Predictability of technical trading rules and non-linear properties of stock returns based on bootstrap methodology: Evidence from China stock market

1
Predictability of technical trading rules and
non-linear properties of stock returns based on
bootstrap methodology Evidence from China stock
market

• PresentationZhigang Wang
• School of management, UESTC.
• 2007.7.7

2
Outline

• Background introduction
• Motivation
• The models
• Empirical results
• Conclusion

3
Background Introduction

• In the early researches on testing the EMH, the
  weak form efficiency was usually
  considered as stock prices following a
  random walk process.
• A random walk process assumes stock returns are
  independent. Indeed, the independence of
  stock return cannot possibly be tested directly,
  for even though no linear correlation is
  confirmed, there may be some nonlinear
  dependence between returns.

4
Background Introduction

• Therefore, testing the predictability of
  technical trading rules is considered as a more
  appropriate method to test the weak form
  efficiency.
• Most of early researchers believed that technical
  analysis could not help investors to forecast
  price changes.
• But these studies only considered the linear
  correlation between stock returns, while the
  nonlinearities of returns dynamic process
  were neglected.
• Therefore, the earlier view of the uselessness of
  technical analysis may have to be
  reconsidered.

5
Background Introduction

• Brock et al. (1992) used a bootstrap methodology
  to test the predictability of technical
  trading rules for the first time.
• They found buy signals of technical rules
  generated higher returns and less
  volatility, while returns following sell signals
  are negative but more volatile.
• Furthermore, the bootstrapping results indicated
  that the asymmetrical patterns of return and
  volatility between buy and sell signals could
  not be explained by four popular linear models of
  returns, especially the negative returns
  following sell signals.

6
Background Introduction

• For the returns properties following buy and sell
  signals obtained from actual price process could
  not be replicated by those popular linear
  models, Brock et al. (1992) suggested there may
  be some nonlinearities in stock returns dynamic
  process.
• Following Brock et al. (1992), many empirical
  researches on other stock markets have also
  found similar evidence. However, these studies
  only tested some linear models of returns dynamic
  process, and all of them did not find why the
  technical trading rules have the predictability
  for stock returns.

7
Motivation

• This paper will test whether the Non-linear
  models of returns can explain the
  predictability of technical trading rules.
• We will construct the Non-linear models of return
  based on the Artificial neural network (ANN)
  models of Gençay (1996) .
• However, the ANN models of Gençay (1996) only
  considered the past information of return
  itself, whereas the asymmetrical patterns of
  volatility were not taken into account.
  Therefore, this paper will extend the
  application of the ANN model to volatility.

8
Motivation

• We will introduce the conditional
  heteroskedasticity structure into the ANN
  models of returns, and then test the returns and
  volatility patterns following buy and sell
  signals during the simulated nonlinear
  process of return with bootstrap method.
• All buy and sell signals to be tested are
  generated from moving average rules in this paper.

9
The models

• In order to test if various structured models of
  return can explain the predictability of moving
  average rules, the distributions of the mean
  return and volatility during buy and sell periods
  under various null models will be estimated
  using the bootstrap methodology developed by
  Efron (1979).

10
The models

• First, four popular linear modelsRandom Walk, AR
  (1), GARCH (1, 1) and GARCH-M (1, 1) are tested.
• Second, the ANN models of returns are compared.
  The ANN model of Gençay (1996) are as following
• This model is a single-layer feed forward neural
  network, where d presents the number of hidden
  units in the hidden layer, and presents the
  weights of units,and G is an activation function
  chosen to be a logistic function in this
  paper.

11
The models

• In order to capture the patterns of buy and sell
  volatility, we introduce a GARCH (1, 1) structure
  into the residuals of this ANN models as
  following
• We first fit the ANN model using actual returns
  data and obtain the residuals series , and
  then estimate the GARCH (1, 1) with the residuals
  data to obtain the parameters of conditional
  heteroskedasticity function. Then the bootstrap
  simulations are generated from the standardized
  residuals , Thus, the
  heteroskedasticity structure captured by the
  residuals is maintained in the nonlinear process
  of returns.

12
The models

• We construct the empirical distributions of buy
  and sell mean return and volatility by
  repeating this procedure 500 times. The fraction
  of the 500 replications, which generates a return
  and volatility larger than those from the
  actual price series, is considered as a simulated
  p-value.

