Modeling Daily Oil Price Data Using Auto-regressive Jump Intensity GARCH Models

Transcription

1 Modeling Daily Oil Price Data Using Auto-regressive Jump Intensity GARCH Models ifo Institute for Economic Research 22 June nd IAEE International Conference San Francisco

2 1 Motivation 2 Descriptive Analysis 3 Method 4 Estimation Results 5 Discussion 6 Conclusions

3 Motivation Explaining the price of oil

4 Motivation Explaining the price of oil Oil as exhaustible resource [Hotelling, 1931] Macroeconomic supply and demand frameworks [Krichene, 2002; Dees et al., 2007] Informal view [Dees et al., 2008; Kaufmann and Ullmann, 2009] Three Epochs of Oil [Dvir and Rogoff, 2009]

5 Motivation Explaining the price of oil Oil as exhaustible resource [Hotelling, 1931] Macroeconomic supply and demand frameworks [Krichene, 2002; Dees et al., 2007] Informal view [Dees et al., 2008; Kaufmann and Ullmann, 2009] Three Epochs of Oil [Dvir and Rogoff, 2009] Forecasting the price of oil

6 Motivation (continued)

7 Motivation (continued) Trends in the price of oil

8 Motivation (continued) Trends in the price of oil Deterministic [Slade, 1982; Lee et al., 2006] vs. stochastic trends [Slade, 1988]

9 Motivation (continued) Trends in the price of oil Deterministic [Slade, 1982; Lee et al., 2006] vs. stochastic trends [Slade, 1988] Theoretical implications of the price of oil

10 Motivation (continued) Trends in the price of oil Deterministic [Slade, 1982; Lee et al., 2006] vs. stochastic trends [Slade, 1988] Theoretical implications of the price of oil Scarcity indicator [Krautkraemer, 1998; Holland, 2008] Optimal depletion paths [Hotelling, 1931; Sinn, 2008]

11 Motivation (continued) Changes in the real price of oil have [...] tended to be (1) permanent, (2) difficult to predict, and (3) governed by very different regimes at different points in time [Hamilton, 2008]

12 Motivation (continued) Changes in the real price of oil have [...] tended to be (1) permanent, (2) difficult to predict, and (3) governed by very different regimes at different points in time [Hamilton, 2008] [...] many economists often think of oil prices as historically having been influenced little or none at all by the issue of exhaustibility. [Hamilton, 2008]

13 Descriptive Analysis Figure: Price of Oil, March November 2008 Oil Price Growth Rates

14 Descriptive Analysis (continued) Figure: Descriptive Statistics I Normal Q Q Plot ACF Sample Quantiles Lag Theoretical Quantiles

15 Descriptive Analysis (continued) Figure: Descriptive Statistics II Kernel Density Kernel Density Kernel Density

16 Descriptive Analysis (continued)

17 Descriptive Analysis (continued) The oil price exhibits financial market data characteristics

18 Descriptive Analysis (continued) The oil price exhibits financial market data characteristics Large oil price movements are not unlikely due to small price elasticities of both oil supply and demand

19 Method

20 Method Chan und Maheu s (2002) ARJI-GARCH model

21 Method Chan und Maheu s (2002) ARJI-GARCH model l y t = µ + φ i y t i + n t h t z t + X t,k (1) i=1 k=1

22 Method Chan und Maheu s (2002) ARJI-GARCH model l y t = µ + φ i y t i + n t h t z t + X t,k (1) i=1 k=1 q p z t NID(0,1) and h t = ω + α i ɛ 2 t i + β i h t i (2) i=1 i=1

23 Method Chan und Maheu s (2002) ARJI-GARCH model y t = µ + l φ i y t i + n t h t z t + X t,k (1) i=1 z t NID(0,1) and h t = ω + k=1 q α i ɛ 2 t i + i=1 p β i h t i (2) i=1 P(n = j Φ t i ) = λj t j! e λt (3) X t,k N(θ t,δ 2 t ) (4)

24 Method (continued) Constant Jump-Intensity Model

25 Method (continued) Constant Jump-Intensity Model λ t = λ, θ t = θ and δ 2 t = δ2

26 Method (continued) Constant Jump-Intensity Model λ t = λ, θ t = θ and δ 2 t = δ2 Auto-Regressive Jump-Intensity Model

27 Method (continued) Constant Jump-Intensity Model λ t = λ, θ t = θ and δt 2 = δ2 Auto-Regressive Jump-Intensity Model r s λ t = λ 0 + ρ i λ t i + γ i ξ t i. (5) i=1 i=1

28 Estimation Results Table: Constant and time-varying jump-intensity models Parameter Constant ARJI µ 2.9E E-04 (0.0930) (0.0384) φ (0.0167) (0.0106) ω 3.5E E-07 (0.0759) (0.0387) α (0.0001) (0.0001) β (0.0001) (0.0001) δ (0.0001) (0.0001) θ -5.7E E-03 (0.0256) (0.0173) λ (0.0001) (0.0002) ρ (0.0001) γ (0.0001) Note: p-values in parentheses.

