Application of neural networks for investigating dayoftheweek effect in stock market

1
Application of neural networks for investigating
day-of-the-week effect in stock market

• Virgilijus Sakalauskas, Dalia Krikciuniene
• Department of Informatics, Vilnius University,
  Lithuania
• 2007-10-30

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Goals of the research

• to discuss
• methods for measuring the day-of-the-week effect
• to examine
• if the dependencies of developed stock markets
  are still important in the emerging securities
  markets with low turnover and comparatively small
  number of market players
• to test
• the effectiveness of the suggested method by
  using empirical data of OMX Vilnius Stock
  Exchange (as of the case of emerging stock
  market), daily return values of the 24 most
  traded shares (out of 44 listed)

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Goals of the research

• to compare
• effectiveness of application of Neural Networks
  for recognizing the day-of-the-week effect, as
  compared to the traditional linear statistical
  methods.
• to explore
• impact of different variables, which could e
  influenced by the day-of-the-week effect and make
  their sensitivity analysis
• to select
• best performing neural network type.

4
Day-of-the-week effect

• In the extensive study of market anomalies,
  nearly 9,500 different calendar effects were
  tested. The research was based on analysis of Dow
  Jones daily data, registered during 100 years
  period, and of about 25 years of SP500 daily
  data (Sullivan, R., Timmermann, A., White,
  H.,1998)
• The day-of-the-week effect is understood as
  significantly different stock returns in
  different days of a week
• The day-of-the-week effect anomaly makes us doubt
  the hypothesis of market efficiency
• Developing methods for predicting any divergences
  from the efficient market hypothesis may allow us
  to develop profitable trading strategies, and to
  decrease the investment risk

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Features of the day-of-the-week effect

• Daily stock returns tend to be lower on Mondays
  and higher on Fridays, or the first and the last
  trading days of a week (Balaban, E., Bayar, A.
  and Kan, O.B. (2001), Flannery, M. J. 1988,
  Kohers, G. 2004)
• The day-of-the-week effect was clearly evident in
  the vast majority of the developed markets,
  starting from 1980 (Kamath, R. 2002, Steeley, J.
  M. 2001)
• The effect is reported to be fading away in the
  1990s (Brooks C. 2001)

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Day-of-the-week in different markets

• Its influence was important in various developed
  markets, such as Korea, UK, and US stock markets
  (Brooks, Steeley, 2001, Kohers, 2004).
• The research of the effect in 21 emerging stock
  markets showed, that it was present only for
  Philippines, Pakistan and Taiwan stock markets
  (Basher, S.,2006)

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Some reasons for research

• Long-run improvements in market efficiency may
  have lowered the effects of certain anomalies in
  recent periods (Kohers, G. 2004)
• The anomalies occur in short periods and in
  comparatively small data subsets
• The diminished significance of the calendar
  effects can be influenced by inability of the
  prevalent statistical methods to recognize them
• The anomalies could be more distinctly observed
  by applying research of higher moments instead of
  traditional statistical analysis
• Applying artificial neural networks should reveal
  new dependencies

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Variables of the research

• The main variable, used for day-of-the-week
  effect investigation is the mean return.
• Other more common indicators are the daily
  closing prices and indexes
• It could be important to analyze all available
  information about the stocks the trading
  volumes, dividends, earnings-price ratios, high
  minus low values, number of deals

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Artificial Neural Networks (ANN)
ANN are mostly used for predicting stock
performance 9,20, classification of stocks,
predicting price changes of stock indexes 10,
forecasting the performance of stock prices
6,12,21 The statistical analysis methods are
prevalent for analysis of the day-of-the-week
effect or to the related questions of the
efficient market hypothesis The reported
research results show that ANN outperform
statistical methods, such as multiple linear
regression analysis, ANOVA, discriminant analysis
and others 11.
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The empirical research strategy

• Define research data set and methodology
• Investigate the day-of-the-week effect by
  applying the traditional statistical methods,
  such as t-test and one-way ANOVA
• Make analysis by applying the classification
  potential of the artificial neural networks
• Use more variables that could help to estimate
  the day-of-the-week effect

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Vilnius Stock Exchange

• Data set was created from Vilnius Stock Exchange
  information (2003-2006).
• The main financial indicators of Vilnius stock
  exchange are market value of 7 billions EUR,
  near 2 million EUR share trading value per
  business day, approximately 600 number of trades
  per business day, and the equity list consising
  of 44 shares.

