Forecasting the Price of Oil

Transcription

1 Forecasting the Price of Oil Ron Alquist Lutz Kilian Robert J. Vigfusson Bank of Canada University of Michigan Federal Reserve Board CEPR Prepared for the Handbook of Economic Forecasting Graham Elliott and Allan Timmermann (eds.) This presentation reflects the authors own views and should not be attributed to the Bank of Canada, the Federal Reserve System, or the Board of Governors of the Federal Reserve System.

2 Motivation Potential to improve forecast accuracy of macroeconomic aggregates and macroeconomic policy responses Forecasts of the prices of oil and its derivatives like gasoline or heating oil important for: Modeling purchases of energy-intensive durables Predicting carbon emissions and climate change Designing regulatory policies (fuel standards, gasoline taxes) Business decisions (e.g., airlines, auto manufacturers, utilities)

3 Key Oil Price Series Since 1948: 1. US Producer Price Index (PPI) for crude oil 2. West Texas Intermediate (WTI) price of crude oil (almost identical with PPI series in pre-1974 era) Since 1974: 1. Refiner s acquisition cost (domestically produced crude oil) 2. Refiner s acquisition cost (imported crude oil) 3. Refiner s acquisition cost (composite) No single oil price series is perfect for all purposes.

4 Key Oil Price Series Import price matters for standard theories of transmission of oil price shocks and is best proxy for global price of oil. Kilian (2009): Refiners acquisition cost (imports) Retail energy price matters for theories of relative price shocks. Hamilton (2003): Crude oil PPI Retail gasoline price Edelstein and Kilian (2009): Retail energy price Retail gasoline price US domestic price series subject to regulation until early 1980s and unrepresentative of actual market price. Mork (1989): Refiners acquisition cost (composite)

5 U.S. Dollars/Barrel Pre-1974 Nominal Price of Oil 4.5 Nominal Price of Oil: Actual WTI Random Draw from Fitted Model

6 U.S. Dollars/Barrel U.S. Dollars/Barrel The Nominal Price of Crude Oil 4.5 Nominal Price of Oil: Nominal Price of Oil: WTI 120 WTI RAC Domestic RAC Imported

7 Percent Change Percent Change Percent Changes in the Real Price of Oil 50 Real Price of Oil: Real Price of Oil: WTI 40 WTI RAC Domestic RAC Imported

8 Selective Survey of Topics in Chapter 1. Predictability in population 2. Forecasting the nominal price of oil 3. Forecasting the real price of oil 4. Joint forecasts of oil prices and US real GDP growth 5. Forecasting oil price volatility and quantifying oil price risks 6. Conclusions: How to forecast the price of oil?

9 1. Predictability in Population

10 Predictability in Population from Macroeconomic Aggregates to Price of Oil It has become more widely accepted that price of oil is endogenous with respect to macroeconomic conditions. Hamilton (1983): Fails to reject null of no Granger causality from US macro aggregates to nominal oil prices pre Thus, lagged macroeconomic aggregates should have predictive power for price of oil in population. Predictability in population is a precondition for out-ofsample forecastability (Inoue and Kilian 2004).

11 Predictors of Nominal Oil Prices US price changes: CPI inflation, %ΔM1 and %ΔM2 Commodity prices: CRB Industrial Raw Materials Index, CRB Metals Index Other: 3-month T-bill rate, trade-weighted USD exchange rate Commodity currencies: AUD, CAD, NZD, SAR (Chen, Rogoff, and Rossi 2010).

12 Summary of Predictability Results Strongest evidence of in-sample predictability for: M1 CRB indices Currencies of some industrial commodity exporters (e.g., CAD) Rejection of Granger non-causality at standard significance levels for WTI and RAC

13 Predictors of Real Oil Prices Quarterly: US real GDP, world industrial production. Monthly: CFNAI, US industrial production, OECD+6 industrial production, global real activity index (Kilian 2009). Where applicable, Granger causality tests conducted on filtered series (e.g., US real GDP): Linear Hodrick-Prescott First difference

14 Summary of Predictability Results Strongest evidence of in-sample predictability for linearly detrended series: World industrial production OECD+6 industrial production Real activity index Rejection of Granger non-causality at standard significance levels for real WTI and RAC

15 Why are linearly detrended global real activity measures good at predicting real price of oil? US is not the world Oil price determined in global market GDP poor proxy for business-cycle driven fluctuations in oil demand because of large share of services Industrial production is better indicator Well-documented long swings in industrial commodity prices such as oil

