The formula for the ADR is:
ADR FORMULA
(The number of issues in a market or index that have increased in price) /( the number of issues that decline in price)
9. Demand Index(DI)
Demand Index, DI, incorporates price and volume to give a ratio of buying pressure to selling pressure. DI is charted on an open scale and fluctuates above and below a zero line. When buying pressure is greater than selling pressure, the DI is above the zero line and vice versa. DI is one of the early volume indicators, developed in the 1970s by James Sibbet.
Many experienced traders feel that weekly studies can be particularly important in identifying the predominant trend, and DI is often assessed using weekly data.
The formula for the DI is:
DI FORMULA
(highest index + lowest index+2*close index)/4
information was reflected in the market transaction prices. In other words, future dynamism is random and unpredictable.
The ANN with fuzzy model has forecast average accuracy as high as 59.25%. With GA, it will have forecast average accuracy as high as 63.25%. In the experiment of two-period with SVM, the average accuracy is 62.3%. In multiperiod experiment the average accuracy is 64.6%.
With any influence factors as input variables, SVM poses average accuracy rate of 63.4%, outperforming 58.6% of ANN and 52.6% of DA. This is because that SVM locates the learning deviation with generalization theories, instead of reducing training deviation in ANN. Thus, overfitting issue from high variable dimensions can be avoided.
Such a feature makes SVM perform better in stock market dynamic forecast.
The SVM with fuzzy model in the study, with experiments of two-period and multiperiod methods, the forecast average accuracy is 70.25% and 71% respectively.
With GA into dynamically adjusted fuzzy model, the forecast accuracy rises to 70.75%
and 75%.
The forecast model in this study boasts the best forecast performance. From the experiment data, when the study includes three kinds of influence factors in proposed integrated model, the forecast accuracy is higher than that from single or two kinds of influence factors. This shows that more input variables help integrated forecast model reflect the relationship between stock market fluctuations. However, when ANN includes two or three kinds of influence factors, the difference between its average accuracy (59.25%)and those with single influence variable(58.6%) is merely 0.65%. This might be due to overfitting of ANN from too many noises.
In this study, GA dynamically adjusts the influential degree of each variable to reflect market changes. Without GA, influence of each variable μA(t) is 1. That is, prior to availability of next new values, the influential degree of each variable remains unchanged.
From the experiment data, for models in multiperiod experiment, GA improves the accuracy of 4%(71% to 75%). It does not provide significant help in models in two-period method. The average accuracy increase is only 0.5%(70.25% to 70.75%).
This is resulted from two-period method being unable to precisely simulate market fluctuations. Therefore, GA and multiperiod method bring high accuracy.
Table 7. Forecasting performance of different input variables with various forecast models
Input variable Accuracy
Hit ratio(%) Prediction
model
Technical indicators in stock market(20)
Macro -econ omic (21)
Technical indicators in future market (20)
multi period
two period
v v v 79 73
v v 77 70
v v 74 71
Proposed model
v v 70 69
Average 75 70.75
v v v 73 73
v v 72 70
V v 70 69
SVM with fuzzy model
v v 69 69
Average 71 70.25
v 67 65
v 69 66
SVM
v 58 56
Average 64.6 62.3
v v v 63
v v 63
v v 64
ANN with Fuzzy
model and
GA v v 63
Average 63.25
v v v 61
v v 62
v v 58
ANN with Fuzzy
model
v v 56
Average 59.25
v 61
v 62
ANN
v 53
Average 58.6
v 53
v 54
DA
v 51
Average 52.6
BH 50
Comparisons in graph are as shown in Figure 7 to Figure 9.
