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:

— 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)

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.

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)

1950 1955 1960 1965 19702

2.5

3

3.5

4

4.5

Nominal Price of Oil: 1948.1-1973.12

U.S

. D

olla

rs/B

arr

el

Actual WTI

Random Draw from Fitted Model

Pre-1974 Nominal Price of Oil

1950 1955 1960 1965 19702

2.5

3

3.5

4

4.5

Nominal Price of Oil: 1948.1-1973.12

U.S

. D

olla

rs/B

arr

el

WTI

1975 1980 1985 1990 1995 2000 2005 20100

20

40

60

80

100

120

140

U.S

. D

olla

rs/B

arr

el

Nominal Price of Oil: 1974.1-2010.4

WTI

RAC Domestic

RAC Imported

The Nominal Price of Crude Oil

1950 1955 1960 1965 1970-50

-40

-30

-20

-10

0

10

20

30

40

50

Real Price of Oil: 1948.2-1973.12

Perc

ent

Change

1975 1980 1985 1990 1995 2000 2005 2010-50

-40

-30

-20

-10

0

10

20

30

40

50

Perc

ent

Change

Real Price of Oil: 1974.2-2010.4

WTI WTI

RAC Domestic

RAC Imported

Percent Changes in the Real Price of Oil

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?

1. Predictability in Population

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-1973.

Thus, lagged macroeconomic aggregates should have predictive power for price of oil in population.

Predictability in population is a precondition for out-of-sample forecastability (Inoue and Kilian 2004).

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).

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

𝑃 𝑡+𝑕|𝑡𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒

= 𝑃𝑡 ,𝑕𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒 ,𝑀𝑆𝐶

𝑕 = 60

Survey Forecasts Relative to No-Change Forecast 𝑕 = 3 𝑕 = 12 𝑕 = 60

MSPE Ratio

Success Ratio

MSPE Ratio

Success Ratio

MSPE Ratio

Success Ratio

𝑆 𝑡+𝑕|𝑡 = 𝑆𝑡 ,𝑕𝐶𝐹

1.519 0.447 0.944 0.539 - - 𝑆 𝑡+𝑕|𝑡 = 𝑆𝑡 ,𝑕

𝐸𝐼𝐴 0.918 0.417 0.973 0.562 - -

𝑃 𝑡+𝑕|𝑡𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒

= 𝑃𝑡 ,𝑕𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒 ,𝑀𝑆𝐶

- - - - 0.765 0.9071

𝑆 𝑡+𝑕|𝑡 = 𝑆𝑡 1 + 𝜋𝑡 ,𝑕𝑀𝑆𝐶 - - 1.047 0.5661 - -

𝑆 𝑡+𝑕|𝑡 = 𝑆𝑡 1 + 𝜋𝑡 ,𝑕𝑆𝑃𝐹 - - 1.016 0.5791 0.855 0.8111

NOTES: Boldface indicates statistical significance at the 10% level. 1 No significance test possible due to lack of variation in success ratio.

1994 1996 1998 2000 2002 2004 2006 2008 20100

100

200

300

400

500

600

1994 1996 1998 2000 2002 2004 2006 2008 20100

100

200

300

400

500

1994 1996 1998 2000 2002 2004 2006 2008 20100

100

200

300

400

500

600

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

Household Expectations of U.S. Retail Gasoline Prices (Cents/Gallon) 1992.11-2010.1

Survey Forecasts Relative to No-Change Forecast 𝑕 = 3 𝑕 = 12 𝑕 = 60

MSPE Ratio

Success Ratio

MSPE Ratio

Success Ratio

MSPE Ratio

Success Ratio

𝑆 𝑡+𝑕|𝑡 = 𝑆𝑡 ,𝑕𝐶𝐹

1.519 0.447 0.944 0.539 - - 𝑆 𝑡+𝑕|𝑡 = 𝑆𝑡 ,𝑕

𝐸𝐼𝐴 0.918 0.417 0.973 0.562 - -

𝑃 𝑡+𝑕|𝑡𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒

= 𝑃𝑡 ,𝑕𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒 ,𝑀𝑆𝐶

- - - - 0.765 0.9071

𝑆 𝑡+𝑕|𝑡 = 𝑆𝑡 1 + 𝜋𝑡 ,𝑕𝑀𝑆𝐶 - - 1.047 0.5661 - -

𝑆 𝑡+𝑕|𝑡 = 𝑆𝑡 1 + 𝜋𝑡 ,𝑕𝑆𝑃𝐹 - - 1.016 0.5791 0.855 0.8111

NOTES: Boldface indicates statistical significance at the 10% level. 1 No significance test possible due to lack of variation in success ratio.

