published_or_final_version / Statistics / Master / Master of Philosophy

Filter trading rule is a technical trading strategy that was very popular amongst practitioners and has been used a lot for testing market efficiency. It has been shown that the filter trading rule is mathematically equivalent to the CUSUM quality control test as both are based on change point detection theory via sequential probability ratio tests (SPRT). To study the operating characteristics of the filter trading rule, many results from the CUSUM literature can be applied. However, some interesting operating characteristics of a technical trading rule such as expected profit per day may not be relevant when put into a quality control setting. In this thesis, we derive formulae for computing these operating characteristics. It is well known that just like any other technical trading rule, the filter trading rule is not effective when the asset price follows a random walk. In this thesis, we studied the statistical properties and effectiveness of the filter trading rule under different asset price models including Markov regime switching model and conditional heteroskedasticity model. The properties of the filter trading rule considered include the waiting time for the first signal in filter trading, the duration of a long or a short cycle in filter trading, the profit return derived from a long or a short cycle and the unit time return of long term filter trading. Built on the above results, we consider the problem of optimizing the performance of a filter trading rule by choosing a suitable filter size. For filter trading rule under the conditional heteroskedasticity model, the change point detection methods lead to a new technical trading rule called generalized filter trading rule in this thesis. The generalized filter trading rule is shown to have a better performance over the ordinary filter trading rule when it is applied to the trading of the Hang Seng Index futures contract. Finally, we have applied the filter trading rule to intraday trading on high frequency Hang Seng Index futures data. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy