# Technical analysis

Technical analysis tries to predict the stock price evolutions by looking at the signals composed by historical prices and volumes. The technique generally focuses on prices and rarely on volumes. It tries to discover the stock market forces and weaknesses by looking at the (time, value) graphs. Typical sub-graphs or diagrams are searched for prediction, such as waves, cups, and head with shoulders.

More simply, technical analysis has produced hundreds of indicators calculated from the (time, value) curve, at different level of granularity. In general, these indicators are able to help in determining the best buy and sell points, for example, when one is crossing a treshold or when two are intersecting. Indicators change value at each time unit (week,day, or hour). Thus, the values of an indicator can be organized as a time series, i.e., a vector giving the value for each instant. Indicators and derived values can be computed by a basic algebra on time series. We develop such an algebra in the next page.

Let us first introduce the indicators we are using. They can be classified in two categories: tendancy indicators and oscilliators. Tendancy indicators follow the price curve and try to anticipate its evolution. Oscillators are indicators trying to determine if a stock is oversold or overbought. As their class name indicates, oscilliators varies in between a minimum and a maximum value (e.g., 0 and 100) while tendancy indicators more or less follow the stock prices.

## Tendancy Indicators

• #### Window Support (SUP)

The maximum price of a stock over a specified time window, i.e., from t0 to t1, with t1>t0. More complex resistances can be computed by selecting several local maximum and averaging them.

• #### Window Resistance (RES)

The minimum price of a stock over a specified time window. More complex supports can be computed by selecting several local minimum and averaging them.

• #### Simple Moving Average (SMA)

The average price of a stock over a specified time window. A window is composed of a number of periods w. SMA smoothes the signal given by the stock prices. The value at time t is computed by averaging the values from( t - w) to t. It can also be obtain by the formula: SMA(t) = SMA(t-1) - Price(t-w)/w +Price(t)/w

• #### Exponential Moving Average (EMA)

The weighted average price of a stock over a specified number of periods. Smooth the signal given by stock prices, giving more importance to the most recent values. The value at time t can be computed by the formula: EMA(t) = Price(t) * Multiplier + EMA(t-1) * (1-Multiplier). The multiplier should remain small (e.g., 0.1). Classical multipliers are 2/(1+w) and 1/w.

• #### High and Low Bollinger Bands (HBB, LBB)

A vision of price volatility obtained by placing a high band and a low band around a moving average. The bands are charted usually two standard deviations away from the average. Thus LBB(t) = SMA(t) - 2*STDEV(p) and HBB(t) = SMA(t) + 2*STDEV(p), Where STDEV(p) is the standard deviation from (t-p) to p.

## Oscilliators

• #### Rate of change (ROC)

The difference between the present price and the one that existed n-time periods ago, i.e., at the begining of the current window. ROC increases when the prices trend up whether it declines when they trend down.

• #### Relative Strenght Index (RSI)

The ratio between the sum of price gains to the sum of recent gains plus losses. RSI is given by the formula RSI = 100 - 100/(1+RS) where RS is gains/losses. An equivalent formula is RSI = 100 * Gains/(Gains+Losses). It is used to try to determine oversold (RSI less than 30) and overbought (RSI greater than 70) stocks.

• #### Moving Average Convergence Divergence (MACD)

The difference between a long period exponential moving average and a short period one. The inventor claims that the best signal is obtained for moving averages on 26 and 12 periods; thus, MACD = EMA(12) - EMA(26) in general. It is believed that a positive MACD is good for buying. The MACD is often used to derive a buy signal when its 9 period SMA crosses up the MACD itself.