Forecasting the BET-C Stock Forecasting the BET-C Stock Index with Artificial Neural Index with Artificial Neural

NetworksNetworks

DOCTORAL SCHOOL OF FINANCE AND BANKING DOFIN

ACADEMY OF ECONOMIC STUDIES

MSc Student: Stoica Ioan-Andrei

Supervisor: Professor Moisa Altar

July 2006

Stock Markets and PredictionStock Markets and Prediction

Predicting stock prices - goal of every investor trying to Predicting stock prices - goal of every investor trying to achieve profit on the stock market achieve profit on the stock market

predictability of the market - issue that has been discussed predictability of the market - issue that has been discussed

by a lot of researchers and academicsby a lot of researchers and academics Efficient Market Hypothesis - Eugene FamaEfficient Market Hypothesis - Eugene Fama three forms:three forms:

Weak: future stock prices can’t be predicted using past Weak: future stock prices can’t be predicted using past stock prices stock prices

Semi-strong: even published information can’t be used Semi-strong: even published information can’t be used

to predict future pricesto predict future prices Strong: market can’t be predicted no matter what Strong: market can’t be predicted no matter what

information is available information is available

Stock Markets and PredictionStock Markets and Prediction

Technical AnalysisTechnical Analysis ‘‘castles-in-the air’ castles-in-the air’ investors behavior and reactions according to these investors behavior and reactions according to these

anticipations anticipations Fundamental Analysis Fundamental Analysis

‘‘firm foundations’firm foundations’ stocks have an intrinsic value determined by present stocks have an intrinsic value determined by present

conditions and future prospects of the companyconditions and future prospects of the company Traditional Time Series AnalysisTraditional Time Series Analysis

uses historic data attempting to approximate future uses historic data attempting to approximate future

values of a time series as a linear combinationvalues of a time series as a linear combination Machine Learning - Artificial Neural NetworksMachine Learning - Artificial Neural Networks

The Artificial Neural NetworkThe Artificial Neural Network

computational technique that computational technique that benefits from techniques similar benefits from techniques similar to those employed in the human to those employed in the human brain brain

1943 - W.S. McCulloch and W. 1943 - W.S. McCulloch and W. Pitts attempted to mimic the Pitts attempted to mimic the ability of the human brain to ability of the human brain to process data and information and process data and information and comprehend patterns and comprehend patterns and dependencies dependencies

The human brain - a complex, The human brain - a complex, nonlinear and parallel computer nonlinear and parallel computer

The neurons:The neurons: elementary information elementary information

processing unitsprocessing units building blocks of a building blocks of a

neural network neural network

The Artificial Neural NetworkThe Artificial Neural Network

semi-parametric approximation methodsemi-parametric approximation method Advantages:Advantages:

ability to detect nonlinear dependenciesability to detect nonlinear dependencies parsimonious compared to polynomial expansionsparsimonious compared to polynomial expansions generalization ability and robustness generalization ability and robustness no assumptions of the model have to be made no assumptions of the model have to be made flexibilityflexibility

Disadvantages:Disadvantages: has the ‘black box’ propertyhas the ‘black box’ property training requires an experienced usertraining requires an experienced user training takes a lot of time, fast computer neededtraining takes a lot of time, fast computer needed overtraining overtraining overfitting overfitting undertraining undertraining underfitting underfitting

The Artificial Neural NetworkThe Artificial Neural Network

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The Artificial Neural NetworkThe Artificial Neural Network

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The Artificial Neural NetworkThe Artificial Neural Network

Overtraining/OverfittingOvertraining/Overfitting

The Artificial Neural NetworkThe Artificial Neural Network

Undertraining/UnderfittingUndertraining/Underfitting

Architecture of the Neural Architecture of the Neural

NetworkNetwork Types of layers:Types of layers:

input layer: number of neurons = number of inputsinput layer: number of neurons = number of inputs output layer: number of neurons = number of outputsoutput layer: number of neurons = number of outputs hidden layer(s): number of neurons = trial and errorhidden layer(s): number of neurons = trial and error

Connections between neurons:Connections between neurons: fully connectedfully connected partially connectedpartially connected

The activation function:The activation function: threshold function threshold function piecewise linear function piecewise linear function sigmoid functionssigmoid functions

The feed forward networkThe feed forward network

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The Feed forward Network with Jump The Feed forward Network with Jump

ConnectionsConnections

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The Recurrent Neural Network - ElmanThe Recurrent Neural Network - Elman

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Training the Neural NetworkTraining the Neural Network

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Ψ – loss function

Ψ nonlinear nonlinear optimization problem

- backpropagation

- genetic algorithm

The Backpropagation AlgorithmThe Backpropagation Algorithm

alternative to quasi-Newton gradient descent alternative to quasi-Newton gradient descent ΩΩ00 – randomly generated – randomly generated

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ρρ – learning parameter, in [.05,.5] – learning parameter, in [.05,.5] after n iterations: after n iterations: μμ=0.9, momentum parameter=0.9, momentum parameter

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problem: local minimum points problem: local minimum points