16 2. Forecasting the Nominal Price of Oil

17 Do Oil Futures Prices Help Predict the Spot Price? No-change (benchmark model) S t+ t = S t = 1, 3, 6, 9, 12 Futures Price S t+ t = F t () = 1, 3, 6, 9, 12 Futures Spread S t+ t = S t 1 + α + β ln(f t /St ), = 1, 3, 6, 9, 12 where α and β are recursive OLS estimates from s t+ = α + β f t st + u t+

18 Forecast Accuracy of Futures Prices Forecast Evaluation Period: Monthly Forecasts Small ( 6%) improvements in forecast accuracy Not statistically significant Daily Forecasts Short-horizon (1-12 months) Similar to monthly forecasts, except at 12-month horizon. Long-horizon (2-7 years) No improvements in forecast accuracy

19 Alternative Monthly Forecasting Methods Local trends and structural change Recursive drift S t+ t = S t 1 + α = 1,, 12 Rolling drift () S t+ t = S t 1 + st = 1,, 12 Random walk in growth S t+ t = S t 1 + s t = 1,, 12 Hotelling (1931) S t+ t = S t 1 + i t, /12 = 3, 6, 12

20 Alternative Monthly Forecasting Methods CRB commodity prices S t+ t = S t 1 + p t com = 1, 3, 6, 9, 12 com S t+ t = S t 1 + pt, = 1, 3, 6, 9, 12 where com ind, met Commodity currencies (Chen, Rogoff, and Rossi 2010) S t+ t = S t 1 + e t i = 1, 3, 6, 9, 12 i S t+ t = S t 1 + et, = 1, 3, 6, 9, 12 where i Canada, Australia, Sout Africa

21 Summary of Forecasting Results CRB Indices Up to 3-month horizon: Large (9-25%) and statistically significant improvements in forecast accuracy. Commodity Currencies Up to 3-month horizon: Small (7-13%) but statistically significant improvements in forecast accuracy for AUD and CAD.

22 Survey Forecasts Monthly oil price forecasts from Consensus Economics, Inc. CF S t+ t = S t, = 3, 12 Quarterly oil price forecasts from Energy Information Administration (EIA) EIA S t+ t = S t, = 3, 12 Monthly Michigan Survey of Consumers (MSC) forecasts of the price of gasoline P gasoline t+ t gasoline = P,MSC t, = 60

23 Survey Forecasts Relative to No-Change Forecast CF S t+ t = S t, EIA S t+ t = S t, P gasoline t+ t = 3 = 12 = 60 MSPE Ratio Success Ratio MSPE Ratio Success Ratio MSPE Ratio Success Ratio MSC SPF gasoline,msc = P t, S t+ t = S t 1 + π t, S t+ t = S t 1 + π t, NOTES: Boldface indicates statistical significance at the 10% level. 1 No significance test possible due to lack of variation in success ratio.

24 Household Expectations of U.S. Retail Gasoline Prices (Cents/Gallon) Expected price 5 years from now Current price Expected real price 5 years from now Current price Expected price 5 years from now Actual price 5 years from now

25 Survey Forecasts Relative to No-Change Forecast CF S t+ t = S t, EIA S t+ t = S t, P gasoline t+ t = 3 = 12 = 60 MSPE Ratio Success Ratio MSPE Ratio Success Ratio MSPE Ratio Success Ratio MSC SPF gasoline,msc = P t, S t+ t = S t 1 + π t, S t+ t = S t 1 + π t, NOTES: Boldface indicates statistical significance at the 10% level. 1 No significance test possible due to lack of variation in success ratio.

26 3. Forecasting the Real Price of Oil

27 Forecasting Models of the Real Price of Oil AR, ARMA, ARIMA Kilian-Murphy (2010) VAR 1. Percent change in world oil production 2. Real activity index 3. Change in inventories 4. Real price of oil Consider two specifications Unrestricted VAR Bayesian VAR (Giannone, Lenza, Primiceri 2010)

28 Summary of Forecasting Results AR(I)MA Models Statistically significant improvements ( 17%) in forecast accuracy at 1-3 month horizon. VAR Models UVAR: Statistically significant improvements in forecast accuracy ( 19%) at 1-6 month horizon. BVAR: Results similar to those from unrestricted VAR Shrinkage improves forecast accuracy in more heavily parameterized model with 24 lags.

