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Classification JEL : Q43, C53, E32
Classification de la Banque : Méthodes économétriques et statistiques; Questions
internationales
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1. Introduction
The realtime nature of data used in forecasting has received increasing attention in recent years
(see, e.g.,
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Clements and Galvão 2010; Croushore 2006, 2011).
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Although the real price of oil is
one of the key variables in the modelbased macroeconomic projections generated by central
banks, private sector forecasters, and international organizations, there have been no studies to
date of how best to forecast the real price of oil in real time.
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This data set allows the
construction of realtime forecasts of the real price of oil from a variety of models. Both
backcasting and nowcasting techniques are used to fill gaps in the realtime data. In section 2, we
show that revisions of most oil market data represent “news” as defined in De
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Jong (1987) and
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Faust, Rogers, and Wright (2005). In other words, there is little scope for improving forecasts by
modeling the revision process. This fact facilitates the construction of nowcasts to fill in gaps in
the availability of realtime data for most series.
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In addition, these VAR models have
consistently and often significantly higher directional accuracy with success ratios as high as
65% in real time in some cases. Such success ratios are high by the standards of the empirical
finance literature (see, e.g.,
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Pesaran and Timmermann 1995).
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Section 3 also contrasts the realtime forecasting results with results for the same
forecasting models based on expost revised data. It is not obvious ex ante whether models
based on expost revised data should forecast more accurately than models based on realtime
data.
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These tools are designed
to allow endusers to interpret oil price forecasts in light of economic models and to evaluate
their sensitivity to alternative assumptions. The concluding remarks are in section 6.
2. The RealTime Data Set
Unlike
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Carlton (2010) and Ravazzolo and Rothman (2010)
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our focus is not on realtime
forecasting of U.S. real GDP growth on the basis of lagged oil prices, but rather on generating
realtime forecasts of the real price of oil. Our analysis is more closely related to the recent
literature on realtime forecasts of the nominal price of oil (see, e.g.
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The RealTime Data Set
Unlike Carlton (2010) and Ravazzolo and Rothman (2010) our focus is not on realtime
forecasting of U.S. real GDP growth on the basis of lagged oil prices, but rather on generating
realtime forecasts of the real price of oil. Our analysis is more closely related to the recent
literature on realtime forecasts of the nominal price of oil (see, e.g.,
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Alquist and Kilian 2010;
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Alquist, Kilian, and Vigfusson 2011). Although the real price of oil is one of the key variables in
the modelbased macroeconomic projections generated by central banks, private sector
forecasters, and international organizations, there have been no studies to date of how best to
forecast the real price of oil in real time.
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Prior to 1996.1 this publication is not available in electronic form. The
construction of the realtime data set from the historical issues of the Monthly Energy Review is
described in detail below. The nominal shipping rate data are obtained from
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Kilian (2009)
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for
1973.1 through 1984.12 and are extrapolated through 2010.12 using the Baltic Dry Cargo Index
(BDI) from Bloomberg. Realtime data for the monthly U.S. consumer price index are obtained
from the Economic Indicators published by the Council of Economic Advisers.
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In constructing the monthly U.S. refiners’ acquisition cost for crude oil imports a further
complication arises because these data are only available starting in 1974.1. We followed the
procedure outlined in
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Mork (1989,
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p. 741) for extrapolating the refiners’ acquisition cost
backwards to 1973.1. This procedure involves scaling the monthly percent rate of change in the
U.S. crude oil producer price index for 1973.11974.1 by the ratio of the growth rate in the
annual refiners’ acquisition cost over the growth rate in the annual U.
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Consistent series for OECD petroleum stocks are not available prior to 1987.12. We
therefore extrapolate the percent change in OECD inventories backwards at the rate of growth of
U.S. petroleum inventories, following
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Kilian and Murphy (2010).
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For the post1987.12 period,
U.S. and OECD petroleum inventory growth rates are highly correlated. We also adjust the realtime OECD petroleum inventory data to account for changes in the set of OECD members
reporting inventories in December 2001.
