9th WSEAS Int. Conf. on MATHEMATICS & COMPUTERS IN BUSINESS AND ECONOMICS (MCBE '08), Bucharest, Romania, June 24-26, 2008 The role of predictability of financial series in emerging market applications GABRIELA PRELIPCEAN*, NICOLAE POPOVICIU,** MIRCEA BOSCOIANU* *Faculty of Economic and Public Administration Stefan cel Mare University of Suceava University Street, No. 13, Suceava – 720229, Romania **Faculty of Mathematics-Informatics Hyperion University of Bucharest Bucharest, Romania, Abstract: A new metric that quantifies the predictability of financial time series based on a mixture between Kaboudan η –metric and Genetic Programming (GP)/ Artificial Neural Networks (ANN) is proposed. The new metrics overcomes the stationary problem and shows how the predictability changes over different subsequences in financial time series. The focus is to develop quantitative metrics that characterize time series according to their ability to be modeled by a particular method, such as the predictability of a time series using the GP approach or an ANN. Keywords: quantitative metrics, predictability, timing detection, portfolio selection, Genetic Programming (GP), Artificial Neural Networks (ANN). 1. Introduction in the predictability of since the predictions made on these time series are financial time series on average more accurate. New time series predictability metric for use with Time series predictability is a measure of how well nonlinear time series modeling techniques is future values y can be forecasted and indicates to t presented. The use of this new metric in what extent the past can be used to determine the conjunction with a time series modeling method in future. In real world, time series are represented by financial modeling applications will show a mixture between deterministic and stochastic significant performance improvement in components. Predictability can be viewed as the comparison to using the time series modeling signal strength of the deterministic component and method alone. can be estimated by using modeling methods. Measuring the predictability tell whether a time series can be predicted under a particular model. Time series analysis builds models that describe the 2. Basic unified view of soft underlying system that generates a time series: computing concepts applications in ARIMA, Box-Jenkins time series analysis, artificial financial series neural networks (ANN), genetic programming Kosaka (1991) demonstrated the effectiveness of (GP). The focus is to develop quantitative metrics applying FL/ NNs to buy/sell timing detection and that characterize time series according to their portfolio selection. Wilson (1994) proposed a fully ability to be modeled by a particular method, such automatic stock trading system based on a five step as the predictability of a time series using the GP procedure. Frick (1996) investigated price-based and ANN approaches. heuristic trading rules by using a heuristic charting Emerging stock exchange applications (portfolio/ method with buy/ sell signals based on price winners selection, investment timing) provides changes and reversals. Based on a binary good examples for the use of this time series representation of those charts, they used GAs to predictability metric. The objective is to identify generate trade strategies from the classification of stocks that are more predictable for a given different price formations. Kassicieh (1997) modeling method by evaluating the predictability examined the performance of GAs in formulating value for each member of a set of financial time market-timing trading rules. The goal was to series, and ranking them according to their develop a strategy for deciding whether to be fully predictability value. Trading on higher ranked invested in a stock portfolio, or a riskless (higher predictability value) financial time series is investment. Inspired from Bauer (1994), their expected to have better return/risk performance ISBN: 978-960-6766-76-3 203 ISSN 1790-5109 9th WSEAS Int. Conf. on MATHEMATICS & COMPUTERS IN BUSINESS AND ECONOMICS (MCBE '08), Bucharest, Romania, June 24-26, 2008 inputs were differenced time series of 10 economic dependent. According to the No Free Lunch (NFL) indicators and the GA used the best three of these theorems [6], there is no search algorithm that can series to make the timing/ switching decision. outperform all other search algorithms over all Allen, Karjalainen (1999) used a GA to learn possible search problems. Kaboudan reported that technical trading rules for an index. The rules were genetic programming (GP) showed an equivalent or able to identify periods to be in the index when better performance in predicting stock price time daily returns were positive and volatility was low series than other