The Genetic AlgorithmThe Genetic Algorithm

based on Darwinian lawsbased on Darwinian laws Population Creation:Population Creation: N random vectors of weights N random vectors of weights Selection Selection (Ωi Ωj) parent vectors(Ωi Ωj) parent vectors Crossover & Mutation Crossover & Mutation C1,C2 C1,C2 children vectors children vectors Election Tournament: Election Tournament: the fittest 2 vectors passed the fittest 2 vectors passed

to the next generationto the next generation Convergence: Convergence: G* generationsG* generations G*G* - large enough so there are no significant - large enough so there are no significant

changes in the fitness of the best individual for changes in the fitness of the best individual for several generationsseveral generations

Experiments and ResultsExperiments and Results

BET-C stock index – daily closing prices, 16 April 1998 until 18 May BET-C stock index – daily closing prices, 16 April 1998 until 18 May 2006 2006

daily returns: daily returns:

conditional volatility - rolling 20-day standard deviation: conditional volatility - rolling 20-day standard deviation:

BDS-Test for nonlinear dependencies:BDS-Test for nonlinear dependencies: HH00: i.i.d. data: i.i.d. data

BDSBDSm,m,εε~N(0,1)~N(0,1)

Data

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ε=1 ε=1.5 ε=1 ε=1.5 ε=1 ε=1.5

OD 16.6526 17.6970 18.5436 18.7202 19.7849 19.0588

ARF 16.2626 17.2148 18.3803 18.4839 19.7618 18.9595

Experiments and ResultsExperiments and Results 3 types of Ann's:3 types of Ann's:

feed-forward networkfeed-forward network feed-forward network with jump connectionsfeed-forward network with jump connections recurrent networkrecurrent network

Input: [Rt-1 Rt-2 Rt-3 Rt-4 Rt-5] & Vt Input: [Rt-1 Rt-2 Rt-3 Rt-4 Rt-5] & Vt Output: next-day-return Rt Output: next-day-return Rt Training: genetic algorithm & backpropagationTraining: genetic algorithm & backpropagation Data divided in:Data divided in:

training set – 90%training set – 90% test set – 10%test set – 10%

one-day-ahead forecasts - static forecastingone-day-ahead forecasts - static forecasting Network: Network:

trained 100 timestrained 100 times best 10 – SSEbest 10 – SSE best 1 - RMSEbest 1 - RMSE

Experiments and ResultsExperiments and Results

In-sample Criteria In-sample Criteria

Out-of-sample CriteriaOut-of-sample Criteria

Pesaran-Timmerman Test for Directional Accuracy: Pesaran-Timmerman Test for Directional Accuracy: HH0 0 : signs of the forecast and those of the real data : signs of the forecast and those of the real data

are independent are independent DA~N(0,1)DA~N(0,1)

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Experiments and ResultsExperiments and Results

ROI - trading strategy based on the sign forecasts:ROI - trading strategy based on the sign forecasts:

+ buy sign+ buy sign - sell sign- sell sign

Finite differences: Finite differences:

Benchmarks

Naïve model: RNaïve model: Rt+1t+1=R=Rtt

buy-and-hold strategybuy-and-hold strategy AR(1) model – LS – overfitting:AR(1) model – LS – overfitting:

RMSERMSE MAEMAE

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Experiments and ResultsExperiments and Results

Naïve AR(1) FFN – no vol FFN FFN-jump RN

R2 - 0.079257 0.083252 0.083755 0.084827 0.091762

SSE - 0.332702 0.331258 0.331077 0.330689 0.328183

RMSE 0.015100 0.011344 0.011325 0.011304 0.011332 0.011319

MAE 0.011948 0.008932 0.008929 0.008873 0.008867 0.008892

HR 55.77% (111) 56.78% (113) 57.79% (115) 59.79% (119) 59.79% (119) 59.79% (119)

ROI 0.265271 0.255605 0.318374 0.351890 0.331464 0.412183

RP 15.02% 14.47% 18.02% 19.92% 18.77% 23.34%

PT-Test - - 14.79 15.01 15.01 14.49

B&H 0.2753 0.2753 0.2753 0.2753 0.2753 0.2753

FFN FFN-jump RN

Volatility -0.1123 -0.1358 -0.1841

Experiments and ResultsExperiments and Results

Actual, fitted ( training sample)

Experiments and ResultsExperiments and Results

Actual, fitted ( test sample)

ConclusionsConclusions

RMSE and MAE < AR(1) RMSE and MAE < AR(1) no signs of overfitting no signs of overfitting RR22 < 0.1 < 0.1 forecasting magnitude is a failure forecasting magnitude is a failure sign forecasting ~60% sign forecasting ~60% success success Volatility: Volatility:

improves sign forecastimproves sign forecast finite differences finite differences negative correlation negative correlation perceived as measure of riskperceived as measure of risk

trading strategy: outperforms naïve model and buy-and-trading strategy: outperforms naïve model and buy-and-holdhold

quality of the sign forecast – confirmed by Pesaran-quality of the sign forecast – confirmed by Pesaran-Timmerman testTimmerman test

Further developmentFurther development

Volatility: other estimatesVolatility: other estimates neural classificator: specialized in sign neural classificator: specialized in sign

forecastingforecasting using data outside the Bucharest Stock using data outside the Bucharest Stock

Exchange:Exchange: T-Bond yields T-Bond yields exchange rates exchange rates indexes from foreign capital markets indexes from foreign capital markets