Journal of Korea Port Economic Association (한국항만경제학회지)

The Korea Port Economic Association (한국항만경제학회)
권호 표지

Estimation of BDI Volatility: Leverage GARCH Models

BDI의 변동성 추정: 레버리지 GARCH 모형을 중심으로

  • Received : 2014.07.28
  • Accepted : 2014.08.21
  • Published : 2014.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper aims at measuring how new information is incorporated into volatility estimates. Various GARCH models are compared and estimated with daily BDI(Baltic Dry Index) data. While most researchers agree that volatility is predictable, they differ on how this volatility predictability should be modelled. This study, hence, introduces the asymmetric or leverage volatility models, in which good news and bad news have different predictability for future. We provide the systematic comparison of volatility models focusing on the asymmetric effect of news on volatility. Specifically, three diagnostic tests are provided: the sign bias test, the negative size bias test, and the positive size bias test. From the Ljung-Box test statistic for twelfth-order serial correlation for the level we do not find any significant serial correlation in the unpredictable BDI. The coefficients of skewness and kurtosis both indicate that the unpredictable BDI has a distribution which is skewed to the left and significantly flat tailed. Furthermore, the Ljung-Box test statistic for twelfth-order serial correlations in the squares strongly suggests the presence of time-varying volatility. The sign bias test, the negative size bias test, and the positive size bias test strongly indicate that large positive(negative) BDI shocks cause more volatility than small ones. This paper, also, shows that three leverage models have problems in capturing the correct impact of news on volatility and that negative shocks do not cause higher volatility than positive shocks. Specifically, the GARCH model successfully reveals the shape of the news impact curve and is a useful approach to modeling conditional heteroscedasticity of daily BDI.

BDI건화물운임지수의 변동성은 환율과 주가의 변동성을 크게 초과할 정도로 대단히 클 뿐만 아니라 변동성이 점차 커지고 있어서 운임을 예측하는데 많은 어려움을 겪고 있다. 이에 본고는 이러한 운임지수의 변동성을 정확히 포착할 수 있는 모형을 찾는데 목적을 둔다. 이를 위해 변동성 분석에 흔히 사용되는 대칭형 변동성 모형인 GARCH 모형과 비대칭 변동성 모형인 AGARCH모형, GJR모형, EGARCH모형을 도입한다. 그것은 나쁜 뉴스가 좋은 뉴스보다 더 큰 변동성을 야기할 가능성이 높기 때문이다. 먼저 운임의 예측불가능요소를 운임의 요일별 특성을 제거한 후 자기회귀를 하여 구한 후 GARCH 분석을 적용하는데 적합한 성격을 갖는가를 조사한다. 비대칭모형의 AGARCH모형에서는 비대칭을 나타내는 계수가 유의하나 부호가 모형의 예상과 달라 나쁜 뉴스가 좋은 뉴스보다 더 큰 변동성을 야기하지 않으며, EGARCH모형의 비대칭계수도 양의 부호로 모형의 예상과 반대일 뿐만 아니라 유의하지 않아 나쁜 뉴스가 좋은 뉴스보다 더 큰 변동성을 야기하지 않는다는 것, 그리고 GJR모형에서도 해당 계수가 음으로 모형과 반대로 유의하지 않아 음의 충격이 양의 충격보다 더 큰 변동성을 유발하지 않음을 보인다. 이에 따라 BDI건화물운임지수의 변동성은 GARCH모형을 이용하는 것이 합리적이라는 점을 보인다.

