Statistical Approach to the Optimisation of the Technical Analysis Trading Tools: Trading Bands Strategies

In this thesis we have proposed several approaches to improve and optimize one of the most popular technical analysis techniques trading bands strategies. Parts I and II concentrate on the optimization of the components of trading bands: the middle line (in the form of the moving average) and bandlines. Part III is dedicated to the improving of the decision-making process. In Part I we proposed the use of kriging method, a geostatistical approach, for the optimization of the moving average weights. The kriging method allows obtaining optimal estimates that depend on the statistical characteristics of the data rather than on the historical data itself as in the case of the simulation studies. Unlike other linear methods usually used in finance, this method can be applied to both equally spaced data (in our context, traditional time series) and data sampled at unequal intervals of time or other axis variables. Part II proposes a method based on the transformation of the data into a normal variable, which enables the definition of the extreme values and, therefore, the bands’ values, without constraining assumptions about the distribution function of the residuals. Finally, Part III presents the application of disjunctive kriging method, another geostatistical approach, for more informative decision making about the timing and the value of a position. Disjunctive kriging allows estimating the probability of certain thresholds being reached in the future. The results of the analysis prove that the proposed techniques can be incorporated into successful trading strategies.