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Development of Vilnius Stock Exchange

• The Securities Commission has allowed the Nasdaq
  Stock Market, Inc. to indirectly acquire the
  block of shares of the Vilnius Stock Exchange for
  3,7 billion USD.
• NASDAQ has also submitted applications to the
  supervisory authorities of Denmark, Island,
  Finland, Sweden, Estonia and Latvia to acquire
  the shares of the OMX exchanges operating in
  respective countries.
• NASDAQ is the largest electronic screen-based
  equity securities market in the United States
  with approximately 3,200 companies (of which 335
  are non-US companies representing 35 countries
  and operating in different sectors of industry).

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Data set

• For the further calculations the return values of
  24 equities were assigned to the variables, named
  correspondingly to their symbolic notation of
  Vilnius Stock Exchange , covering the time
  interval since 2003-01-01 till 2006-11-21.
• The traditional understanding of return is
  presented by expression (1), where return Rt on
  time moment t, is evaluated by logarithmic
  difference of stock price Pt over time interval
  (t-1,t

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Summary statistics

• The stocks were sorted by ascending average daily
  trading volume.
• The initial analysis by summary statistics of the
  data set, revealed quite big differences in
  return for different days of a week.
• It may be observed that only in the case of more
  intensive stock trade, Monday/Friday effect is
  noticed the Monday mean return is the lowest,
  and Friday the highest among all days of a
  week.

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Day-of-the-week Summary Statistics
.
16
T-test and ANOVA results
17
Nonparametric Kolmogorov-Smirnov test
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Application of neural networks

• In our research two standard types of neural
  networks were applied by using the STATISTICA
  Neural Networks standard module MLP (Multilayer
  Perceptrons) and RBF (Radial Basis Function
  Networks), as evaluated for good performance of
  classification tasks.
• MLP units are defined by their weights and
  threshold values, which provide equation of the
  defining line and the rate of falloff from that
  line.
• Radial basis function network (RBF) has a hidden
  layer of radial units, each modeling a Gaussian
  response surface.

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Sensitivity analysis

• Neural networks were used to distinct Monday and
  Friday from the other trading days of the week.
• More variables were used mean return, number of
  deals and shares, turnover, H-L (high minus low
  price).
• Neural networks were used for classification in
  order to choose most influential variables to the
  final result, and make their sensitivity
  analysis.
• In the next figure, the TEO securities data set
  segment was used for calculations and Sensitivity
  analysis

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Sensitivity analysis
21
Sensitivity analysis (Summary)
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Day-of-the-week effect (TEO equities)

• For calculation we used the Statistica Neural
  Network Intelligent Problem Solver tool.
• The data processing procedure by applying ANN for
  one of the securities (TEO), was aimed to
  distinct Monday from other days of the week. Same
  procedure was applied for each 24 securities data
  set.
• We select DAY as output (dependent) variable and
  DEALS, NO_OF_SH, TURNOVER, RETURN, H_L as input
  (independent) variables. The performance of best
  found network is presented in generated report by
  Intelligent Problem Solver (Fig. 2).

23
Intelligent Problem Solver report of TEO equities
Applying ANN and classifying the cases we shall
presume that prior probabilities for
Monday/Friday and other days of the week are
equal.
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Day-of-the-week effect (Summary)
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Summary and Conclusions I

• The research revealed that day-of-the-week effect
  has no significant influence on Vilnius Stock
  Exchange OMX Index return, and there were only
  few equities, where this effect could be
  substantiated.
• Comparative analysis of the groups indicated that
  the highest value of return and lowest volatility
  were in the group with medium daily turnover. The
  lowest return and the biggest volatility values
  were in the third group with the highest trading
  volume.
• The analysis by applying various methods and
  tests revealed that daily trade volume had no
  significant effect for the occurrence of
  day-of-the-week effect to trading stocks, but had
  influence on the liquidity of the stock and
  increased volatility and risk.

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Summary and Conclusions II

• The investigation was based on analysis of
  numerous variables return, deals, number of
  shares, turnover, H-L (high minus low price).
  Sensitivity analysis of variables showed, that
  the most important impact to define
  day-of-the-week effect was made by variables
  DEALS, H_L and RETURN.
• By applying Statistica Neural Network software
  the best classifying neural networks were
  selected, though no preference could be given for
  MLP and RBF neural networks due to their similar
  performance
• The research results helped to conclude the
  effectiveness of application of neural networks,
  as compared to the traditional linear statistical
  methods for such type of classification problem,
  where the effect is vaguely expressed and its
  presence is difficult to confirm.

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Thank you for your attention

• Department of Informatics
• Vilnius University, Muitines 8, LT-44280
• Kaunas, Lithuania
• virgis_at_vukhf.lt , dalia.kriksciuniene_at_vukhf.lt