How long does the river remember...?

1
Academy of Economic Studies Doctoral School of
Finance and Banking- DOFIN
Exploring Dual Long Memory in Returns and
Volatility across the Central and Eastern
European stock markets
Msc. Student Mihaela Sandu Supervisor
PhD.Professor Moisa Altar
Bucharest, July 2009
2
Dissertation paper outline

• Importance of long memory
• Aims of the paper
• Data Methodology
• Nonparametric semiparametric aproaches
• Parametric approach ARFIMA / FIGARCH
• Structural breaks
• The joint ARFIMA-FIGARCH model
• Model distributions
• Empirical results
• Conclusions and further improvements
• References

3
Long memory

• Contradicts the EMH weak-form by allowing
  investors and portfolio managers to make
  prediction and to construct speculative
  strategies
• The price of an asset determined in an efficient
  market should follow a martingale process in
  which each price change is unaffected by its
  predecessor and has no memory . Pricing
  derivative securities with martingale methods may
  not be appropriate if the underlying continuous
  stochastic processes exhibit long memory
• Implications to assest allocation decisions and
  risk management

4
Aims of the paper

• To ivestigate the presence of long memory in
  stock returns via non-, semi- and parametric
  techniques
• To distinguish between long memory and structural
  breaks within return series
• To found evidences of dual long memory processes
  within CEE emerging stock markets

5
Short vs. Long memory processes
vs.
6
The Data

• Six indices representing five CEE emerging stock
  markets BET, BET-FI, SOFIX, BUX, WIG, PX
• Daily closing stock prices transformed into
  continuously compounded returns
• The estimations and tests were performed in R
  version 2.9.0.
• For estimating ARFIMA-FIGARCH model, the Ox
  Console version 5.10, together with the G_at_rch
  Console 4.2 were used.

7
Methodology

• Unit root tests
• ADF
• KPSS statistic

• Rescaled range statistic

• Wavelet based estimator

• Log-periodogram estimator (GPH)

• ARFIMA model

8
Methodology

• FIGARCH model

• Model distributions

• Pearson goodness-of-fit test

9
Empirical results

• Unit root tests

• For all indices we can reject the null of a I(1)
  process, as well as the null of I(0) process

10

• Nonparametric and semiparametric estimates

• For most of the indices, the estimates indicate
  the presence of long memory in returns, squared
  and absolute returns
• In case of SOFIX, the estimate of H using R/S
  and wavelet analysis indicate no long memory in
  return series.

11

• Parametric estimates - ARFIMA model

Following Cheung(1993), we estimate different
specifications of the ARFIMA (p, ?, q) with
p,q02 for each return series. The Akaikes
information Criterion (AIC), is used to choose
the best model that describes the data.
Ln(L) is the value of the maximized Gaussian
Likelihood AIC is the Akaike information
criteria the Q(20) is the Ljung-Box test
statistic with 20 degrees of freedom based on the
standardized residuals
12

• Parametric estimates - ARFIMA model

• the long memory parameter ? significantly
  differs from zero for all return series (for WIG
  at 5 level of significance)
• the results seem to confirm the idea that long
  memory is a property of emerging markets rather
  than developed markets.
• the standardized residuals display skewness and
  excess kurtosis, the departure from normality
  beeing also confirmed by the J-B statistic
• Q-statistic indicate that the residuals are not
  independent, except for BET-FI and WIG , for
  which we cannot reject the null of independent
  residuals

13

• Testing for structural breaks

We use the Supremum F test proposed by Andrews
and the methodology of Bai and Perron for
detecting structural breaks in return series

• for BET, BET-FI, SOFIX and WIG the breakpoint
  corespond to the historical maximum value of the
  index.
• For BUX, the F statistic indicate that the null
  hypothesis of no structural break cannot be
  rejected
• we further split the sample in two subsamples
  depending on the breakdate, and we reestimate all
  the procedures for each subsample

14

• Subsamples technique non and semiparametric
  procedures

For most of the series, the subsamples appear to
keep the full sample properties For SOFIX
although the Hurst exponent is still below 0.5
for each subsample , indicating no long memory
properties, the log-periodogram estimate indicate
a significant value for ? on the second
subsample. We therefore examine the ARFIMA
estimates on each subsample in order to conclude
upon the reliability of the initially findings.
15

• Subsamples technique ARFIMA estimates

For BET, BET-FI and PX the estimate of fractional
parameter is significant for both subsamples In
case of SOFIX and WIG it can be clearly observed
that the long memory patterns of the full sample
are based in fact only on the second subsample,
after the structural break
16
ARFIMA-FIGARCH for the Romanian stock market
indices
17
ARFIMA-FIGARCH- Remarks

• the sum of the estimates of a1 and ß1 in the
  ARFIMAGARCH model is very close to one,
  indicating that the volatility process is highly
  persistent
• the estimates of ß1 in the GARCH model are very
  high, suggesting a strong autoregressive
  component in the conditional variance process
• in the ARFIMAFIGARCH model, the estimates of
  both long memory parameters ? and d are
  significantly different from zero
• the results indicate that the ß1 estimates are
  lower in the FIGARCH than those of in the GARCH
  model.
• according to the AIC, the FIGARCH models fit the
  return series better than the GARCH models
• P(60) test statistics reconfirm the relevance of
  skewed Student-t

18
ARFIMA-FIGARCH estimates for PX and BUX
FIGARCH estimates for WIG and SOFIX
19
Conclusions and further improvements

• The tests and estimated models show evidence of
  dual long memory in Romanian, Czech Republic and
  Hungarian stock markets, while Bulgarian and
  Polands markets show evidence of long memory in
  volatility.
• The results support the idea that the detection
  of long memory properties in emerging markes is
  more likely than in developed markets, having
  implications in portfolio diversification,
  speculative strategies and risk management.
• However, one should use various methods and
  techniques when investingating the presence of
  long memory, due to the sensitivity of the
  results to the selected estimation method.
• Structural breaks and regime shifts can
  significantly affect the results. Therefore, one
  should use such techniques designed to account
  for these processes which could induce to a short
  memory process similar patterns with a long
  memory process.
• Further research could be conducted using the
  models developed by Baillie and Morana
  (2007,2009), namely Adaptive-FIGARCH and
  Adaptive-ARFIMA, and their generalisation for
  dual long memory processes, the
  A2-ARFIMA-FIGARCH model, beeing designed to take
  into account for both long memory and structural
  change in the conditional mean and variance.