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realtime CPI data from the Federal
Reserve Bank of Philadelphia, exploiting the fact that observations shown in each vintage
represent the data that were available in the middle of the quarter.
2.4. Data Transformations
The real price of oil is constructed by deflating the nominal price of oil by the U.S. consumer
price index. World oil production is expressed in growth rates. Following
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Kilian and Murphy (2010),
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a proxy for the change in world crude oil inventories is constructed by scaling U.S. crude
oil inventories by the ratio of OECD over U.S. petroleum inventories. This approximation is
required because there are no monthly crude oil inventory data for other countries.
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Finally, as is
standard in the literature, the measure of global real activity is constructed by cumulating the
growth rate of the index of nominal shipping rates, the resulting nominal index is deflated by the
U.S. consumer price index, and a linear deterministic trend representing increasing returns to
scale in ocean shipping is removed from the real index (see, e.g.,
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Kilian 2009).
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The resulting
index is designed to capture business cycle fluctuations in global industrial commodity markets.
In constructing the realtime version of this index of global real activity, the linear deterministic
trend is recursively reestimated in real time.
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This hypothesis
implies that revisions must be mean zero because otherwise revisions would be predictable. It
can be shown that there is no statistically significant bias in the revisions for any of the three
transformed realtime variables.
As noted by
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Faust et al. (2005),
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bias is the simplest form of predictability in revision.
Even in the absence of bias, however, revisions may be predictable based on preliminary data
releases. A more general specification of the news hypothesis implies that 0αβ== in
ptttRXuαβ=++
where tu may be serially correlated.
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RegressionBased Forecasts
Table 1 summarizes the realtime forecast accuracy of ARMA and AR models of the real U.S.
refiners’ acquisition cost for crude oil imports and of the fourvariable VAR oil market model of
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Kilian and Murphy (2010).
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The VAR model includes the percent change in global crude oil
production, the Kilian (2009) measure of global real activity (in deviations from trend), the
change in global crude oil inventories and the real U.
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RegressionBased Forecasts
Table 1 summarizes the realtime forecast accuracy of ARMA and AR models of the real U.S.
refiners’ acquisition cost for crude oil imports and of the fourvariable VAR oil market model of
Kilian and Murphy (2010). The VAR model includes the percent change in global crude oil
production, the
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Kilian (2009)
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measure of global real activity (in deviations from trend), the
change in global crude oil inventories and the real U.S. refiners’ acquisition cost for crude oil
imports, as a measure of the real price of crude oil in global oil markets.
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This forecasting success is perhaps unexpected given the common view
that the price of oil should be viewed as an asset price and like all asset prices is inherently
unpredictable. Our findings are fully consistent, however, with recent work showing that the
price of oil most of the time contains only a small asset price component (see
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Kilian and Murphy 2010; Kilian and Vega 2011).
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It is also consistent with evidence that the nominal WTI price of
oil is predictable based on economic fundamentals at short horizons (see Alquist, Kilian, and
Vigfusson 2011).
Although we report tests of statistical significance for the success ratios in Table 1b and
2b, we do not provide measures of statistical significance for the MSPE reductions in Tables 1a
and 2a.
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The reason is that such tests are not available. The problem is that the underlying time
series are not stationary because they include data that have been revised to different degrees
(see, e.g., Koenig, Dolmas, and Piger 2003;
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Clements and Galvão 2010; Croushore 2011).
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This
feature of the regression analysis violates the premise of standard asymptotic tests of equal
predictive accuracy. Clark and McCracken (2009) recently proposed an alternative test of equal
predictive accuracy for realtime data, the construction of which requires further assumptions on
the nature of the data revisions and evidence that these assumptions are met in the realtime data.
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The problem is that the underlying time
series are not stationary because they include data that have been revised to different degrees
(see, e.g., Koenig, Dolmas, and Piger 2003; Clements and Galvão 2010; Croushore 2011). This
feature of the regression analysis violates the premise of standard asymptotic tests of equal
predictive accuracy.
