen.Pareto, Johnson SB and Log-logistic distributions. The best fitted time series models for closing price are AR(1) ARCH(1) and Constant mean model with ARCH(1) and turnover and their ratio (closing price and turnover) are ARMA(1,1) GARCH(1,1). The goodness of fit of mean model is accessed through the Mean Error (ME), Mean Square Error (MSE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) and the goodness of fit for variance model is accessed with the help of Loss function. This research gives a new idea that MCB is the best bank among the banking sector of Karachi Stock Exchange (KSE-100) for a new investor to invest. 94 Pakistan Journal of Social Sciences Vol. 32, No. 1