20
References
Andrews, D.W.K. (1993), Tests for parameter
instability and structural change with unknown
change point, Econometrica 61, 821-856 Bai, J.,
and P. Perron (2003), Computation and Analysis
of Multiple Structural-Change Models, Journal of
Applied Econometrics, 18, 1-22 Baillie,R.T.
(1996), Long memory processes and fractional
integration in econometrics, Journal of
Econometrics 73, 5-59 Baillie,R.T., T. Bollerslev
and H.O. Mikkelsen (1996), Fractionally
integrated generalized autoregressive conditional
heteroskedasticity, Journal of Econometrics, 74,
3-30 Baillie, R. T., and C. Morana (2007),
Modelling long memory and structural breaks in
conditional variances An adaptive FIGARCH
approach, Journal of economic, dynamics
control, 33, 1577-1592 Baillie, R. T., and C.
Morana (2009), Investigating inflation dynamics
and structural change with an adaptive arfima
approach, Applied mathematics working paper
series. Barkoulas, J. T., C. F. Baum and N.
Travlos, Long memory in the greek stock market,
Applied Financial Economics, 10,
177-184(8) Beine, M., S. Laurent, and C. Lecourt
(1999), Accounting for conditional leptokurtosis
and closing days effects in FIGARCH models of
daily exchange rates
21
References
Bolerslev, T., and H.O. Mikkelsen (1996) ,
Modeling and pricing long memory in stock market
volatility, Journal of Econometrics,
73,151-154 Breidt, F.J., N. Crato, and P. Lima
(1998), The detection and estimation of long
memory in stochastic volatility, Journal of
Econometrics, 83, 325-348 Cajueiro, D. O., and B.
M. Tabak (2005), Possible causes of long-range
dependence in the Brazilian stock-market,
Physica A, 345, 635-645 Cheung, Y. W. (1995), A
search for long-memory, Journal of International
Money and Finance, 14, 597-615 Diebold, F. X.,
and A. Inoue (2001), Long memory and regime
switching, Journal of econometrics, 105,
131-159 Geweke ,J. and S. Porter-Hudak
(1983),The estimation and application of
long-memory Time series models, Journal of Time
Series Analysis, 4, 221-238 Granger, C.W.J and
R.Joyeux (1980), An introduction to long-memory
times series modrls and fractional
differencing,Journal of time series analysis
1,15-29 Granger, C.W.J and N. Hyung (1999),
Occasional structural breaks and long memory ,
Discussion Paper 99-14 Granger, C.W.J and N.
Hyung (2004), Occasional structural breaks and
long memory with an application to the SP 500
absolute stock returns, Journal of Empirical
Finance, 11, 399 421.
22
References
Granger, C.W.J., Z. Ding (1996), Varieties of
long memory models, Journal of econometrics, 73,
61-76 Henry, O.T. (2002), Long memory in stock
returns some international evidence, Applied
Financial Economics, 12, 725-729 Kang, S. H., and
S. M. Yoon (2007), Long memory properties in
return and volatility - Evidence from the Korean
stock market, Physica A, 385, 591-600 Kasman,
A., S. Kasman and E.Torun (2008), Dual long
memory property in returns and volatility
Evidence from the CEE countries stock markets,
Emerging Markets Review, Liu, M. (2000),
Modeling long memory in stock market
volatility, Journal of econometrics, 99,
139-171 Lo, A. W. (1991), Long-Term Memory in
Stock Market Prices, Econometrica, 59,
1279-1313 Lobato, I. N., and N. E. Savin (1998),
Real and spurious long memory properties of
stock-market data, Journal of business
economic statistics, 16, 261-268 McMillan, D.G.,
and I. Ruiz (2009), Volatility persistence, long
memory and time-varying unconditional mean
Evidence from 10 equity indices, The Quarterly
Review of Economics and finance, 49,
578-595 Shimotsu, K. (2006), Simple (but
effective) tests of long-memory versus structural
breaks, Queens Economics Department Working
Paper, 1101
23
References
Sowell, F. (1992), Maximum likelihood estimation
of stationary univariate fractionally integrated
time series models, Journal of econometrics, 53,
165-188 Taqqu, M., V. Teverovsky and W. Willinger
(1995), Estimators for long-range dependence an
empirical study Teyssiere, G. (1997), Double
long memory financial time series, GREQAM
(Groupement de Recherche en Economie Quantitative
dAix-Marseille ) Teyssiere, G., A.P.Kirman
(2007), Long memory in economics, Springer
editure Turhan, K., E.I.Cevik, N. Ozatac (2009),
Testing for long memory in ISE using
ARFIMA-FIGARCH model and structural break test,
International Research Journal of Finance and
Economics, 26 Willinger, W., Taqqu, M.S. andV.
Teverovsky (1999), Stock market prices and
long-range dependence, Finance and Stochastics,
3, 1-13