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

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

Vivek Vijay (Indian Institute of Technology Jodhpur, Jodhpur, India) and Parmod Kumar Paul (Indian Institute of Technology Jodhpur, Jodhpur, India)
DOI: 10.4018/IJAMSE.2015070103
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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.
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2. Bollinger Band

Traders attempt to profit on short terms price fluctuations. An active trader normally holds an asset for a very short period of time, sometimes minutes and sometimes even seconds. The decision of a trader is based upon technical analysis. There are several technical indicators which predict the trends of movements. Some of them are based on moving average, some are based on volatility. There are some indicators which are free of statistical parameters, for example, PVO (Percentage Volume Oscillator). One of the most reliable and useful technical indicator is Bollinger Band. These bands are plotted at standard deviation levels above or below moving averages. The bands are volatility adjusting bands, that is, during more volatile market widening can be observed. A Bollinger band consists of:

  • 1.

    An N’-period moving average (MA);

  • 2.

    An upper band at K times the N’-period standard deviation above the moving average (MA +Kσ);

  • 3.

    A lower band at K times the N’-period standard deviation below the moving average (MA - K σ);

  • 4.

    A middle band consists of values between (MA +Kσ) and (MA -Kσ).

The values of K and N’ are considered to be K= ± 1.5 and N’ = 20 (for details, see, Bollinger 2002).

We construct Bollinger bands for BSE monthly data (April 2007 - October 2013), Crude oil intra-day data of 22 Mar 2007 and Nifty intra-day 03-05 Jan 2011 data. Also, we assume N’=20 and K =0.75 and 1.5. These bands are given in Figure 2, 3 and 4 in Appendix.

Figure 2.

Bollinger band of BSE Sensex April 2007 - Oct 2013

Figure 3.

Bollinger band of crude oil intra-day data

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