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Clark and McCracken (2009)
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recently proposed an alternative test of equal
predictive accuracy for realtime data, the construction of which requires further assumptions on
the nature of the data revisions and evidence that these assumptions are met in the realtime data.
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proposed an alternative test of equal
predictive accuracy for realtime data, the construction of which requires further assumptions on
the nature of the data revisions and evidence that these assumptions are met in the realtime data.
That test is not designed for iterated forecasts, however, and could not be applied in our context
even if our realtime data satisfied the assumptions of
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Clark and McCracken (2009).
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Nor is it
possible to rely on standard bootstrap methods to simulate the critical values of tests of equal
predictive accuracy in our iterated realtime setting. In section 3.2, we will show, however, that
the same regression models generate highly statistically significant rejections of the null of equal
predictive accuracy when applied to expost revised data.
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The reductions in MSPE range from 0% to 9% with a tendency to
increase with the forecasting horizon. Very similar results would be obtained using expost
revised data. However, none of the reductions in MSPEs are statistically significant based on the
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Diebold and Mariano (1995)
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test. When forecasting the real WTI price instead, this futuresbased
forecasting method is even less successful. Only at horizons of 9 and 12 are there any noticeable
reductions in the MSPE, and, again, none of the reductions are statistically significant.
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To
the extent that industrial commodity prices are driven by the same fluctuations in global real
economic activity as the price of oil, one would expect them to be a good proxy for one of the
key predictors included in the VAR model of
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Kilian and Murphy (2010).
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For the same reason, it
is no surprise that the forecast accuracy of the model based on industrial commodity prices
further improves when using expost revised data.
One obvious limitation of forecasting models based on nonoil industrial commodity
prices is that they can be expected to perform well as long as the real price of oil is driven by the
global business cycle as opposed to geopoli
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An equally important
limitation is that such forecasting methods do not convey how sensitive the real oil price
forecasts are to hypothetical events in the global market for crude oil. Forecasts that condition on
such hypothetical events can be viewed as conditional forecasts (see, e.g.,
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Waggoner and Zha 1999).
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They are also known as forecast scenarios. For example, a user may be interested in how
a temporary oil production shortfall would affect the forecast of the real price of oil. Similarly,
one may be interested in exploring the possible consequences of civil unrest in Libya, or in
exploring how much a period of unexpectedly low global demand for crude oil caused by a
global recession would lowe
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in exploring the possible consequences of civil unrest in Libya, or in
exploring how much a period of unexpectedly low global demand for crude oil caused by a
global recession would lower the real price of oil. The construction of such forecast scenarios
requires the use of structural econometric models.
Structural models of the global market for crude oil have recently been developed by
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Kilian (2009), Kilian and Murphy (2010, 2011), and Baumeister and Peersman (2010),
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among
others. In this section, we focus on the structural vector autoregressive model proposed in Kilian
and Murphy (2010). This model was designed to help us distinguish, in particular, between
unexpected oil production shortfalls, unexpected changes in the global demand for crude oil
driven by the global business cycle, and shocks to the demand for aboveground crude oil
inventories driven
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Structural models of the global market for crude oil have recently been developed by
Kilian (2009), Kilian and Murphy (2010, 2011), and Baumeister and Peersman (2010), among
others. In this section, we focus on the structural vector autoregressive model proposed in
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Kilian and Murphy (2010).
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This model was designed to help us distinguish, in particular, between
unexpected oil production shortfalls, unexpected changes in the global demand for crude oil
driven by the global business cycle, and shocks to the demand for aboveground crude oil
inventories driven by speculative motives.
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that the spot and
6 More specifically, the identifying assumptions are that: (1) a negative oil supply shock shifts the supply curve to
the left along the oil demand curve, resulting in a decrease in oil production and an increase in the price of oil, which
futures markets for crude oil are linked by an arbitrage condition (see
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Alquist and Kilian 2010).
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Thus, any speculation taking place in the oil futures market implies a shift in inventory demand
in the spot market by construction. This fact allows us to abstract from the oil futures market
altogether.
