The Stock Market prediction task divides researchers and academics into two groups those who believe that we can devise mechanisms to predict the market and those who believe that the market is efficient and whenever new information comes up the market absorbs it by correcting itself, thus there is no space for prediction (EMH). Furthermore they believe that the Stock Market follows a Random Walk, which implies that the best prediction you can have about tomorrow's value is today's value.

In literature a number of different methods have been applied in order to predict Stock Market returns. These methods can be grouped in four major categories: i) Technical Analysis Methods, ii) Fundamental Analysis Methods, iii) Traditional Time Series Forecasting and iv) Machine Learning Methods. Technical analysts, known as chartists, attempt to predict the market by tracing patterns that come from the study of charts which describe historic data of the market. Fundamental analysts study the intrinsic value of an stock and they invest on it if they estimate that its current value is lower that its intrinsic value. In Traditional Time Series forecasting an attempt to create linear prediction models to trace patterns in historic data takes place. These linear models are divided in two categories: the univariate and the multivariate regression models, depending on whether they use one of more variables to approximate the Stock Market time series. Finally a number of methods have been developed under the common label Machine Learning these methods use a set of samples and try to trace patterns in it (linear or non-linear) in order to approximate the underlying function that generated the data.

~~STOCK MARKETS AND PREDICTION~~

Investment Theories:An investment theory suggests what parameters one should take into account before placing his (or her) capital on the market. Traditionally the investment community accepts two major theories: the Firm Foundation and the Castles in the Air. Reference to these theories allows us to understand how the market is shaped, or in other words how the investors think and react. It is this sequence of 'thought and reaction' by the investors that defines the capital allocation and thus the level of the market.

There is no doubt that the majority of the people related to stock markets is trying to achieve profit. Profit comes by investing in stocks that have a good future (short or long term future). Thus what they are trying to accomplish one way or the other is to predict 16 the future of the market. But what determines this future? The way that people invest their money is the answer; and people invest money based on the information they hold. Therefore we have the following schema:

INFORMATION → INVESTOR → MARKET LEVEL

The factors that are under discussion on this schema are: the content of the 'Information' component and the way that the 'Investor' reacts when having this info.

On the other hand, according to the Castles in the Air theory the investors are triggered by information that is related to other investors' behavior. So for this theory the only concern that the investor should have is to buy today with the price of 20 and sell tomorrow with the price of 30, no matter what the intrinsic value of the firm he (or she) invests on is.

Prediction Methods:The prediction of the market is without doubt an interesting task. In the literature there are a number of methods applied to accomplish this task. These methods use various approaches, ranging from highly informal ways (e.g. the study of a chart with the fluctuation of the market) to more formal ways (e.g. linear or non-linear regressions). We have categorized these techniques as follows:

**1.Technical Analysis:**

"Technical analysis is the method of predicting the appropriate time to buy or sell a stock used by those believing in the castles-in-the-air view of stock pricing". The idea behind technical analysis is that share prices move in trends dictated by the constantly changing attributes of investors in response to different forces. Using technical data such as price, volume, highest and lowest prices per trading period the technical analyst uses charts to predict future stock movements. Price charts are used to detect trends, these trends are assumed to be based on supply and demand issues which often have cyclical or noticeable patterns.

From the study of these charts trading rules are extracted and used in the market environment. The technical analysts are known and as 'chartists'. Most chartists believe that the market is only 10 percent logical and 90 percent psychological. The chartist's belief is that a careful study of what the other investors are doing will shed light on what the crowed is likely to do in the future.

This is a very popular approach used to predict the market, which has been heavily criticized. The major point of criticism is that the extraction of trading rules from the study of charts is highly subjective therefore different analysts might extract different trading rules by studying the same charts. Although it is possible to use this methodology to predict the market on daily basis we will not follow this approach on this study due to its subjective character.

