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.
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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.
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:
Commodity currencies: AUD, CAD, NZD, SAR (Chen, Rogoff,
and Rossi 2010).
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
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
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
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
2. Forecasting the Nominal Price of Oil
Do Oil Futures Prices Help Predict the Spot Price?
No-change (benchmark model)
𝑆 𝑡+ |𝑡 = 𝑆𝑡 = 1, 3, 6, 9, 12
Futures Price
𝑆 𝑡+ |𝑡 = 𝐹𝑡()
= 1, 3, 6, 9, 12
Futures Spread
𝑆 𝑡+ |𝑡 = 𝑆𝑡 1 + 𝛼 + 𝛽 ln(𝐹𝑡
/𝑆𝑡) , = 1, 3, 6, 9, 12
where 𝛼 and 𝛽 are recursive OLS estimates from
∆𝑠𝑡+ = 𝛼 + 𝛽 𝑓𝑡
− 𝑠𝑡 + 𝑢𝑡+
Forecast Accuracy of Futures Prices
Forecast Evaluation Period: 1991.1-2009.12
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
Alternative Monthly Forecasting Methods
Local trends and structural change
Recursive drift 𝑆 𝑡+|𝑡 = 𝑆𝑡 1 + 𝛼 = 1,… , 12
Rolling drift
𝑆 𝑡+|𝑡 = 𝑆𝑡 1 + ∆𝑠 𝑡()
= 1,… , 12
Random walk in growth
𝑆 𝑡+|𝑡 = 𝑆𝑡 1 + ∆𝑠𝑡 = 1,… , 12
Hotelling (1931)
𝑆 𝑡+|𝑡 = 𝑆𝑡 1 + 𝑖𝑡 , /12
= 3, 6, 12
Alternative Monthly Forecasting Methods
CRB commodity prices 𝑆 𝑡+ |𝑡 = 𝑆𝑡 1 + ∆𝑝𝑡
𝑐𝑜𝑚 = 1, 3, 6, 9, 12
𝑆 𝑡+ |𝑡 = 𝑆𝑡 1 + ∆𝑝 𝑡 ,𝑐𝑜𝑚 = 1, 3, 6, 9, 12
where 𝑐𝑜𝑚 ∈ 𝑖𝑛𝑑,𝑚𝑒𝑡
Commodity currencies (Chen, Rogoff, and Rossi 2010)
𝑆 𝑡+ |𝑡 = 𝑆𝑡 1 + ∆𝑒𝑡𝑖
= 1, 3, 6, 9, 12
𝑆 𝑡+ |𝑡 = 𝑆𝑡 1 + ∆𝑒 𝑡 ,𝑖 = 1, 3, 6, 9, 12
where 𝑖 ∈ 𝐶𝑎𝑛𝑎𝑑𝑎,𝐴𝑢𝑠𝑡𝑟𝑎𝑙𝑖𝑎, 𝑆𝑜𝑢𝑡 𝐴𝑓𝑟𝑖𝑐𝑎
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.
Survey Forecasts
Monthly oil price forecasts from Consensus Economics, Inc.
𝑆 𝑡+|𝑡 = 𝑆𝑡 ,𝐶𝐹 = 3, 12
Quarterly oil price forecasts from Energy Information Administration (EIA)
𝑆 𝑡+|𝑡 = 𝑆𝑡 ,𝐸𝐼𝐴 = 3, 12
Monthly Michigan Survey of Consumers (MSC) forecasts of the price of gasoline
Forecast Accuracy Relative to Monthly No-Change Forecast Evaluation Period: January 1991- December 2009
𝐹𝑡()
𝑆𝑡 1 + 𝛼 + 𝛽 ln(𝐹𝑡()
/𝑆𝑡)
MSPE Ratio Success Ratio MSPE Ratio Success Ratio
1 0.988 0.465 1.001 0.539
3 0.998 0.465 1.044 0.531
6 0.991 0.509 1.051 0.535
9 0.978 0.548 1.042 0.583
12 0.941 0.557 1.240 0.537
NOTES: Boldface indicates statistical significance at the 10% level.
Forecast Accuracy Relative to Daily No-Change Forecast Evaluation Period: Since January 1986
𝐹𝑡()
MSPE Ratio Success Ratio
1 0.963 0.522
3 0.972 0.516
6 0.973 0.535
9 0.964 0.534
12 0.929 0.562
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.
Forecast Accuracy Relative to Daily No-Change Forecast
NOTES: Boldface indicates statistical significance using Leamer’s (1978) critical value.
(in years) Starting date
Sample size
MSPE Ratio
Success Ratio
2 11/20/90
3283
1.159
0.515
3 05/29/91
515
1.168
0.518
4 11/01/95
194
1.212
0.294
5 11/03/97
154
1.280
0.247
6 11/03/97
134
1.158
0.276
7 11/21/97
22
1.237
0.500
Forecast Accuracy Relative to No-Change Forecast Evaluation Period: January 1991- December 2009
𝑆𝑡 1 + ∆𝑝 𝑡 ,𝐶𝑅𝐵 ,𝑖𝑛𝑑 𝑆𝑡 1 + ∆𝑝 𝑡 ,
𝐶𝑅𝐵 ,𝑚𝑒𝑡
MSPE Ratio Success Ratio MSPE Ratio Success Ratio
1 0.913 0.583 1.031 0.579
3 0.782 0.601 0.750 0.601
6 1.055 0.583 1.219 0.623
9 1.076 0.553 1.304 0.575
12 1.035 0.548 1.278 0.539
NOTES: Boldface indicates statistical significance at the 10% level.
Recursive Forecasts of Real Price of Oil from AR and ARMA Models U.S. Refiners’ Acquisition Cost for Imported Crude Oil
Evaluation period: 1991.12-2009.8 = 1 = 3 = 6 = 9 = 12 MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR