Traders exploiting automated trading strategies have probably the most significant advantage over discretionary traders in the possibility of using comprehensive and accurate statistical analysis. Nowadays, traders can execute many statistical operations within few seconds thanks to large range of analytical and programming trading software (such as TradeStation , Multicharts, Microsoft Excel, Matlab etc.) which are widely accessible for the individual traders. Every professional trader who wants to fully exploit the potential of algorithmic trading has to understand statistics and to know the most widely used statistical methods which can be useful for evaluating the potential robustness of trading strategies.
It has to be pointed out that no statistical methods are needed where there is no uncertainty. If all students from the high school “A” successfully graduated whilst all the students from the high school “B” did not, then there is no need for statistical analysis. However, when the potential consequences of observed data are uncertain, the statistical analysis is the only way to outline reasonable conclusions. In such a uncertain environment as the exchange is the statistical analysis is the only way to differentiate between the rules that are statistically significant from those that are not. Technical analysis in trading aims to identify the recurrent rules based on historical data in the form of price patterns or various indicators and then to extrapolate them on future data. Nevertheless, the inherent characteristic of extrapolation is uncertainty. When speaking real money trading, the uncertainty is not the word the trader wants to hear. If we, however, understand which statistical methods are relevant and how to use them, the probability of successful and profitable trading gets significantly increased.
The basic principle of all statistical methods is statistical hypothesis testing. It allows assessing if experimentally retrieved data comply with the presumption defined before the testing. When testing statistical hypothesis, it is always necessary to compare two hypotheses. One hypothesis, so called null hypothesis H0, is the hypothesis which is undergoing the test. For example, it can be testing of hypothesis that all high school students in Czech Republic will have better final exam results of English language than technical school students in Czech Republic. On the other hand, the alternative hypothesis H1 presumes that the high school students will not have better results in final exam of English language than technical school students in Czech Republic. For testing the null hypothesis H0 against the alternative hypothesis H1 we shall use so called T statistics which is called the testing criterion. The testing criterion is the function of random selection. This function is related to the null hypothesis H0. The distribution of this function is known provided that the null hypothesis is not rejected. Let’s now demonstrate the statistical hypothesis testing and its meaning in exchange trading:
The Null Hypothesis H0
This hypothesis is based on the presumption that none of the rules of technical analysis (no matter if he uses price patterns, indicators, etc.) has predictive power and that the profitable backtest was nothing more than a coincidence. For our purpose the coincidence means positive but accidental conformity between the rule’s signal and subsequent market trends on the historical data sample (so called in-sample data) used for testing the rule.
The Alternative Hypothesis H1
On the other hand, if market observations are contrary to predictions made by the null hypothesis, the null hypothesis got rejected. Instead, the alternative hypothesis H1 gets accepted and is based on the presumption that the rule of technical analysis has predictive power. The alternative hypothesis H1 serves as an evidence that the rate of return is too high to be reasonably assigned to coincidence. If the rule of the technical analysis had no predictive power, the rate of return would be less or equal zero on unknown data (so called out-of-sample data). If using detrended data, the rate of return would equal zero. The principle of testing detrended data and why to use detrended data will be explained in following articles.
In this chapter, we introduced the importance of using statistical analysis in trading. The basic presumption of statistical analysis in trading is that technical analysis aims to reveal recurrent rules from historical data in the form of patterns or various indicators and then to extrapolate them to the future. The Null Hypothesis H0 presumes that all rules of technical analysis are without predictive power. It is a contrary to alternative hypothesis H1 which presumes that the rule does have predictive power. In the next article we will focus on explaining the principle of testing criterion.