An Optimal Band for Prediction of Buy and Sell Signals and Forecasting of States

Abstract

A trading band, based on historical movements of a security price, suggests buy or sell pattern. Bollinger band is one of the most famous bands based on moving average and volatility of the security. The authors define a new trading band, namely Optimal Band, to forecast the buy or sell signals. This optimal band uses a linear function of local and absolute extrema of a given financial time series. The parameters of this linear function are then estimated by simple linear optimization technique. The authors then define different states using various upper and lower values of Bollinger band and the optimal band. The approach of Markov and Hidden Markov Models are used to forecast the future states of given time series. The authors apply all the techniques on the closing price of Bombay stock exchange and intra-day price series of crude oil and Nifty stock exchange.