3. Forecasting the Real Price of Oil

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)

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.

2010 2011-100

-50

0

50

100

Forecast Adjustment Based on U.S. Oil Production Stimulus Scenario

Perc

ent

2010 2011-100

-50

0

50

100

Forecast Adjustment Based on 2007-08 World Recovery Scenario

Perc

ent

2010 2011-100

-50

0

50

100

Forecast Adjustment Based on Iran 1979 Speculation Scenario

Perc

ent

Forecasting Scenarios for Real Price of Oil based on Kilian-Murphy SVAR Conditional Forecast Expressed Relative to Baseline Forecast

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

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

Bivariate VAR Models

Unrestricted VAR

∆𝑟𝑡 = 𝛼1 + 𝐵11,𝑖∆𝑟𝑡−𝑖4𝑖=1 + 𝐵12,𝑖∆𝑦𝑡−𝑖

4𝑖=1 + 𝑒1,𝑡

∆𝑦𝑡 = 𝛼2 + 𝐵21,𝑖∆𝑦𝑡−𝑖4𝑖=1 + 𝐵22,𝑖∆𝑟𝑡−𝑖

4𝑖=1 + 𝑒2,𝑡

where 𝑟𝑡 is the real price of oil; and 𝑦𝑡 is US real GDP. Restricted VAR Assume oil price is exogenous (𝐵12,𝑖 = 0 ∀ 𝑖)

Summary Only small (1-8%) improvements in forecast accuracy at 3-8

quarter horizon relative to AR(4) benchmark.

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010-10

-5

0

5

10

Perc

ent

at

Annual R

ate

s

(a) Four Quarters Ahead

Realizations

AR Forecast

Linear VAR Forecast

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010-10

-5

0

5

10

Perc

ent

at

Annual R

ate

s

(b) One Quarter Ahead

Realizations

AR Forecast

Linear VAR Forecast

Autoregressive Forecasts of Cumulative Real GDP Growth based on the Real Price of Oil

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

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

∆𝑟𝑡 = 𝛼1 + 𝐵11,𝑖∆𝑟𝑡−𝑖4𝑖=1 + 𝐵12,𝑖∆𝑦𝑡−𝑖

4𝑖=1 + 𝑒1,𝑡

∆𝑦𝑡 = 𝛼2 + 𝐵21,𝑖∆𝑦𝑡−𝑖4𝑖=1 + 𝐵22,𝑖∆𝑟𝑡−𝑖

4𝑖=1 + 𝛿𝑖𝑟 𝑡−𝑖

4𝑖=1 + 𝑒2,𝑡

where 𝑟 𝑡 ∈ ∆𝑟𝑡𝑛𝑒𝑡 ,+,3𝑦𝑟

,∆𝑟𝑡𝑛𝑒𝑡 ,+,1𝑦𝑟

,∆𝑟𝑡+ is censored oil-price

increase variable (e.g., ∆𝑟𝑡𝑛𝑒𝑡 ,+,3𝑦𝑟

= max{0, 𝑟𝑡 − 𝑟𝑡∗} and 𝑟𝑡

∗ is the

maximum log real price of oil during the past 3 years).

Summary of Nonlinear Forecasting Results

Can forecast US GDP growth using model with:

— Exogenous oil prices (𝐵12,𝑖 = 0 ∀ 𝑖) and

— No feedback from lagged oil prices to GDP (𝐵22,𝑖 = 0 ∀ 𝑖)

— Models that combine restrictions 𝐵12,𝑖 = 0 ∀ 𝑖 and

𝐵22,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.

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010-10

-5

0

5

10

Perc

ent

(Annual R

ate

s)

4-Quarter Ahead Recursive Forecasts of Cumulative Real GDP Growth

Actual

Nonlinear Forecast Based on 3-Year Net Oil Price Increase

1992 1994 1996 1998 2000 2002 2004 2006 20080

0.5

1

1.5

2

4-Quarter Ahead Recursive MSPE Ratio Relative to AR(4) Benchmark

MS

PE

Ratio

Nonlinear Forecasts of Cumulative Real GDP Growth: Forecasting Success?