S+M+F S+M M+F S+F 60
65 70 75 80
ProposedModel SVM with fuzzy model
Fig. 7. Comparison between proposed model and SVM with fuzzy model under multiperiod method
S+M+F S+M M+F S+F
0 20 40 60 80
ProposedModel SVM with fuzzy model
ANN with Fuzzy model and GA ANN with Fuzzy model
Fig. 8. Comparison among each model under twoperiod method and integrated different influence factors
SVM ANN DA BH
S F 0
20 40 60 80
S M F
Fig. 9. Comparison between each model under twoperiod method and single kind of influence factors
Chapter Five Conclusion
We propose a forecast model integrating fuzzy theory, GA and SVM to forecast movements of stock market in Taiwan. The new dynamic fuzzy model proves not only effectively simulating market volatility but also covering influence factors of different features. The integrated high dimension variable, with features of SVM, increases the forecast accuracy of the integrated model. The higher stock market forecast dynamism accuracy represents that the forecast model better evaluates the internal mechanism of the market. The integrated forecast model in this study can serve as a valuable evaluation reference for researches on internal mechanism of stock market.
In this study, our main purpose is to design a forecast model to integrate various factors to deal the dynamic of stock market. However, due to the complicate and dynamic nature of stock market, merely estimating influence degree of each factor is not enough.
In real world, each factor may interact in every moment. In the future, factors interaction should be study more details.
References
1. Black, A.J., Mcmillan, D.G.: Non-linear Predictability of Value and Growth Stocks and Economic Activity. Journal of Business Finance & Accounting, Vol.31. Blackwell Publishing, Oxford(2004) 439-474
2. Lo, A., Mamaysky, H., Wang, J.: Foundations of Technical Analysis: Computational Algorithm, Statistical Inference, and Empirical Implementation. The Journal of Finance, Vol. 55. Blackwell Publishing, Oxford(2000) 1705-1765
3. Lo, A.: The Adaptive Markets Hypothesis: Market Efficiency from an Evolutionary Perspective. Journal of Portfolio Management, Vol. 30. Institutional Investor, NewYork(2004) 15-44
4. Kou, R.J.: A Decision Support System for The Stock Market through Integration of Fuzzy Neural Networks and Fuzzy Delphi. Applied Artificial Intelligence, Vol. 12.
Taylor & Francis Group, Philadelphia(1998) 501-520
5. Armano, G., Murru, A., Roli, F.: Stock Market Prediction By A Mixture of Genetic-Neural Experts. International Journal of Pattern Recognition and Artificial Intelligence, Vol. 16. World Scientific Publishing, Singapore(2002) 501-526
6. Matilla-Garcia, G.,Arguellu, C.: A Hybrid Approach based on Neural Networks and Genetic Algorithm to the Study of Profitability in the Spanish Stock Market. Applied Economics Letter, Vol. 12. Routledge part of the Taylor & Francis Group, Philadelphia(2005) 303-308
7. Oh, K.J., Kim, K.J.: Analyzing Stock Market Tick Data Using Piecewise Nonlinear Model. Expert Systems with Application, Vol. 22. Elsevier Science, Oxford(2002) 249-255
8. Azeem, M.F., Hanmandlu, M., Ahmad, N.: Evolutive Learning Algorithm for Fuzzy Modeling. International Journal of Smart Engineering System Design, Vol. 5. Taylor
& Francis Group, Philadelphia(2003) 205-224
9. Huang, W., Nakamori, Y., Wang, S.Y.: Forecasting Stock Market Movement Direction with Support Vector Machine. Computers and Operations Research, Vol. 32. Elsevier Science, Oxford(2004) 2513-2522
10. Yu, L., Wang, S., Lai, K.K.: Mining Stock Market Tendency Using GA-Based Support Vector Machines. Lecture Notes in Computer Science, Vol. 3828.
Springer-Verlag, Berlin Heidelberg(2005) 336-345
11. Schwert, G.W.: Why Does Stock Market Volatility Change Over Time. The Journal of Finance, Vol. 44. Blackwell Publishing, Oxford(1989) 1115-1167
12. Cristianini, N., Taylor, J.S.: An Introduction to Support Vector Machines. Cambridge University, New York(2000)
13. Noever, D., Baskaran, S.: Genetic Algorithms Trading on S&P 500. The Magazine of Artificial Intelligence in Finance, Vol. 1. Miller Freeman, San Francisco(1994) 41-50 14. Mahfoud, S., Mani, G.: Financial Forecasting Using Genetic Algorithms. Applied
Artificial Intelligence, Vol. 10. Taylor & Francis Group, Philadelphia(1996) 543-565 15. Muhammad, A., King, G.A.: Foreign Exchange Market Forecasting Using
Evolutionary Fuzzy Networked. Proc. IEEE 1997 Computational Intelligence for Financial Engineering, March 1997, 213-219
16. Kai, F., Xu, W.: Trading Neural Network with Genetic Algorithms for Forecasting the Stock Price Index. Proc. IEEE 1997 Int. Conf. Intelligent Processing Systems 1, Beijing China, Oct. 1997, 401-403