29 Percent Percent Percent Forecasting Scenarios for Real Price of Oil based on Kilian-Murphy SVAR Conditional Forecast Expressed Relative to Baseline Forecast 100 Forecast Adjustment Based on U.S. Oil Production Stimulus Scenario Forecast Adjustment Based on World Recovery Scenario Forecast Adjustment Based on Iran 1979 Speculation Scenario

30 4. Joint Forecasts of Oil Prices and US Real GDP Growth

31 Joint Forecasting Models A key reason price of oil considered important is its perceived predictive power for US real GDP. Examining this predictive power requires joint forecasting model of price of oil and domestic real activity. Two Models: VAR models Nonlinear dynamic forecasting models

32 Bivariate VAR Models Unrestricted VAR 4 4 r t = α 1 + i=1 B 11,i r t i + i=1 B 12,i y t i y t = α i=1 B 21,i y t i + i=1 B 22,i r t i 4 + e 1,t + e 2,t where r t is the real price of oil; and y t is US real GDP. Restricted VAR Assume oil price is exogenous (B 12,i = 0 i) Summary Only small (1-8%) improvements in forecast accuracy at 3-8 quarter horizon relative to AR(4) benchmark.

33 Percent at Annual Rates Percent at Annual Rates 10 Autoregressive Forecasts of Cumulative Real GDP Growth based on the Real Price of Oil (a) Four Quarters Ahead Realizations AR Forecast Linear VAR Forecast (b) One Quarter Ahead Realizations AR Forecast Linear VAR Forecast

34 Possible Explanations for Limited Success of Linear Forecasting Models Reflects inability to forecast more accurately real price of oil No. Can rule this out. Underlying predictive relationship is weak Predictive relationship between oil prices and domestic macroeconomic aggregates is time-varying: 1. Variation in the expenditure share of energy (Edelstein and Kilian 2009) 2. Variation in the extent of price regulation (Ramey and Vine 2010) 3. Variation due to changes in composition of underlying oil demand and oil supply shocks (Kilian 2009) Linear forecasting models inherently misspecified

35 Nonlinear Dynamic Forecasting Models Relationship between oil prices and US real GDP may be asymmetric in that only oil-price increases matter (Mork 1989; Hamilton 1996, 2003). Unrestricted multivariate nonlinear forecasting model r t = α 1 + y t = α i=1 B 11,i r t i + i=1 B 12,i y t i e 1,t i=1 B 21,i y t i + i=1 B 22,i r t i + i=1 δ i rt i 4 + e 2,t where rt r t net,+,3yr, r t net,+,1yr, r t + is censored oil-price increase variable (e.g., r t net,+,3yr = max{0, r t r t } and r t is the maximum log real price of oil during the past 3 years).

36 Summary of Nonlinear Forecasting Results Can forecast US GDP growth using model with: Exogenous oil prices (B 12,i = 0 i) and No feedback from lagged oil prices to GDP (B 22,i = 0 i) Models that combine restrictions B 12,i = 0 i and B 22,i = 0 i 3-year net nominal and real oil-price increases achieve forecast-accuracy improvements for US real GDP growth at 4-quarter horizon.

37 MSPE Ratio Percent (Annual Rates) Nonlinear Forecasts of Cumulative Real GDP Growth: Forecasting Success? 10 4-Quarter Ahead Recursive Forecasts of Cumulative Real GDP Growth Actual Nonlinear Forecast Based on 3-Year Net Oil Price Increase Quarter Ahead Recursive MSPE Ratio Relative to AR(4) Benchmark

38 5. Forecasting Oil Price Volatility and Quantifying Oil Price Risks

39 12-Month Ahead Predictive Density of the Real WTI Price as of Based on No-Change Forecast Dollars/Barrel

40 Percent Percent Percent Alternative Measures of Nominal Oil Price Volatility 40 1-Month Implied Volatility Realized Volatility Recursive GARCH Volatility

41 Limitations of Volatility Measures Models of delayed investment decisions require long-run, real oil price volatility, not short-run nominal volatility. Volatility is not risk. Consumers are not concerned with real oil-price volatility associated with price decreases. Risks depend on the predictive distribution of the variable of interest and on user s loss function (Machina and Rothschild 1987). Need to distinguish between upside and downside risk.

42 Oil Price Risks Consider event of Rt exceeding an upper threshold of R (upside h risk) or falling below the lower threshold of R (downside risk): Examples: DR α UR β R R R R t+ α df R t+ R t+ R β df R t+ 1. α = β = 0 DR 0 = Pr R t+ < R UR 0 = Pr R t+ > R, α 0, β 0 2. α = β = 1 DR 1 = E R t+ R R t+ < R Pr R t+ < R UR 1 = E R t+ R R t+ > R Pr R t+ > R.

43 12-Month-Ahead Upside and Downside Risks in the Real WTI Price Based on No-Change Forecast Target Probabilities UR(0)>80 DR(0)< Probability Weighted Expected Excess/Shortfall UR(1)>80 DR(1)<

44 6. Conclusions: How to Forecast the Price of Oil?

