Title: Predicting Stock Prices
Abstract
This paper examines the use of Markov–switching model in predicting stock prices. It also examines the market long-runs and reversals. They are two advantages of this approach. First, data will be used to classify the market and second, accountability of the possible movements in the market both prior and during the holding period. It will also examine the methodology used in developing the Markov–switching model in the paper. Historically, they have been various attempts made in trying to explain, understand and predict future stock prices. The paper will look into some of the models and why they have not been that successful when compared to the Markov Model.
Introduction
A lot of research has been done to understand and predict both short and long-term price movements. Attempts in developing risk-based models to accurately predict these changes in price have largely been unsuccessful (Cooper et al 2003). However, various theories have been developed to help explain, understand and predict possible price movements. One such theory DeBondt and Thaler (1985) and Jegadeesh and Titman (1993) developed as a behavioral model explain the anomalies that occur in the market and result in prices changes (Cooper, Gutierrez, and Hameed, 2003). Therefore, the theory attempts to explain an investor reaction to new information in the market.
However, in this proposal Markov –switching model was used. Therefore, using this approach has two advantages in trying to explain this market phenomenon. First, data will be used to classify the market and second, accountability of the possible movements in the market both prior and during the holding period. Therefore, empirical studies can be carried out.
Purpose of the Study
This project aims to evaluate the Markov forecasting model which predicts the state of an object in a period of time to the future using the probability vector of the prior state and the transition probability matrix. This is made possible using the Markov chain.
An efficient stock market with no constant price shows the homogeneous allocation of market information, though there is the possibility of predicting the probable future tendency of the stock market by analysis of the past data. This information offers the investors with appropriate reference model so as to evade poor tendencies.
Literature Review
The Markov chain, named after its proprietor Andrey Markov, refers to a mathematical system that transition from one state to another, between a countable or finite number probable state. It is a random process where the next state depends purely on the present state as opposed to the sequence of events that came before it. In other words, the method has the property that, considering the present, the future is largely conditionally independent of the past.
Debate is however rife as to whether one is able to predict the stock market. The price shift in the stock is connected to alterations in just fundamental values. Prior studies have been unable to predict non-linear aspects in the data sets. In the current time, the Artificial Intelligence and neutral networks have been applied to predict the cost of stock for organizations.
Traders are known to apply technical tools to help them in investing choices (Daniel, Hirshleifer and Subrahmanyam, 1998). They depend on more than one method to determine future price of shares. In another interesting study, the use of stochastic model for example Markov Chains to the stocks is useful to getting a better understanding of the stock price changes. In general, a number of studies are targeted at predicting future prices but none looks at the trend in the market.
Thesis
This study looks to apply the Markov Chain framework to determine the stock market tendency of a number of world stock indices. The outcome of the tendency prediction applying the Markov Chain Model is contrasted with the outcome acquired using the traditional tendency methods. The prediction of the tendency applying the Markov Chain Method is done for over a period of time, short to long term.
Methods
The Markov chain has the property that the probabilities using how the procedure will change in coming times rely on the current state as well as the independent events that past. The stochastic process {Xt} has the Markovian property if P {Xt+1 = j/X0 = k0, X1 = k1,…..Xt-1 = kt-1, Xt = i} = P { Xt+1 = j/Xi = I, for t =0,1,….and sequence I, j, k0, kj,.. kt-1.
The Markovian property states that the conditional forecast of a future happening with availability of the past happening and current situation Xt = I is not reliant on the past happening and relies just on the current state (Vasanthi, et al, 2011). The situational probabilities P{Xt+1 = j/Xt = i} pij are termed to as transitional probabilities. They may be arranged in the form of a matrix called Transitional Probability Matrix;
P = p11 p12 – p1n
p21 p22 – p2n
- – – –
pn1 – – pnn
The matrix has these attributes,
Pij > 0 for all I and j.
Summation of pij = 1 for 1 and j showing the total probability of the transition from I to another state.
The diagonal aspect shows the transition.
To use Markov to share market trend, the share price is attributed as a system that is changing between states (Vasanthi, et al, 2011). A transition probability matrix is created from the past trends and this matrix in connection to probability values of the current state is applied to know the probabilities of the following state.
The value on time n is rn (n = 1,2, N+1). A definition of the random aspects is given.
Yn = 0 with the share index < 0,
Yn = 1, with share index > 0
Taking that Yn uses a stationary first order Markov chain and future trend of Yn relying on the current state.
If the transition matrix of Yn is: P = p11, p12
P21, p22
0<pij<1,Pil + Pi2 = 1 for I=1,2 ; j=1,2
Pij will be the conditional probability of shifting to j from i.
Analysis and Discussion
The Markov Chain is used stocks within a certain period of time. So as to acquire efficiency of this model in predicting stock index tendency, it is linked with the present state. With the application of the forecast models, the stock index figures of chosen indices are forecast for that period and the approximated figures are changed to probability. The probability is hence placed into comparison with the Markov Chain.
The stock market additionally has the ability to predict with the application of the Markov Model within any time period. The outcome is place into tables, where they are comparing with the real tendency and it is noted that Markov Model has predicted the tendency correctly for indices applied.
Conclusions
Markov Chain Model is applied to predict the tendency on a daily basis of a number of world stock indices and placed into comparison with the outcome of the traditional models applied. The Markov Model is way better than the traditional models as it has a high level of accuracy, this may be attributed to the daily alteration of the index figures and sets them into Bullish and Bearish conditions (Maheu and McCurdy, 2000). Moreover, the movement from a state to another is computed using the transition probability matrix model. This is as it is applied to predict the future tendency. The mode is useful in that it is vital in noting the future tendency of the stock market. It would be vital indicator for the investor to acquire a better form of investment choices.
References
Cooper, M., Gutierrez, R., and Hameed, A. (2003), “Market States and Momentum”, Working
paper, forthcoming in Journal of Finance 2004.
Daniel, K., Hirshleifer, D. and Subrahmanyam, A., (1998), “Investor Psychology and Security
Market Under- and Overreactions”. Journal of Finance, Vol. LIII, No. 6.
Maheu, J.M., and McCurdy, T., (2000), “Identifying bull and bear markets in stock returns”,
Journal of Business & Economic Statistics, Jan 2000, 18, 1, 100-112
Vasanthi, S., et al (2011), An Empirical Study On Stock Index Trend Prediction Using Markov Chain Analysis, JBFSIR , Vol. 1, Issue 1.