methods. Artificial neural and out of the index when the reverse was true, but networks (ANN) are also recognized to be effective these latter results could largely be explained by in the problem of financial market forecasting [7]. low-order serial correlation in stock index returns. By design, the computed metric should approach Fernandez, Rodriguez (1999) investigated the zero for a complex signal that is badly distorted by profitability of a simple technical trading rule noise. Alternatively, the computed metric should based on NNs. In the absence of trading costs, the approach one for a time series with low complexity technical trading rule is always superior to a buy- and strongly deterministic signal. Kaboudan's η- and-hold strategy for both "bear" and "stable" metric measures the level of GP-predictability of a markets but that the reverse holds during a "bull" time series. market. Baba (2000) integrated NNs and GAs in an The goal is to investigate new time series intelligent decision support system (IDSS) capable predictability metrics with better behavior than to optimize decisions and based on the average Kaboudan's, which represents an original projected value and the then-current value. contribution in the field of time series analysis and Lowe (1994) demonstrated the efficiency of the data mining. This provides an explicit measure of use of NNs in effective portfolio optimization and time series predictability. short-term prediction of multiple equities. Wendt (1995) builded a portfolio efficient frontier by using 3.1. Autoregressive Integrated Moving GA technique. Guo, Huang (1996) proposed a Average (ARIMA) method for optimizing asset allocation by using The ARIMA model of order (p, P, q, Q), Zimmermann's fuzzy programming method. φ B φ B L z = δ + θ B L a , is limited by Jackson (1997) applied a GA to the problem of p ( ) P ( ) t Q ( ) t asset allocation, first using the traditional mean the requirement of stationarity; additionally, the variance approach and then using a direct utility residuals, the differences between the time series maximization method for a step utility function. He and the ARIMA model, are independent and compared the performance of GAs with the normally distributed. classical method of optimization and demonstrated the robustness to discontinuities in the search 3.2 Genetic Programming space, and sensitive to the starting values. Genetic algorithms (GA) adapt concepts Fogel [3] added noise to data generated by the (reproduction, recombination, mutation, survival of Lorenz system and the logistic system. Using GP the fittest, and populations) from evolutionary and Akaike's information criterion (AIC) [9], it was biology to fields of engineering, optimization, and demonstrated that signals with no noise are more machine learning. Such algorithms evolve predictable (measured by average prediction error) populations of candidate solutions to a problem than noisy ones. Their results suggest the potential with the goal of finding near optimal candidates. for evolving models of chaotic data, even in Koza [8] extended this genetic approach and background noise. Evolutionary programming can introduced the concept of genetic programming be used to optimize parameter estimates associated (GP). Each candidate solution in the search space is with models of chaotic time series in light of represented by a genetic program. Genetic observed data. Kaboudan [4] applied GP to programming is now widely recognized as an estimate the predictability of stock price time series. effective search paradigm in artificial intelligence, He tried to find the best-fit model for a time series databases, classification, robotics and many other using GP by minimizing the sum of squared error areas. (SSE). His predictability metric was defined based The major difference between GP and GA is that on comparing the SSE between the original time genetic program structures are not encoded as series and its reshuffled version. linear genomes, but as terms/ simple symbolic expressions. The units being mutated and recombined do not consist of characters or 3. Time series analysis, data mining command sequences but of functional modules, and time series predictability which can be represented as tree-structured chromosomes. The advantages of GP include its Time series modeling selection may be application ability to evolve arbitrarily complex equations ISBN: 978-960-6766-76-3 204 ISSN 1790-5109 9th WSEAS Int. Conf. on MATHEMATICS & COMPUTERS IN BUSINESS AND ECONOMICS (MCBE '08), Bucharest, Romania, June 24-26, 2008 without requiring a model with an a priori structure, terms of the objective function, f ()xi . and the flexibility in selecting the terminal set and 3. Mutate each parent x ,η to create a single function