5. Forecasting Oil Price Volatility and Quantifying Oil Price Risks

0 20 40 60 80 100 120 140 160 180 2000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

2009.12 Dollars/Barrel

12-Month Ahead Predictive Density of the Real WTI Price as of 2009.12 Based on No-Change Forecast

2002 2003 2004 2005 2006 2007 2008 2009 20100

10

20

30

40

1-Month Implied Volatility

Perc

ent

2002 2003 2004 2005 2006 2007 2008 2009 20100

10

20

30

40

Perc

ent

Realized Volatility

2002 2003 2004 2005 2006 2007 2008 2009 20100

10

20

30

40

Recursive GARCH Volatility

Perc

ent

Alternative Measures of Nominal Oil Price Volatility

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.

Oil Price Risks

Consider event of t hR

exceeding an upper threshold of 𝑅 (upside

risk) or falling below the lower threshold of 𝑅 (downside risk):

𝐷𝑅𝛼 ≡ − 𝑅 − 𝑅𝑡+𝑕 𝛼𝑑𝐹 𝑅𝑡+𝑕

𝑅

−∞, 𝛼 ≥ 0

𝑈𝑅𝛽 ≡ 𝑅𝑡+𝑕 − 𝑅 𝛽𝑑𝐹 𝑅𝑡+𝑕 ∞

𝑅 , 𝛽 ≥ 0

Examples:

1. 𝛼 = 𝛽 = 0 ⇒ 𝐷𝑅0 = −Pr 𝑅𝑡+𝑕 < 𝑅

𝑈𝑅0 = Pr 𝑅𝑡+𝑕 > 𝑅

2. 𝛼 = 𝛽 = 1 ⇒ 𝐷𝑅1 = 𝐸 𝑅𝑡+𝑕 − 𝑅|𝑅𝑡+𝑕 < 𝑅 Pr 𝑅𝑡+𝑕 < 𝑅

𝑈𝑅1 = 𝐸 𝑅𝑡+𝑕 − 𝑅 |𝑅𝑡+𝑕 > 𝑅 Pr 𝑅𝑡+𝑕 > 𝑅 .

2002 2003 2004 2005 2006 2007 2008 2009 2010-1

-0.5

0

0.5

1

Target Probabilities

UR(0)>80

DR(0)<45

2002 2003 2004 2005 2006 2007 2008 2009 2010-30

-20

-10

0

10

20

30

40

50

60

Probability Weighted Expected Excess/Shortfall

UR(1)>80

DR(1)<45

12-Month-Ahead Upside and Downside Risks in the Real WTI Price Based on No-Change Forecast

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

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

Background Slides

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: 1973.1-2009.12 1975.2-2009.12

Monthly Predictors:

WTI WTI RAC Oil Imports

RAC Domestic Oil

RAC Composite

CPI

0.004 0.108 0.021 0.320 0.161

M1

0.181 0.039 0.010 0.000 0.000

M2

0.629 0.234 0.318 0.077 0.209

CRB Industrial Raw Materials Index

0.000 0.000 0.000 0.000 0.000

CRB Metals Index

0.000 0.002 0.005 0.000 0.003

3-Month T-Bill Rate

0.409 0.712 0.880 0.799 0.896

Trade-Weighted Exchange Rate

- 0.740 0.724 0.575 0.746

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: 1973.1-

2009.12 1975.2-2009.12

Monthly

Predictors: WTI WTI RAC

Oil Imports RAC

Domestic Oil RAC

Composite

Australia

0.038 0.066 0.073 0.017 0.044

Canada

0.004 0.003 0.002 0.006 0.002

New Zealand

0.128 0.291 0.309 0.045 0.169

South Africa

0.017 0.020 0.052 0.021 0.037

Predictability from Selected Real Aggregates to the Real Price of Oil (p-values of the Wald test statistic for Granger Non-Causality)

Evaluation Period: 1973.I-2009.IV 1975.II-2009.IV

Quarterly Predictors:

WTI WTI RAC Oil Imports

RAC Domestic Oil

RAC Composite

U.S. Real GDP LT

0.353

0.852

0.676

0.397

0.561

HP 0.253 0.821 0.653 0.430 0.573 DIF 0.493 0.948 0.705 0.418 0.578

World Industrial Production

LT 0.032 0.095 0.141 0.081 0.098 HP 0.511 0.766 0.800 0.665 0.704 DIF 0.544 0.722 0.772 0.668 0.691

Predictability from Selected Real Aggregates to the Real Price of Oil (p-values of the Wald test statistic for Granger Non-Causality)

Evaluation Period: 1973.1-2009.12 1976.2-2009.12

Monthly WTI WTI RAC

Oil Imports RAC

Domestic Oil RAC Composite

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)