Keywords

References

  1. 최병옥.김원태, "참외 주산지와 도매시장 가격의 동태적 인과성 분석", 농촌경제 제30권 제3호, 2007, 69-85.
  2. Berg, L. and J. Lyhagen, "Short and Long-Run Dependency in Swedish Stock Returns," Applied Financial Economics, Vol. l8, 1998, 435-443.
  3. Black, F., "Studies in Stock Price Volatility Changes," Proceedings of the 1976 Business Meeting of the Business and Economics Statistics Section, American Statistical Association, 1976, 177-181.
  4. Bollerslev, T., "Generalized Autoregressive Conditional Heteroscedasticity," Journal of Econometrics, Vol. 31, 1986, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  5. Campbell, J. and L. Hentschel, "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Journal of Financial Economics, Vol. 31, 1992, 81-318.
  6. Chou, R., "Volatility Persistence and Stock Valuations: Some Empirical Evidence Using GARCH," Journal of Applied Econometrics, Vol. 3, 1988, 279-294. https://doi.org/10.1002/jae.3950030404
  7. Christie, A., "The Stochastic Behavior of Common Stock Variance: Value, Leverage and Interest Rate Effects," Journal of Financial Economics, Vol. 10, 1982, 407-432. https://doi.org/10.1016/0304-405X(82)90018-6
  8. Dickey, D.A., and W.A. Fuller, "Distribution of the Estimators for Autoregressive Time Series with a Unit Root," Journal of the American Statistical Association, Vol. 74, 1979, 427-431.
  9. Dickey, D.A., and W.A. Fuller, "The Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,"Econometrica, Vol. 49, 1981, 1057-1072. https://doi.org/10.2307/1912517
  10. Ederington, L. H. and W. Guan, "Forecasting Volatility," Journal of Futures Markets, Vol. 25, No. 55, 2005, 465-490. https://doi.org/10.1002/fut.20146
  11. Engle, R., Wald Likelihood Ratio, and Lagrange Multiplier Tests in Econometrics, in: Z. Grrliches and M.D. Intriigator, eds.: Handbook of Econometrics, Vol. 2, North Holland, Amsterdam, 1984.
  12. Engle, R., and D. Kraft, "Multiperiod Forecast Error Variances of Inflation Estimated from ARCH Models," in A. Zellner, ed.: Applied Time Series Analysis of Economic Data, Bureau of the Census, Washington, D.C., 1983, 293-302.
  13. Engle, R.F. and V.K. Ng, "Measuring and Testing the Impact of News on Volatility," Journal of Finance, Vol. 48, 1993, 1749-1778. https://doi.org/10.1111/j.1540-6261.1993.tb05127.x
  14. French, K., G.W. Schwert, and R. Stambaugh, "Expected Stock Returns and Volatility," Journal of Financial Economics, Vol. 19, 1987, 3-29. https://doi.org/10.1016/0304-405X(87)90026-2
  15. Fuller, W.A., Introduction to Statistical Time Series, New York, Wiley, 1976.
  16. Glosten, L., R. Jaganathan, and D. Runkle, "On the Relation Between the Expected Value and Volatility of The Nominal Excess Return on Stocks," Journal of Finance, Vol. 48, 1993, 1779-1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
  17. Gonzalez-Rivera, G., T-H. Lee, and S. Mishra, "Forecasting Volatility: A Reality Check Based on Option Pricing, Utility Function, Value-at-Risk, and Predictive Likelihood," International Journal of Forecasting, Vol. 20, 2004, 629-645. https://doi.org/10.1016/j.ijforecast.2003.10.003
  18. Henry, O., "Modelling the Asymmetry of Stock Market Volatility," Applied Financial Economics, Vol. 8, 1998, 145-153. https://doi.org/10.1080/096031098333122
  19. Hillebrand, E., "Neglecting Parameter Changes in GARCH Models," Journal of Econometrics, 129, 2005, 121-138. https://doi.org/10.1016/j.jeconom.2004.09.005
  20. Lopez, J., "Evaluating the Predictive Accuracy of Volatility Models," Journal of Forecasting, Vol. 20, 2001, 87-109. https://doi.org/10.1002/1099-131X(200103)20:2<87::AID-FOR782>3.0.CO;2-7
  21. Merton, R.C., "On Estimating the Expected Return on the Market: An Exploratory Investigation," Journal of Financial Economics, Vol. 8, 1980, 323-361. https://doi.org/10.1016/0304-405X(80)90007-0
  22. Mikosch, T. and C. Starica, "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," Review of Economics and Statistics, 86, 2004, 378-390. https://doi.org/10.1162/003465304323023886
  23. Nelson, D., "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Vol. 6, 1990, 318-334. https://doi.org/10.1017/S0266466600005296
  24. Nelson, D., "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Vol. 59, 1991, 347-370. https://doi.org/10.2307/2938260
  25. Newey, W.K., and West, K.D., "A Simple, Positive Semi-Definite, Heterosedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Vol. 55, 1987, 703-708. https://doi.org/10.2307/1913610
  26. Pagan, A. and G. Schwert, "Alternative Models for Common Stock Volatility," Journal of Econometrics, Vol. 45, 1990, 267-290. https://doi.org/10.1016/0304-4076(90)90101-X
  27. Poon, S. H. and C. Granger, "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, Vol. 41, 2003, 478-539. https://doi.org/10.1257/.41.2.478
  28. Rapach, D. E. and J. K. Struass, "Structural Breaks and GARCH Models of Exchange Rate Volatility," Journal of Applied Econometrics, Vol. 23, 2008, 65-90. https://doi.org/10.1002/jae.976
  29. Schwert, G.W., "Stock Volatility and the Crash of 87," Review of Financial Studies, Vol. 3, 1990, 77-102 https://doi.org/10.1093/rfs/3.1.77