Abstract
This paper compares the accuracy of three hybrid intelligent systems in forecasting ten international stock market indices; namely the CAC40, DAX, FTSE, Hang Seng, KOSPI, NASDAQ, NIKKEI, S&P500, Taiwan stock market price index, and the Canadian TSE. In particular, genetic algorithms (GA) are used to optimize the topology and parameters of the adaptive time delay neural networks (ATNN) and the time delay neural networks (TDNN). The third intelligent system is the adaptive neuro-fuzzy inference system (ANFIS) that basically integrates fuzzy logic into the artificial neural network (ANN) to better model information and explain decision making process. Based on out-of-sample simulation results, it was found that contrary to the literature GA-TDNN significantly outperforms GA-ATDNN. In addition, ANFIS was found to be more effective in forecasting CAC40, FTSE, Hang Seng, NIKKEI, Taiwan, and TSE price level. In contrary, GA-TDNN and GA-ATDNN were found to be superior to ANFIS in predicting DAX, KOSPI, and NASDAQ future prices.
TopIntroduction
Since trading financial assets is a highly risky task, investors and portfolio managers need accurate predicting systems. However, financial assets time series are nonlinear and non-stationary. Therefore, they mostly follow a noisy path. The nonlinearity implies that asset prices do not follow a linear pattern, and non-stationary implies that their dynamics change over time. As a result, sophisticated systems were proposed to model the underlying financial time series by capturing the above patterns in order to provide accurate forecasts (Lahmiri, 2013, 2014a, 2014b, 2014c; Lahmiri & Boukadoum, 2014a, 2014b; Lahmiri, Boukadoum, & Chartier, 2014a, 2014b; Lahmiri & Boukadoum, 2015a, 2015b). In the 2000s, nonlinear and adaptive forecasting models such as artificial neural networks (ANNs) have become popular intelligent systems widely used in stock market modeling and forecasting (Zimmermann, Neuneier & Grothmann, 2001; Yao & Tan, 2000; Atsalakis & Valavanis, 2009; Huang & Wu, 2010; Hsieh, Hsiaso & Yeh, 2011; Wang et al, 2011). In general, previous works (Zimmermann, Neuneier & Grothmann, 2001; Yao & Tan, 2000; Atsalakis & Valavanis, 2009a) have shown that ANNs were superior to traditional statistical models such as the well known auto-regressive integrated moving average (ARIMA) models (Box & Jenkins, 1970). Indeed, ARIMA models are based on the assumptions that the time series are stationary and that the errors of the model are normally distributed. Unfortunately, financial data do not meet those criteria and, as a result, the techniques based on statistical approaches could not provide accurate financial forecasts. However, the ANN systems suffer several disadvantages, namely dependency on network architecture, type of transfer function, parameters choice, and being considered as a black-box.
To overcome these disadvantages, hybrid soft computing systems were proposed in the literature. These systems combine synergistically ANNs and other soft computing models to obtain complementary hybrid intelligent system models. For instance, genetic algorithms (Goldberg, 1989) were proposed to automatically optimize the topology and parameters of ANNs (Yao, 1999), and fuzzy logic (Zadeh, 1965) was incorporated into ANN resulting in adaptive neuro-fuzzy inference system (ANFIS) (Jang, 1993). In particular, in one hand ANN is capable to recognize patterns and adapt to data. On the other hand, fuzzy inference systems incorporate human knowledge and expertise to make fuzzy inference and decision (Jang, 1993; Atsalakis & Valavanis, 2009b).
Key Terms in this Chapter
Artificial Neural Network: An artificial neural network is an information processing system which is inspired by the human nervous system for information processing. It can be trained to simulate a number of outputs in response to provided inputs.
Fuzzy Logic: It is a type of reasoning designed to mathematically represent uncertainty and vagueness where logical statements are not only true or false. Fuzzy logic is a formalized mathematical tool which is useful to deal with imprecise problems.
Stock Market: It is a particular market where stocks and bonds are issued by companies and are publically traded.
Genetic Algorithm: It is a stochastic but not random method of search used for optimization or learning. Genetic algorithm is basically a search technique that simulates biological evolution during optimization process.
Backpropagation algorithm: It is a training algorithm for artificial neural network based on calculation of the gradient of a loss function to optimize weights in neural network.
Learning Algorithm: A learning algorithm is a method used to process data to extract patterns appropriate for application in a new situation. In particular, the goal is to adapt a system to a specific input-output transformation task.