**2.Fundamental Analysis:**

"Fundamental analysis is the technique of applying the tenets of the firm foundation theory to the selection of individual stocks". The analysts that use this method of prediction use fundamental data in order to have a clear picture of the firm (industry or market) they will choose to invest on. They are aiming to compute the 'real' value of the asset that they will invest in and they determine this value by studying variables such as the growth, the dividend payout, the interest rates, the risk of investment, the sales level, the tax rates an so on. Their objective is to calculate the intrinsic value of an asset (e.g. of a stock). Since they do so they apply a simple trading rule. If the intrinsic 21 value of the asset is higher than the value it holds in the market, invest in it. If not, consider it a bad investment and avoid it. The fundamental analysts believe that the market is defined 90 percent by logical and 10 percent by physiological factors. This type of analysis is not possible to fit in the objectives of our study. The reason for this is that the data it uses in order to determine the intrinsic value of an asset does not change on daily basis. Therefore fundamental analysis is helpful for predicting the market only in a long-term basis.

**3.Traditional Time Series Prediction**:

The Traditional Time Series Prediction analyzes historic data and attempts to approximate future values of a time series as a linear combination of these historic data. In econometrics there are two basic types of time series forecasting: univariate (simple regression) and multivariate (multivariate regression). These types of regression models are the most common tools used in econometrics to predict time series. The way they are applied in practice is that firstly a set of factors that influence (or more specific is assumed that influence) the series under prediction is formed. These factors are the explanatory variables xi of the prediction model.

Then a mapping between their values xit and the values of the time series yt (y is the to-be explained variable) is done, so that pairs {xit , yt} are formed. These pairs are used to define the importance of each explanatory variable in the formulation of the to-be explained variable. In other words the linear combination of xi that approximates in an optimum way y is defined. Univariate models are based on one explanatory variable (I=1) while multivariate models use more than one variable (I>1). Regression models have been used to predict stock market time series. A good example of the use of multivariate regression is the work of Pesaran and Timmermann (1994) .

They attempted prediction of the excess returns time series of S&P 500 and the Dow Jones on monthly, quarterly and annually basis. The data they used was from Jan 1954 until Dec 1990. Initially they used the subset from Jan 1954 until Dec 1959 to adjust the coefficients of the explanatory variables of their models, and then applied the models to predict the returns for the next year, quarter and month respectively.

**Machine Learning Methods**:

Several methods for inductive learning have been developed under the common label "Machine Learning". All these methods use a set of samples to generate an approximation of the underling function that generated the data. The aim is to draw conclusions from these samples in such way that when unseen data are presented to a model it is possible to infer the to-be explained variable from these data. The methods we discuss here are: The Nearest Neighbor and the Neural Networks Techniques. Both of these methods have been applied to market prediction; particularly for Neural Networks there is a rich literature related to the forecast of the market on daily basis.

**PREDICTION USING NEURAL NETWORKS**

The experiment consisted of three phases (Figure A). In the first phase a genetic algorithm (GA) searched the space of NNs with different structures and resulted a generation with the fittest of all networks searched based on a metric which was either: TheilA or TheilB or TheilC or MAE. The GA search was repeated three times for each metric. Then the best three networks were selected from each repetition of the GA search and for each one of the metrics.

The output of the first phase was a set of thirtysix network structures. In the second phase for each one of the thirty-six resulting network structures we applied the following procedure. We trained (on Training1 set) and validated (on Validation1 set) the network. Then we used the indicated number of epochs from the validation procedure and based on it we retrained the network on the Training1 plus the Validation1 set. Finally we tested the performance of the network on unseen data (Validation2 set).

This procedure was repeated 50 times for each network structure for random initializations of its weights. From the nine networks for each performance statistic, we selected the most stable in terms of standard deviation of their performance. Thus the output of the second phase was a set of four network structures. During the third phase for each one of these four networks we applied the following procedure 50 times. We trained each network on the first half of the Training Set and we used the remaining half for validation. Then, using the indicated epochs by the validation procedure, we retrained the network on the complete Training Set. Finally we tested the network on the Test Set calculating all four metrics.

The performance for each network on each metric was measured again in terms of standard deviation and mean of its performance over 50 times that it was trained, validated and tested.

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