17. Vapnik V.N.: Statistical Learning Theory. New York: Wiley; 1998.
18. Vapnik V.N.: An Overview of Statistical Learning Theory. IEEE Transactions of Neural Networks, Vol. 10. IEEE(1999) 988–99.
19. Cao L.J., Tay, F.: Financial Forecasting Using Support Vector Machines. Neural Computing Applications, Vol. 10. (2001) 184–92
20. Tay, F., Cao L.J.: Application of Support Vector Machines in Financial Time Series Forecasting. Vol.29. Omega(2001) 309–17
21. Tay, F., Cao L.J.: A Comparative Study of Saliency Analysis and Genetic Algorithm for Feature Selection in Support Vector Machines. Vol.5. Intelligent Data Analysis(2001) 191–209
22. Tay F., Cao L.J.: Improved Financial Time Series Forecasting by Combining Support Vector Machines with Self-Organizing Feature Map. Vol.5. Intelligent Data Analysis (2001) 339–54
23. Tay F., Cao L.J.: Modified Support Vector Machines in Financial Time Series
Forecasting. Vol.48. Neurocomputing(2002) 847–61
24. Min, J.H., Najand, M.: A Futher Investigation of the Lead-Lag Relationship between the Spot Market and Stock Index Future: Early Evidence From Korea. Journal of Futures Markets, Vol. 19. John Wiley & Sons, New Jersey(1999) 217-232
25. Dickinson, D.G..: Stock Market Integration and Macroeconomic Fundamentals: An Empirical Analysis. Applied Financial Economics, Vol. 10. Routledge part of the Taylor & Francis Group, Philadelphia(2000) 261-276
26. Edwards, R. D.: Technical Analysis of Stock Trend. Boston, Mass. J. Magee Inc. New York(1992)
Appendix A Introduction to Fuzzy Theory
Fuzzy Sets
Fuzzy Set Theory was formalized by Professor Lofti Zadeh at the University of California in 1965. What Zadeh proposed is very much a paradigm shift that first gained acceptance in the Far East and its successful application has ensured its adoption around the world.
A paradigm is a set of rules and regulations which defines boundaries and tells us what to do to be successful in solving problems within these boundaries. For example the use of transistors instead of vacuum tubes is a paradigm shift - likewise the development of Fuzzy Set Theory from conventional bivalent set theory is a paradigm shift.
Bivalent Set Theory can be somewhat limiting if we wish to describe a 'humanistic' problem mathematically. For example, Fig 1 below illustrates bivalent sets to characterize the temperature of a room.[1]
The most obvious limiting feature of bivalent sets that can be seen clearly from the diagram is that they are mutually exclusive - it is not possible to have membership of more than one set ( opinion would widely vary as to whether 50 degrees Fahrenheit is 'cold' or 'cool' hence the expert knowledge we need to define our system is mathematically at odds with the humanistic world). Clearly, it is not accurate to define a
transiton from a quantity such as 'warm' to 'hot' by the application of one degree Fahrenheit of heat. In the real world a smooth (unnoticeable) drift from warm to hot would occur.
This natural phenomenon can be described more accurately by Fuzzy Set Theory. Fig.2 below shows how fuzzy sets quantifying the same information can describe this natural drift.[1]
Fuzzy Set Operations
Definitions
Universe of Discourse
The Universe of Discourse is the range of all possible values for an input to a fuzzy system.
Fuzzy Set
A Fuzzy Set is any set that allows its members to have different grades of membership (membership function) in the interval [0,1].
