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

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