CSI 779 / STAT 789

Patterns in Technical Analysis

Technical analysts use a variety of indicators to forecast the near-term performance of the price of an asset.

Some indicators are based on the relationship of the current price to a smoothed trend of the stock ("above or below the 30-day moving average"). Other indicators are based on smooth bands around past prices.

Many indicators are based on the relationships of a sequence of extremes in the prices of the stock.

The prices may be actual trades; they may be closing prices, daily, weekly, etc.; or they may be a smoothed sequence of prices.

There are two kinds of extremes, high and low. A high extreme is a price that is greater than the preious price and the next price. Extremes, by their nature, must alternate between high and low.

For whichever kind of price data is used, the definition of an extreme may include further restrictions, such as ratios between successive that must be exceeded and bounds on the time intervals during which extremes can occur.

If prices are smoothed, and are related to time by a function of the form
P = S(t) + e,
then the extremes can be defined in terms of a change in the sign of the derivative of S. If the derivative goes from positive to negative, the extreme is a (local) maximum.

Patterns of Extremes Studied by Lo, Mamaysky, and Wong

Lo, Mamaysky, and Wong studied 10 patterns. Each required 5 sucessive extremes, E1, E2, E3, E4, E5. The condition E1>E2 or E1<E2 defines whether the extremes are maxima or minima. Their definitions of the patterns are standard, except for the restrictions on the ratios.

Head and Shoulders (HS)
- E1>E2
- E3>E1 and E3>E5
- E1 and E5 within 1.5%
- E2 and E4 within 1.5%
Inverted Head and Shoulders (IHS)
- E1<E2
- E3<E1 and E3<E5
- E1 and E5 within 1.5%
- E2 and E4 within 1.5%
Broadening Top (BTOP)
- E1>E2
- E1<E3<E5
- E2>E4
Broadening Bottom (BBOT)
- E1<E2
- E1>E3>E5
- E2<E4
Triangle Top (TTOP)
- E1>E2
- E1>E3>E5
- E2<E4
Triangle Bottom (TBOT)
- E1<E2
- E1<E3<E5
- E2>E4
Rectangle Top (RTOP)
- this pattern can persist over many extremes
- E1>E2
- tops within 0.75% of average
- bottoms within 0.75% of average
- lowest top > highest bottom
Rectangle Bottom (RBOT)
- this pattern can persist over many extremes
- E1<E2
- tops within 0.75% of average
- bottoms within 0.75% of average
- lowest top > highest bottom
Double Top (DTOP)
- this pattern can persist over many extremes
- E1>E2
- let Ek be the highest maximum after E1
- E1 and Ek are within 1.5% of average
- E1 and Ek are at least 22 days apart
Double Bottom (DBOT)
- this pattern can persist over many extremes
- E1<E2
- let Ek be the lowest minimum after E1
- E1 and Ek are within 1.5% of average
- E1 and Ek are at least 22 days apart

Assignment

Incorporate these patterns (one at a time) into your program for finding patterns.