13
Empirical results

• Traditional tests
• Similar to Brock et al. (1992) and other related
  literatures, our study reveals that moving
  average rules can help to predict stock price
  changes in China stock market using the data of
  Shanghai stock market index from 2 January 1996
  to 30 December 2005.
• We also find buy signals generate higher return
  and less volatility, while returns following sell
  signals are negative but more volatile.
• That is to say, not only do the buy signals
  select out periods with higher mean returns, but
  also they can pick up periods with lower
  volatility.

14
Empirical results

• Bootstrap tests Random walk and AR (1) processes
  
• The random walk model underestimates the buy
  return, buy-sell return difference and sell
  volatility, while overestimates the sell return.
  We especially point out that the sell returns
  from actual prices are all negative, while the
  simulated sell returns are all positive.
• Therefore, the random walk model cant explain
  the predictability of moving average rules in the
  actual prices, and more precise and complex
  structured models must be developed to test.

mr(b) mr(s) mr(b-s) var(b) var (s)
Rules Average p-value 0.0297 0.084 0.0366 0.928 -0.0069 0.018 0.0167 0.648 0.0167 0.094
15
Empirical results

• Bootstrap tests GARCH-M (1, 1) and GARCH (1, 1)
  processes
• The GARCH-M (1, 1) model underestimates the
  buy-sell difference and overestimates the buy
  volatility, and either can not replicate the
  negative sell returns like actual prices .
• Therefore, we also reject the null hypothesis
  that actual returns are a GARCH-M (1, 1) process
  , and then we still did not find the
  reasons of the predictability of moving average
  rules.

mr(b) mr(s) mr(b-s) var(b) var (s)
Rules Average p-value 0.1056 0.442 0.0655 0.966 0.0401 0.12 0.0233 0.922 0.0203 0.5900
16
Empirical results

• Bootstrap tests Nonlinear processes
• A most improvement is that, the ANN model can
  replicate the negative sell returns from
  the actual prices, which is never achieved by any
  linear models of returns tested by Brock et al.
  (1992) and other related papers.
• However, the ANN model underestimates the sell
  volatility, then needs to improve the
  predictability of volatility.

mr(b) mr(s) mr(b-s) var(b) var (s)
Rules Average p-value 0.0413 0.09 -0.0124 0.73 0.0537 0.118 0.0167 0.614 0.0168 0.062
17
Empirical results

• Bootstrap tests Nonlinear processes introduced
  conditional heteroskedasticity
• Most intriguing, the p value of sell volatility
  is not significant anymore, comparing with the p
  value of 0.062 of ANN model of Gençay (1996).
• Besides, the revised ANN model can also better
  explain the asymmetrical patterns between buy and
  sell returns, for The p value of buy return
  increases to 0.238, and that increases to 0.18
  for buy-sell returns, and also can generate
  negative sell returns.

mr(b) mr(s) mr(b-s) var(b) var (s)
Rules Average p-value 0.0548 0.238 -0.0044 0.71 0.0593 0.18 0.0211 0.864 0.0213 0.724
18
Conclusion

• In this paper, we find that the return and
  volatility behavior of buy and sell signals
  following the moving average rules is
  significantly asymmetrical in China stock market.
  
• Returns following buy signals are higher and less
  volatile, while returns following sell signals
  are negative but more volatile. Our results
  provide strong support for these technical
  rules.
• Moreover, the bootstrapping results indicate that
  this predictability of moving average rules can
  not be explained by four popular linear
  models of return, especially the phenomenon of
  negative sell returns.

19
Conclusion

• We then test the nonlinear dynamic process of
  returns. Although the existing ANN model can
  explain away the negative sell returns, it fails
  to capture the volatility patterns of buy and
  sell returns.
• Furthermore, we introduce the conditional
  heteroskedasticity structure into the ANN
  model and find the revised ANN model not only can
  explain the predictability of returns, but
  also can capture the pattern of buy and sell
  volatility, which are never achieved by any
  linear models of returns tested by the related
  work.

20
Conclusion

• Therefore, we conclude that moving average rules
  reveal some hidden nonlinear properties in
  returns dynamic process, and that technical
  trading rules can pick up some of the nonlinear
  patterns may be the reason why they can be
  used to predict price changes.

21

• Many Thanks and Any Questions and Suggestions
  Are Welcome!