Mining optimal technical trading rules with genetic algorithms

Abstract

In recent years technical trading rules are widely known by more and

more people, not only the academics many investors also learn to apply

them in financial markets. One approach of constructing technical

trading rules is to use technical indicators, such as moving average(MA)

and filter rules. These trading rules are widely used possibly because

the technical indicators are simple to compute and can be programmed

easily. An alternative approach of constructing technical trading rules

is to rely on some chart patterns. However, the patterns and signals

detected by these rules are often made by the visual inspection through

human eyes. As for as I know, there are no universally acceptable methods

of constructing the chart patterns. In 2000, Prof. Andrew Lo and

his colleagues are the first ones who define five pairs of chart patterns

mathematically. They are Head-and-Shoulders(HS) & Inverted Headand-

Shoulders(IHS), Broadening tops(BTOP) & bottoms(BBOT), Triangle

tops(TTOP) & bottoms(TBOT), Rectangle tops(RTOP) & bottoms(

RBOT) and Double tops(DTOP) & bottoms(DBOT).

The basic formulation of a chart pattern consists of two steps: detection

of (i) extreme points of a price series; and (ii) shape of the pattern.

In Lo et al.(2000), the method of kernel smoothing was used to identify

the extreme points. It was admitted by Lo et al. (2000) that the

optimal bandwidth used in kernel method is not the best choice and

the expert judgement is needed in detecting the bandwidth. In addition,

their work considered chart pattern detection only but no buy/sell

signal detection. It should be noted that it is possible to have a chart

pattern formed without a signal detected, but in this case no transaction

will be made. In this thesis, I propose a new class of technical

trading rules which aims to resolve the above problems. More specifically,

each chart pattern is parameterized by a set of parameters which

governs the shape of the pattern, the entry and exit signals of trades.

Then the optimal set of parameters can be determined by using genetic

algorithms (GAs). The advantage of GA is that they can deal with a

high-dimensional optimization problems no matter the parameters to

be optimized are continuous or discrete. In addition, GA can also be

convenient to use in the situation that the fitness function is not differentiable

or has a multi-modal surface.