0.823 0.951

0.735 0.952

0.881 0.998

0.707 0.979

0.784 0.995

U.S. Industrial Production

LT 0.411 0.633 0.370 0.645 0.410 0.746 0.091 0.421 0.182 0.510 HP 0.327 0.689 0.357 0.784 0.415 0.878 0.110 0.549 0.194 0.668 DIF 0.533 0.859 0.458 0.866 0.473 0.909 0.114 0.490 0.222 0.699

OECD Industrial Production1

LT 0.028 0.001 0.009 0.033 0.023 0.199 0.021 0.187 0.018 0.230 HP 0.195 0.034 0.072 0.278 0.138 0.714 0.121 0.530 0.114 0.706 DIF 0.474 0.060 0.130 0.353 0.182 0.741 0.174 0.604 0.209 0.757

Global Real Activity Index

0.041 0.000

0.055 0.020

0.141 0.034

0.004 0.004

0.028 0.018

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

AR(12) 0.849 0.599 0.921 0.552 0.969 0.522 1.034 0.441 1.022 0.517 AR(24) 0.898 0.576 0.978 0.557 1.008 0.565 1.056 0.446 1.058 0.453 AR(SIC) 0.826 0.613 0.936 0.557 1.015 0.488 1.039 0.515 1.007 0.532 AR(AIC) 0.842 0.613 0.940 0.562 0.983 0.483 1.013 0.500 0.989 0.527 ARMA(1,1) 0.837 0.580 0.932 0.514 0.982 0.493 1.006 0.510 0.992 0.527 ARI(11) 0.856 0.604 0.939 0.571 1.003 0.517 1.095 0.471 1.091 0.512 ARI(23) 0.898 0.561 0.978 0.538 1.009 0.546 1.068 0.500 1.068 0.508 ARI(SIC) 0.833 0.594 0.951 0.605 1.041 0.546 1.053 0.505 1.016 0.527 ARI(AIC) 0.849 0.604 0.958 0.605 1.008 0.556 1.042 0.500 1.015 0.527 ARIMA(0,1) 0.841 0.599 0.945 0.581 1.009 0.546 1.032 0.515 1.017 0.512

NOTES: Boldface means significance at the 10% level.

Recursive Forecasts of Real Price of Oil from Kilian-Murphy (2010) VAR Model

U.S. Refiners’ Acquisition Cost for Imported Crude Oil

Evaluation period: 1991.12-2009.8

UVAR BVAR 𝑝 𝑕 MSPE Ratio SR MSPE Ratio

12 1 0.814 0.561 0.800 3 0.834 0.567 0.876 6 0.940 0.546 0.967 9 1.047 0.564 1.052 12 0.985 0.632 1.004

24 1 0.961 0.561 0.801 3 1.081 0.614 0.883 6 1.298 0.604 0.993 9 1.476 0.583 1.095 12 1.415 0.647 1.059

NOTES: Model includes the four oil market variables used in Kilian and Murphy (2010). BVAR based on Giannone, Lenza, and Primicieri (2010).

MSPE Ratios of VAR and VARX Models Relative to AR(4) Benchmark Cumulative U.S. Real GDP Growth Rates

Evaluation Period: 1990.Q1-2010.Q2

Real RAC Price of Imports Nominal RAC Price of Imports

Horizon Oil Price Endogenous

Oil Price Exogenous

Oil Price Endogenous

Oil Price Exogenous

1 1.10 1.10 1.11 1.11 2 1.04 1.04 1.05 1.05 3 0.99 0.98 1.00 0.99 4 0.97 0.96 0.98 0.97 5 0.96 0.95 0.96 0.96 6 0.95 0.94 0.95 0.95 7 0.92 0.92 0.92 0.92 8 0.92 0.92 0.92 0.92

MSPE Ratios for Alternative Specifications of Restricted Exogenous Model Cumulative U.S. Real GDP Growth Rate

Oil Price Series 1990.Q1-2010.Q2 1990.Q1-2007.Q4 Horizon Horizon 1h 4h 1h 4h

Real RAC imports 0.91 0.85 1.11 1.71 RAC composite 1.16 0.99 1.49 2.05 RAC domestic 1.23 0.89 1.55 1.73 WTI 1.03 0.70 1.23 1.22 PPI 1.24 1.09 1.63 2.28 Nominal RAC imports 1.01 0.74 1.22 1.37 RAC composite 1.26 0.82 1.58 1.54 RAC domestic 1.23 0.80 1.50 1.40 WTI 0.92 0.66 1.02 1.08 PPI 1.23 0.88 1.59 1.78