Modeling and Forecasting the Markets Volatility and VaR Dynamics of Commodity

The purpose of this paper is to model and forecast the risk of six commodities namely, crude oil, copper, gold, silver, palladium, and platinum during the period from 02/01/2002 to 29/04/2016 using volatility, value at risk and expected shortfall as risk measures. After showing that squared returns of all six commodities have a significant long memory, the volatility, the value at risk and expected shortfall based on fractional GARCH models are estimated and forecasted. Both forecast performance of volatility models and backtest for value at risk indicate that in many cases FIAPARCH model outperforms the other GARCH models. Then volatility, value at risk and expected shortfall estimates based on FIAPARCH model show that the volatility and market risk of oil is much higher than the other commodities. This casts doubt on the use of oil as a hedging tool.

Emtia Piyasalarının Oynaklık ve Riske Maruz Değer Dinamiklerinin Modellenmesi ve Öngörüsü

Bu çalışmanın amacı, ham petrol, bakır, altın, gümüş, paladyum ve platinden oluşan altı temel emtiaya ait zaman serisinin 02/01/2002 - 29/04/2016 arasını kapsayan dönemde, oynaklık, riske maruz değer ve beklenen açık risk ölçümlerini kullanarak, emtia piyasalarının riskini modellemek ve öngörmektir. Bu altı emtianın getiri karelerinin önemli ölçüde uzun hafıza özelliğine sahip olduğu gösterildikten sonra oynaklık, riske maruz değer ve beklenen açık, kesirli bütünleşik GARCH modelleri kullanılarak tahmin edilmiş ve öngörülmüştür. Hem oynaklık modellerinin öngörü performansı hem de riske maruz değer için yapılan geri testler birçok durumda FIAPARCH modelinin diğer GARCH modellerinden bariz biçimde üstün olduğunu göstermektedir. FIAPARCH modelini kullanarak yapılan oynaklık, riske maruz değer ve beklenen açık tahmin sonuçları petrolün diğer emtialardan daha riskli olduğunu göstermekte ve petrolün riskten korunma aracı olarak kullanılmasını sorgulanır hale getirmektedir.

Kaynakça

1. Aloui, C. and Mabrouk S.. (2010). Value-at-risk estimations of energy commodities via long- memory, asymmetry and fat-tailed GARCH models, Energy Policy, 38 (5). 2326–2339.

2. Arouri, M. Hammoudeh, S. Lahiani, A. Nguyen, D. K.. (2012a). Long memory and structural breaks in modeling the return and volatility dynamics of precious metals, The Quarterly Review of Economics and Finance, 52: 207–218.

3. Arouri, M. Lahiani, A,. Lévy, A. Nguyen, D. K.. (2012b). Forecasting the conditional volatility of oil spot and futures prices with structural breaks and long memory models, Energy Economics, 34 (1):283–293.

4. Baillie, R. T.. (1996). Long memory processes and fractional integration in econometrics, Journal of Econometrics, 73: 5–59.

5. Baillie, R. T. Bollerslev, T. and Mikkelsen, H. O.. (1996). „Fractionally integrated generalized autoregressive conditional heteroskedasticity, J. Econometrics, 74:3-30.

6. Bollerslev, T.. (1986). Generalized autoregressive conditional heteroscedasticity, Journal of econometrics, 31(3), 307-327. 7. Bollerslev, T. and Mikkelsen, H. O.. (1996). Modelling and pricing long memory in stock market volatility, Journal of Econometrics, 73:151–184.

8. Beine, M. and Laurent, S.. (2003). Central bank interventions and jumps in double long memory models of daily exchange rates, Journal of Empirical Finance, 10:641–660.

9. Cheng, W. H. and Hung, J. C.. (2011). „Skewness and leptokurtosis in GARCH-typed VaR estimation of petroleum and metal asset returns, Journal of Empirical Finance, 18:160–173.

10. Cheong, C. W.. (2009). Modeling and forecasting crude oil markets using ARCH-type models, Energy Policy, 37:2346–2355.

11. Chkili, W. Hammoudeh, S. D. and Nguyen, K.. (2014). Volatility forecasting and risk management for commodity markets in the presence of asymmetry and long memory, Energy Economics, 41:1-18.

12. Choi, K. and Hammoudeh, S.. (2009). Long memory in oil and refined products markets, Energy Journal, 30: 97–116. 13. Conrad, C.. (2010). Non-negativity conditions for the hyperbolic GARCH model, Journal of Econometrics, 157(2):441-457.

14. Conrad, C. and Haag, B. R.. (2006). „Inequality constraints in the fractionally integrated GARCH model, Journal of Financial Econometrics, 4:413–449.

15. Conrad, C. and Karanasos, M.. (2005a). On the inflation-uncertainty hypothesis in the USA, Japan and the UK: a dual long memory approach, Japan and the World Economy, 17:327–343.

16. Conrad, C. and Karanasos, M.. (2005b). „Dual long memory in inflation dynamics across countries of the Euro area and the link between inflation uncertainty and macroeconomic performance, Studies in Nonlinear Dynamics & Econometrics, 4 (5).

17. Conrad, C. Karanasos, M. and Zeng, N.. (2011). Multivariate fractionally integrated APARCH modelling of stock market volatility: multi-country study, Journal of Empirical Finance, 18:147–159.

18. Creti, A. Joëts, M. and Mignon, V.. (2013). On the links between stock and commodity markets’ volatility, Energy Econonomics, 37:16–28.