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This fact allows us to abstract from the oil futures market
altogether. Indeed, it can be shown that the structural shocks identified by this model are
fundamental in that the oil futures spread does not Grangercause the other variables included in
the model (see
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Giannone and Reichlin 2006).
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The reducedform representation of the Kilian and Murphy (2010) model corresponds to
the fourvariable VAR model we already considered in sections 2 and 3 and showed to be quite
accurate compared with the nochange benchmark as well as competing models.
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Indeed, it can be shown that the structural shocks identified by this model are
fundamental in that the oil futures spread does not Grangercause the other variables included in
the model (see Giannone and Reichlin 2006). The reducedform representation of the
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Kilian and Murphy (2010)
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model corresponds to
the fourvariable VAR model we already considered in sections 2 and 3 and showed to be quite
accurate compared with the nochange benchmark as well as competing models. Conditional
forecasts may be constructed from the structural moving average representation of the VAR
model also used for the historical decomposition by feeding in sequences of future oil demand
and oil s
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We begin in
section 5.1 with a brief structural analysis of the sources of fluctuations in the real price of oil
since the late 1970s and especially in recent years.
5.1. Historical Decompositions
Our analysis updates that in
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Kilian and Murphy (2010)
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from 2009.8 until 2010.6, the last date for
which we have available expost revised data. Although the model is only setidentified, all
admissible models can be shown to be quite similar, allowing us to focus on one such model with
little loss of generality.
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In
contrast, the decline in the real price of oil in 1998, for example, can be attributed primarily to an
unexpected decline in flow demand for crude oil following the Asian crisis.
These and other episodes have already been discussed in
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Kilian and Murphy (2010).
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Our
focus in this paper is on the additional evidence for the aftermath of the financial crisis. Figure 2
illustrates that much of the surge in the real price of oil between 2003 and mid2008 was caused
by repeated unexpected increases in the global business cycle as opposed to positive speculative
demand shocks or negative oil supply shocks.
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Figure 2
illustrates that much of the surge in the real price of oil between 2003 and mid2008 was caused
by repeated unexpected increases in the global business cycle as opposed to positive speculative
demand shocks or negative oil supply shocks. This finding is also consistent with independent
evidence on revisions to professional realGDP growth forecasts for the largest economies in
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Kilian and Hicks (2010).
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Kilian and Hicks documented that these forecast surprises were
associated with unexpected growth in emerging Asia.
As financial markets collapsed in the second half of 2008, so did global real activity and
hence demand for industrial commodities such as crude oil.
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such fears could be arbitrarily weak or strong, making it difficult to assess the
quantitative importance of this channel, but the historical experience of earlier episodes in Figure
2 provides some guidance.
One contagion scenario can be motivated by focusing on the surge in speculative demand
that occurred preceding and following the invasion of Kuwait in August of 1990. As discussed in
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Kilian (2008) and Kilian and Murphy (2010),
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among others, the invasion not only caused oil
production in Kuwait and Iraq to cease, but raised concerns that Saudi Arabia and its smaller
neighbors would be invaded next, causing a surge in speculative demand that only subsided after
the U.
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Clearly, forecast scenarios could alternatively
be constructed from DSGE models, provided that these models incorporate suitable structural oil
market models. One reason for focusing on the model in
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Kilian and Murphy (2010)
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instead is
7 Note that this sample period does not include the period of Libyan unrest and turmoil in oil markets that started in
February 2011.
that currently available DSGE models are still rather simplistic when it comes to modeling the
global oil market to be useful for policy analysis.
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Our focus in this paper is on illustrating the use of
structural models in constructing forecast scenarios rather than on advocating one type of
structural model over another.
6. Conclusion
The importance of realtime forecasting is well recognized in the literature (see, e.g.,
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Croushore 2011).
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Much of the work on realtime forecasting to date has focused on domestic
macroeconomic aggregates. In contrast, our focus in this paper has been on generating realtime
forecasts for the real price of oil, which is widely considered one of the key global
macroeconomic indicators.
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