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.

Technical analysis is useful for forecasting the price movement through the analysis of historic data. This sort of movement has Turn of the year effect also and useful for short term prediction. If the direction of price of two or more assets is same, it becomes necessary to analyze the returns also. We first use optimal band to predict the direction of price and create a contingency table of the data to analyze the pattern (movement) against returns. We use log-linear modeling for the analysis of the contingency table. We next include the volume of transactions as one more variable in the contingency table. The table consisting of three variables, Pattern, Returns and Volume is further analyzed by using log-linear modeling. We test various hypotheses of association for these variables by using Chi-square test for contingency tables.

For selecting and interpreting appropriate behaviour of proportion between buy/neutral/sell patterns and high/moderate/low returns, the prediction error reduction index is a very useful tool. It is operationally interpretable in terms of the proportional reduction in error of estimation. We first obtain the buy/sell pattern using an Optimal Band. The analysis of the association between patterns and returns is based on the Goodman–Kruskal prediction error reduction index ( λ ). Empirical analysis suggests that the prediction of returns from patterns is more impressive or of less error as compared to the prediction of patterns from returns. We demonstrated the prediction index for Index NIFTY 50, BANK-NIFTY, and NIFTY-IT of NSE (National Stock Exchange), for the period 2010–2020.