19. Dahl, C. M. and Iglesias, E. M.. (2009). „Volatility spillovers in commodity spot prices: new empirical results, Economic Modelling, 26:601–607.

20. Davidson, J.. (2004). Moment and memory properties of linear conditional heteroscedasticity models, and a new model, Journal of Business and Economic Statistics, 22:16–29.

21. Ding, Z. Granger, C. W. J. and Engle, R. F.. (1993). A Long Memory Property of Stock Market Returns and a New Model, Journal of Empirical Finance, 1:83-106

22. Engle, R. F.. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation, Econometrica, 50 (4):987– 1008.

23. Engle, R. F. Lilien, D. M. and Robins, R. P.. (1987). Estimating time varying risk premia in the term structure: The ARCH-M model, Econometrica: Journal of the Econometric Society, 391-407.

24. Geweke, J. and Porter-Hudak, S.. (1983). The estimation and application of long memory time series models, Journal of Time Series Analysis, 4:221-238.

25. Granger, C.. (1980). Long Memory Relationships and the Aggregation of Dynamic Models, Journal of Econometrics, 14:227-238.

26. Granger, C. and Joyeux, R.. (1980). An Introduction to Long-Memory Time Series Models and Fractional Differencing, Journal of Time Series Analysis, 1:15-29.

27. Hosking, J.. (1981). Fractional Differencing, Biometrika, 68:165-176.

28. Hung, J. C. Lee, M. C. and Liu, H. C.. (2008). Estimation of value-at-risk for energy commodities via fat-tailed GARCH models, Energy Ecoonomics. 30:1173–1191.

29. Hurst, H. E.. (1951). Long-term storage capacity of reservoirs, Transactions of the American Society of Civil Engineers, 116:770-799.

30. Jain A,.Biswal P.C(2016) Dynamic linkages among oil price, gold price, exchange rate, and stock market in India, Resources Policy, 49,179-185

31. Jarque, C. M. and Bera, A. K.. (1987). A Test for Normality of Observations and Regression Residuals, International Statistical Review / Revue Internationale de Statistique, 55(2):163-172.

32. Kang, S. H. Kang, S. M. and Yoon, S. M.. (2009). Forecasting volatility of crude oil markets, Energy Economics, 31:119–125.

33. Kang, S. H. McIver R. and Yoon, S. M. (2016). Modeling Time-Varying Correlations in Volatility Between BRICS and Commodity Markets Emerging Markets Finance & Trade, 52(7), 1698-1723.

34. Kang, S. H. McIver R. and Yoon, S. M. (2017). Dynamic spillover effects among crude oil, precious metal, and agricultural commodity futures markets, Energy Economics, 62,19-32.

35. Kang, S. H. and Yoon, S. M.. (2013). Modeling and forecasting the volatility of petroleum futures prices, Energy Economics, 36:354–362.

36. Kumar, D.. (2014). Long Memory in the Volatility of Indian Financial Market:

An Empirical Analysis Based on Indian Data. Anchor Academic Publishing, Hamburg. 37. Lo, A. W.. (1991). Long-term memory in stock market prices, Econometrica, 59:1279-1313.

38. Lobato, I. N. and Savin, N. E.. (1998). Real and spurious long memory properties of stock market data, Journal of Business and Economic Statistics, 16:261–268.

39. Mandelbrot, B. B.. (1971). When Can Price be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models, Review of Economics and Statistics, 53(3):225-236.

40. Mandelbrot, B. B, and Wallis, J. R.. (1969). „Some long-run properties of geophysical records, Water Resouces. Research, 5(2):321-340.

41. Mohammadi, H. and Su, L.. (2010). International evidence on crude oil price dynamics: applications of ARIMA-GARCH models, Energy Economics, 32:1001–1008.

42. Muth, J. F.. (1961). Rational expectations and the theory of price movements, Econometrica: Journal of the Econometric Society, 315-335.

43. Regnier, E.. (2007). Oil and energy price volatility, Energy Economics, 29:405–427.

44. Robinson, P. M.. (1991). Testing for Strong Serial Correlation and Dynamic Conditional Heteroscedasticity in Multiple Regression, Journal of Econometrics, 47:67–84.

45. Robinson, P. M. and Henry, M.. (1999). Long and short memory conditional heteroskedasticity in estimating the memory parameter of levels, Econometric Theory, 15(3):299-336.

46. Thuraisamy, K. S. Sharma, S. S. and Ahmed, H. J. A.. (2013). The relationship between Asian equity and commodity futures markets, Journal of Asian Economics, 28: 67–75.

47. Tsay R S(2010). Analysis of Financial Time Series 3rd Edition, Wiley 48. Tse, Y.. (1998). The conditional heteroscedasticity of the yen–dollar ex- change rate, Journal of Applied Economics, 13:49–55.

49. Vivian, A. and Wohar, M. E.. (2012). Commodity volatility breaks, Journal of International Financial Markets Institutions and Money, 22:395–422.

50. Wang, Y. Wei, Y. and Wu, C.. (2010). Auto-correlated behavior of WTI crude oil volatilities: A multiscale perspective, Physica A: Statistical Mechanics and its Applications, 389(24):5759-5768.

51. Wei, Y. Wang, Y. and Huang, D.. (2010). „Forecasting crude oil market volatility: further evidence using GARCH-class models, Energy Economics 32:1477–1484.

52. Yajima, Y.. (1985). On estimation of long memory time series models, Australian Journal of Statistics, 27:303-20.

Kaynak Göster