45 How to Forecast the Price of Oil? Nominal price of oil Futures prices generally poor predictors of spot prices 1-3 months: Adjust no-change forecast by recent price change in industrial raw materials 6-48 months: No-change forecast 60 months: Adjust no-change forecast by expected inflation Real price of oil 1-6 months: Recursive VAR forecast Beyond 6 months: No-change forecast

46 Background Slides

47 Predictability from Nominal U.S. Aggregates to the Nominal Price of Oil (p-values of the Wald test statistic for Granger Non-Causality) Evaluation Period: Monthly WTI WTI RAC RAC RAC Composite Predictors: Oil Imports Domestic Oil CPI M M CRB Industrial Raw Materials Index CRB Metals Index Month T-Bill Rate Trade-Weighted Exchange Rate

48 Predictability from Selected Bilateral Nominal Dollar Exchange Rates to the Nominal Price of Oil (p-values of the Wald test statistic for Granger Non-Causality) Evaluation Period: Monthly WTI WTI RAC RAC RAC Predictors: Oil Imports Domestic Oil Composite Australia Canada New Zealand South Africa

49 Predictability from Selected Real Aggregates to the Real Price of Oil (p-values of the Wald test statistic for Granger Non-Causality) 1973.I-2009.IV Evaluation Period: 1975.II-2009.IV Quarterly Predictors: WTI WTI RAC Oil Imports RAC Domestic Oil RAC Composite U.S. Real GDP LT HP DIF World Industrial Production LT HP DIF

50 Predictability from Selected Real Aggregates to the Real Price of Oil (p-values of the Wald test statistic for Granger Non-Causality) Evaluation Period: WTI WTI RAC RAC RAC Composite Monthly Oil Imports Domestic Oil Predictors: p = 12 p = 24 p = 12 p = 24 p = 12 p = 24 p = 12 p = 24 p = 12 p = 24 Chicago Fed National Activity Index (CFNAI) U.S. Industrial Production LT HP DIF OECD Industrial Production 1 LT HP DIF Global Real Activity Index

51 Forecast Accuracy Relative to Monthly No-Change Forecast Evaluation Period: January December 2009 F t () S t 1 + α + β ln(f t () /St ) MSPE Ratio Success Ratio MSPE Ratio Success Ratio NOTES: Boldface indicates statistical significance at the 10% level.

52 Forecast Accuracy Relative to Daily No-Change Forecast Evaluation Period: Since January 1986 F t () MSPE Ratio Success Ratio NOTES: There are 5968, 5926, 5861, 5744, and 5028 daily observations at horizons of 1 through 12 months, respectively. Boldface indicates statistical significance at Leamer s (1978) critical value.

53 Forecast Accuracy Relative to Daily No-Change Forecast (in years) Starting Sample MSPE Success date size Ratio Ratio 2 11/20/ /29/ /01/ /03/ /03/ /21/ NOTES: Boldface indicates statistical significance using Leamer s (1978) critical value.

54 Forecast Accuracy Relative to No-Change Forecast Evaluation Period: January December 2009 CRB,ind CRB,met S t 1 + pt, S t 1 + pt, MSPE Ratio Success Ratio MSPE Ratio Success Ratio NOTES: Boldface indicates statistical significance at the 10% level.

55 Recursive Forecasts of Real Price of Oil from AR and ARMA Models U.S. Refiners Acquisition Cost for Imported Crude Oil Evaluation period: = 1 = 3 = 6 = 9 = 12 MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR AR(12) AR(24) AR(SIC) AR(AIC) ARMA(1,1) ARI(11) ARI(23) ARI(SIC) ARI(AIC) ARIMA(0,1) NOTES: Boldface means significance at the 10% level.

56 Recursive Forecasts of Real Price of Oil from Kilian-Murphy (2010) VAR Model U.S. Refiners Acquisition Cost for Imported Crude Oil Evaluation period: UVAR BVAR p MSPE Ratio SR MSPE Ratio NOTES: Model includes the four oil market variables used in Kilian and Murphy (2010). BVAR based on Giannone, Lenza, and Primicieri (2010).

57 MSPE Ratios of VAR and VARX Models Relative to AR(4) Benchmark Cumulative U.S. Real GDP Growth Rates Evaluation Period: 1990.Q Q2 Real RAC Price of Imports Nominal RAC Price of Imports Horizon Oil Price Endogenous Oil Price Exogenous Oil Price Endogenous Oil Price Exogenous

58 MSPE Ratios for Alternative Specifications of Restricted Exogenous Model Cumulative U.S. Real GDP Growth Rate Oil Price Series 1990.Q Q Q Q4 Horizon Horizon h 1 h 4 h 1 h 4 Real RAC imports RAC composite RAC domestic WTI PPI Nominal RAC imports RAC composite RAC domestic WTI PPI