1. Crude Oil Price Volatility Ana María Herrera, Liang Hu, Daniel Pastor March 22, 2013

2. Why the Crude Oil Market? Many implications of crude oil price uncertainty on the macroeconomy. Higher oil prices lead to higher production costs, which have a negative effect on GDP growth. The Federal Reserve considers oil price volatility when setting monetary policy. Large movements in oil prices may cause firms to delay investments or to alter production. 2

3. Previous Work Poon and Granger (2003) Gray (1996) Klaassen (2002) Marcucci (2005) 3

4. Main Focus Model and forecast crude oil price volatility. GARCH and MS-GARCH models. 4

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6. Data Monthly spot prices for West Texas Intermediate (WTI) crude oil. Sample period: January 2, 1986 to December 31, 2012. Daily returns. Returns are characterized by mean reversion, fat-tails, asymmetry, and volatility clustering. Student’s t or Generalized Error Distribution (GED) is appropriate. 6

7. Descriptive Statistics 7 Mean Standard DeviationMinMaxVarianceSkewnessKurtosis 0.018772.5731-40.639519.15066.6213-0.756717.5698 Note: Descriptive statistics for WTI rates of return. The sample period is January 2, 1986 to December 31, 2012 for 6812 observations.

8. GARCH Model Where μ t is the time varying conditional mean. α 0, α 1, and γ 1 are all positive α 1 + γ 1 < 1 Distributions for η t Student’s t and GED 8

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10. MS-GARCH Model Both μ St and h t are subject to the hidden Markov chain S t Transition probability matrix: However, estimation is intractable due to path dependence. 10

11. Klaassen’s (2002) Solution Klaassen’s approach eliminates path dependence Multi-step ahead volatility forecasts are relatively straightforward. 11

12. GARCH Results Maximum Likelihood Estimates GARCH-N δ 0.0281 (0.0216) σ 2.5668 (0.0125) α1α1 0.1065 (0.0042) γ1γ1 0.8737 (0.0055) α 1 + γ 1 0.9802 Log(L)-11369.1015 12

13. MS-GARCH Results This confirms there are two volatility states for all models. State two is dominant. Table 3: Selected Maximum Likelihood Estimates of MS-GARCH Models MRS-GARCH-NMRS-GARCH-t2MRS-GARCH-GED σ (1) 4.4564 1.47190.4627 (0.3712)(0.0622)(0.0313) σ (2) 1.62422.59982.3075 (0.0122)(0.0272)(0.0318) π1π1 0.14640.28660.4127 π2π2 0.85360.71340.5873 α (1) 1 + γ (1) 1 0.78550.88870.9674 α (2) 1 + γ (2) 1 0.9812 0.9825 0.9808 13

14. MS-GARCH Results Table 3: Selected Maximum Likelihood Estimates of MS-GARCH Models MRS-GARCH-NMRS-GARCH-t2MRS-GARCH-GED ν (1) -6.56241.3579 (1.0273)(0.0266) ν (2) -6.0386 (0.4622) Log(L)-14520.1688 -14369.9502 -14410.1269 N. of Par.101211 14

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17. Evaluation of Volatility Forecasts Seven different loss functions used for in sample comparison of MS-GARCH models. MS-GARCH-t2 ranks first or second in all but one. A model where the degrees of freedom parameter is allowed to switch between regimes seems the best. Out-of-sample forecast evaluation forthcoming. 17

18. Questions? 18