Forecasting the BET-C Stock Index with

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Forecasting the BET
-
C Stock Index with
Artificial Neural Networks

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 Prediction



Predicting stock prices
-

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


predictability of the market
-

issue that has been discussed by a lot of
researchers and academics



Efficient Market Hypothesis
-

Eugene Fama


three forms:


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


Semi
-
strong: even published information can’t be used to predict future
prices



Strong: market can’t be predicted no matter what information is available

Stock Markets and Prediction


Technical Analysis


‘castles
-
in
-
the air’


investors behavior and reactions according to these anticipations


Fundamental Analysis


‘firm foundations’


stocks have an intrinsic value determined by present conditions and
future prospects of the company


Traditional Time Series Analysis


uses historic data attempting to approximate future values of a time series
as a linear combination



Machine Learning
-

Artificial Neural Networks

The Artificial Neural Network


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


1943
-

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


The human brain
-

a complex,
nonlinear and parallel computer


The neurons:


elementary information
processing units


building blocks of a
neural network

The Artificial Neural Network


semi
-
parametric approximation method



Advantages:


ability to detect nonlinear dependencies


parsimonious compared to polynomial expansions


generalization ability and robustness


no assumptions of the model have to be made


flexibility


Disadvantages:


has the ‘black box’ property


training requires an experienced user


training takes a lot of time, fast computer needed



overtraining


overfitting


undertraining


underfitting


The Artificial Neural Network

The Artificial Neural Network

The Artificial Neural Network

Overtraining/Overfitting

The Artificial Neural Network

Undertraining/Underfitting

Architecture of the Neural Network



Types of layers:


input layer: number of neurons = number of inputs


output layer: number of neurons = number of outputs


hidden layer(s): number of neurons = trial and error



Connections between neurons:


fully connected


partially connected


The activation function:


threshold function


piecewise linear function


sigmoid functions

The feed forward network


m = number of hidden layer neurons

n = number of inputs

The Feed forward Network with Jump Connections


The Recurrent Neural Network
-

Elman

allows the neurons to depend on their own lagged values


building ‘memory’ in their evolution

Training the Neural Network


Objective: minimizing the discrepancy between real data and the output of the network

Ω
-

the set of parameters

Ψ


loss function

Ψ nonlinear


nonlinear optimization problem

-

backpropagation

-

genetic algorithm


The Backpropagation Algorithm


alternative to quasi
-
Newton gradient descent


Ω
0



randomly generated


ρ



learning parameter, in [.05,.5]


after n iterations:
μ
=0.9, momentum parameter


problem: local minimum points

The Genetic Algorithm


based on Darwinian laws


Population Creation:

N random vectors of weights


Selection


(Ωi Ωj) parent vectors


Crossover & Mutation


䌱ⱃ,

children vectors


Election Tournament:
the fittest 2 vectors passed to the next
generation


Convergence:
G* generations


G*

-

large enough so there are no significant changes in the
fitness of the best individual for several generations

Experiments and Results



BET
-
C stock index


daily closing prices, 16 April 1998 until 18 May 2006


daily returns:






conditional volatility
-

rolling 20
-
day standard deviation:





BDS
-
Test for nonlinear dependencies:


H
0
: i.i.d. data


BDS
m,
ε
~N(0,1)




Data

Series

m=2

m=3

m=4

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 Results


3 types of Ann's:


feed
-
forward network


feed
-
forward network with jump connections


recurrent network


Input: [Rt
-
1 Rt
-
2 Rt
-
3 Rt
-
4 Rt
-
5] & Vt


Output: next
-
day
-
return Rt


Training: genetic algorithm & backpropagation


Data divided in:


training set


90%


test set


10%


one
-
day
-
ahead forecasts
-

static forecasting


Network:


trained 100 times


best 10


SSE


best 1
-

RMSE

Experiments and Results


In
-
sample Criteria





Out
-
of
-
sample Criteria






Pesaran
-
Timmerman Test for Directional Accuracy:


H
0
: signs of the forecast and those of the real data are independent


DA~N(0,1)


Evaluation Criteria

Experiments and Results


ROI
-

trading strategy based on the sign forecasts:


+ buy sign



-

sell sign


Finite differences:

Benchmarks


Naïve model: R
t+1
=R
t


buy
-
and
-
hold strategy


AR(1) model


LS


overfitting:


RMSE


MAE


Experiments and Results

Naïve

AR(1)

FFN


no vol

FFN

FFN
-
jump

RN

R
2

-

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 Results

Actual, fitted ( training sample)

Experiments and Results

Actual, fitted ( test sample)

Conclusions


RMSE and MAE < AR(1)


no signs of overfitting


R
2

< 0.1


forecasting magnitude is a failure


sign forecasting ~60%


success


Volatility:


improves sign forecast



finite differences


negative correlation


perceived as measure of risk


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


quality of the sign forecast


confirmed by Pesaran
-
Timmerman
test

Further development



Volatility: other estimates


neural classificator: specialized in sign forecasting


using data outside the Bucharest Stock Exchange:


T
-
Bond yields


exchange rates


indexes from foreign capital markets