Support
The Support of a fuzzy set F is the crisp set of all points in the Universe of Discourse U such that the membership function of F is non-zero.
Crossover point
The Crossover point of a fuzzy set is the element in U at which its membership function is 0.5.
Fuzzy Singleton
A Fuzzy singleton is a fuzzy set whose support is a single point in U with a
membership function of one.
Fuzzy Set Operations Union
The membership function of the Union of two fuzzy sets A and B with membership functions and respectively is defined as the maximum of the two individual membership functions[1]:
Fig. 3 Introduction of Union
The Union operation in Fuzzy set theory is the equivalent of the OR operation in Boolean algebra.
Complement
The membership function of the Complement of a Fuzzy set A with membership function is defined as
Fig. 4 Introduction of Complement
The following rules which are common in classical set theory also apply to Fuzzy set theory.
De Morgans law
, Associativity
Commutativity
Distributivity
Reference
1. http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/sbaa/report.fuzzysets.html
2. Maneil, D., Freiberger, P.: Fuzzy Logic. New York Simon & Schusterc1993, New York(1993)
Appendix B Introduction to Genetic Algorithm
Among the set of search and optimization techniques, the development of Evolutionary Algorithms (EA) has been very important in the last decade. EAs are a set of modern heuristics used successfully in many applications with great complexity. It success on solving difficult problems.
Genetic Algorithms
A Genetic Algorithm (GA) is an heuristic used to find a vector x * (a string) of free parameters with associated values in an admissible region for which an arbitrary quality criterion is optimized:
A sequential genetic algorithm proceeds in an iterative manner by generating new populations of string from the old ones. Every string is the encoded version of a tentative solution. An evaluation function associates a fitness measure to every string indicating its suitability to the problem. The algorithm applies stochastic operators such as selection, crossover and mutation on an initially random population in order to compute a whole generation of new strings.
Since GAs apply operations drawn from nature, the nomenclature used in this field is closely related to the terms we can find in biology. The next table summarizes the meaning of these special terms in the aim of helping novel researchers.[1]
Table Nomenclature in EA[1]
Genotype The code, devised to represent the parameters of the problem in the form of a string.
Chromosome One encoded string of parameters (binary, Gray, floating point number, etc...).
Individual One of more chromosomes with an associated fitness value.
Gene The encoded version of a parameter of the problem being solve.
Allele Value which a gene can assume (binary, integer, etc...).
Locus The position that the gene occupies in the chromosome.
Phenotype Problem version of the genotype (algorithm version), suited for being evaluated.
Fitness Real value indicating the quality of an individual as a solution to the problem.
Environment The problem. This is represented as a function indication the suitability of phenotypes.
Population A set of individuals with their associated statistics (fitness average, Hamming distances, ...).
Selection Policy for selecting one individual from the population (selection of the fittest,...).
Crossover Operation that merges the genotypes of two selected parents to yield two new children.
Mutation Operation than spontaneously changes one or more alleles of the genotype.
.
Unlike most other optimization techniques, GAs maintain a population of tentative solution that are manipulated competitively by applying some variation operators to find a global optimum. This characteristic although is very useful to escape from local
optimum, it requires high computational resources (large memory and search times, for example), and thus various studies are being studied to design efficient GAs. With this goal numerous advances are continuously being achieved by designing new operators, hybrid algorithms, and more. One very important of such improvements consists in using parallel models of GAs (PGAs).
PGAs are not only parallel versions of sequential GAs. In fact they actually reach the ideal goal of having a parallel algorithm whose behavior is better than the sum of separate behaviors of its component sub-algorithms.
Sequential Genetic Algorithms
The sequential genetic algorithm operates on a population of strings or, in general, structures of arbitrary complexity representing tentative solutions. In textbook versions of GAs, every string is called an individual and it is composed of one or more chromosomes and a fitness value. Normally, an individual contains just one chromosome that represents the set of parameters called genes. Every gene is in turn encoded in (usually) binary by using a given number of alleles(0,1)[1][2].
Figure Some details on the genotype.
Algorithm 1. Pseudo-code for a sequential evolutionary algorithm.