29 Estimation Results (continued) Figure: Autoregressive Jump Intensity Q4 1986Q1 1986Q Q3 1990Q4 1991Q1 Oil Price Growth Rate Oil Price Growth Rate Q4 1986Q1 1986Q Q3 1990Q4 1991Q1 Jump Intensity Jump Intensity

30 Discussion

31 Discussion Theoretical aspects

32 Discussion Theoretical aspects Holland (2008) argues that the oil price is the better scarcity indicator than oil production is

33 Discussion Theoretical aspects Holland (2008) argues that the oil price is the better scarcity indicator than oil production is Hotelling (1931) rule: in optimum, the price of oil grows at the rate of interest

34 Discussion Theoretical aspects Holland (2008) argues that the oil price is the better scarcity indicator than oil production is Hotelling (1931) rule: in optimum, the price of oil grows at the rate of interest Sinn (2008) extends Hotelling s model by the issue of global warming

35 Discussion Theoretical aspects Holland (2008) argues that the oil price is the better scarcity indicator than oil production is Hotelling (1931) rule: in optimum, the price of oil grows at the rate of interest Sinn (2008) extends Hotelling s model by the issue of global warming Implication: long-run upward trend in the price of oil

36 Discussion Theoretical aspects Holland (2008) argues that the oil price is the better scarcity indicator than oil production is Hotelling (1931) rule: in optimum, the price of oil grows at the rate of interest Sinn (2008) extends Hotelling s model by the issue of global warming Implication: long-run upward trend in the price of oil The presence of jumps implies that the oil price does not settle around a long-run trend

37 Discussion Theoretical aspects Holland (2008) argues that the oil price is the better scarcity indicator than oil production is Hotelling (1931) rule: in optimum, the price of oil grows at the rate of interest Sinn (2008) extends Hotelling s model by the issue of global warming Implication: long-run upward trend in the price of oil The presence of jumps implies that the oil price does not settle around a long-run trend Inclusion of stochastic oil price is necessary [Pindyck, 1981]

38 Discussion (continued)

39 Discussion (continued) Trends in the price of oil

40 Discussion (continued) Trends in the price of oil Quadratic [Slade, 1982] and deterministic trends with structural breaks [Lee et al., 2006]

41 Discussion (continued) Trends in the price of oil Quadratic [Slade, 1982] and deterministic trends with structural breaks [Lee et al., 2006] Stochastic trends [Slade, 1988]

42 Discussion (continued) Trends in the price of oil Quadratic [Slade, 1982] and deterministic trends with structural breaks [Lee et al., 2006] Stochastic trends [Slade, 1988] Stochastically fluctuating trends [Pindyck, 1999]

43 Discussion (continued) Trends in the price of oil Quadratic [Slade, 1982] and deterministic trends with structural breaks [Lee et al., 2006] Stochastic trends [Slade, 1988] Stochastically fluctuating trends [Pindyck, 1999] The results are consistent with Pindyck s (1999) notion of stochastically fluctuating trends

44 Conclusions

45 Conclusions Applying Chan and Maheu s (2002) method yields strong evidence of conditional jump behavior of the price of oil

46 Conclusions Applying Chan and Maheu s (2002) method yields strong evidence of conditional jump behavior of the price of oil The oil price does not settle around a long-run trend

47 Conclusions Applying Chan and Maheu s (2002) method yields strong evidence of conditional jump behavior of the price of oil The oil price does not settle around a long-run trend Both finding optimal depletion paths and the transition to alternative technologies is hampered

48 Conclusions Applying Chan and Maheu s (2002) method yields strong evidence of conditional jump behavior of the price of oil The oil price does not settle around a long-run trend Both finding optimal depletion paths and the transition to alternative technologies is hampered The apparent non-existence of a long-run trend leads to a current overextraction of oil