Futures Prices are Useful Predictors of the Spot Price of Crude Oil

How well do futures prices forecast the spot price of crude oil? Contrary to the established view, futures prices significantly improve upon the accuracy of monthly no-change forecasts. This results from two innovations. First, we document that independent of the construction of futures-based forecasts, longer-horizon futures prices have become better predictors of crude oil spot prices since the mid-2000s. Second, we show that futures curves constructed using end-of-month prices instead of average prices have consistently been able to generate large accuracy-improvements for short-horizon forecasts of average prices. These findings are remarkably robust and apply to all major crude oil benchmarks.


INTRODUCTION
Given the importance of crude oil as a macroeconomic determinant used in models of central banks, in investment decisions, and in oil-intensive goods purchases, there is wide interest in accurately predicting the price of crude oil. 1 A frequently cited result in this literature is that futures prices are not particularly useful to forecast the spot price of crude oil (Alquist and Kilian, 2010;Reeve and Vigfusson, 2011;Baumeister and Kilian, 2012;Alquist et al., 2013;Baumeister and Kilian, 2014).In this paper, we document that future-based forecasts have always been useful for short-horizon forecasts of the average spot price of crude oil and are now very accurate at longer horizons.This occurs for two reasons.
First, we show that futures curves constructed using end-of-month prices contain substantive predictive power for future average prices at short horizons.Incorporating end-of-period information improves the mean-squared prediction error (MSPE) and the directional accuracy relative to the no-change forecast for average spot prices by 40 percent at the one-month horizon.The improvements remain statistically significant for forecasts up to 12 months ahead.They are remarkably robust and independent of the sample period.
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Second, the predictive content of crude oil futures prices at longer forecast horizons has improved since the mid-2000s.We show that, whenever the end of the forecast evaluation period is extended beyond 2014, futures-based forecasts are found to be statistically significantly more accurate predictors of the spot price than the no-change forecast at horizons of one year to five years ahead.This result holds for forecasts of both nominal prices (as in Alquist and Kilian, 2010) and real prices (as in Baumeister and Kilian, 2012).It is particularly strong for multi-year-ahead forecasts, which were previously difficult to evaluate due to the lack of a proper evaluation period for longer-dated futures contracts.This corroborates and generalizes some existing evidence on the usefulness of future-based forecasts of real prices at longer horizons. 2 key insight from our exercises is that futures-based forecasts should always be constructed using end-of-period prices rather than the average price that is standard in forecasts of the real price of oil (Baumeister and Kilian, 2012;Alquist et al., 2013).This seemingly innocuous difference yields substantial improvements for short-horizon forecasts.The use of end-of-period prices is preferable because averaging changes the underlying data process (Rossana and Seater, 1995), which leads to a mechanical loss of information that is particularly relevant for forecasting persistent processes (Wei, 1978;Lütkepohl, 1984).Ellwanger and Snudden (2021) propose a parsimonious solution to the information loss via period-end price sampling (PEPS).They show that real end-ofmonth spot prices can improve the forecast accuracy of no-change forecasts and of model-based forecasts by preserving the informational content of the last available price.In this paper, we show that the same principle can be applied to forecasts constructed from futures prices.
Futures curves constructed with end-of-month prices have previously been used in Alquist and Kilian (2010) in the context of forecasting of the end-of-month nominal crude oil price.However, the model was never used to forecast average spot prices, which are standard for real prices.While the distinction between end-of-period and average futures prices is crucial, the role of the deflator appears to be negligible for our results: using information from end-of-period futures prices work similarly well for forecasting average nominal and real prices.
The results contribute to a recurring debate on the role of futures prices in forecasting oil prices.Because of their simplicity and ease of implementation, futures-based forecasts are popular among policy makers, investors and market participants.Early results from the academic literature documented some predictability from oil futures prices, at least at specific horizons (Ma, 1989;Kumar, 1992;Chinn et al., 2005;Coppola, 2008).However, influential reviews that extended the sample period beyond the early 2000s found little evidence that futures-based forecasts are helpful to forecast oil prices and recommended against their use (Alquist and Kilian, 2010;Baumeister and Kilian, 2012).Still, futures prices have remained a steady ingredient in the construction of forecast combinations (Baumeister and Kilian, 2015;Funk, 2018;Garratt et al., 2019), while other approaches focused on improving futures-based forecast by separating their expectations component from the risk premium (Baumeister and Kilian, 2016).Our results show that a decade's worth of additional data, as well as a simple modification to the originally proposed implementation, changes the assessment of futures-based forecasts of the price of oil.

FUTURES-BASED FORECASTS
The goal of this paper is to study the predictive content of oil futures for the spot price of crude oil.The spot price of oil is determined in market transactions for immediate delivery and used as a key macroeconomic indicator by both academics and policy makers (see, e.g.Alquist and Kilian, 2010).By contrast, futures contracts are financial instruments that allow traders to lock in today a price at which to buy or sell a fixed quantity of oil on a predetermined date in the future.The inherent forward-looking nature of these contracts contributes to the wide-spread interest of futures as predictors of spot prices.
Following existing practice, we construct futures-based forecasts for monthly data using the percentage spread of the futures price with maturity h, , h t x F , over the spot price, , where t denotes the current month, h denotes the forecast horizon, and x is an indicator for the price series that distinguishes between end-of-period observations ( = x n) and monthly average obser- vations ( = x a).The monthly average price is the average of the n daily closing prices within the month, ≡ ∑ .In a similar fashion, futures-based forecasts for real prices are constructed via: where ( ) E π is the expected U.S. inflation rate over the next h periods, and , , is the monthly measure of the real price of crude oil.
The distinction between average and end-of-period futures and spot prices clarifies the use of alternative futures-spreads and spot prices in the literature.For example, Alquist and Kilian (2010)  F F . 4 By contrast, average prices are typically considered to be more economically relevant for the construction of macroeconomic variables and total payoffs to oil intensive physical investments.As such, the standard series for the real price of oil used in structural work and forecasting applications has always been the average monthly price, , t a R (see, e.g., Kilian, 2009; Alquist et al.,  2013; Baumeister and Kilian, 2014, 2015).
In most applications, the futures-based forecast for real prices, , t a R , has been constructed with average futures prices, , h t a F . 5 However, averaging oil prices can lead to a loss of information about price levels relative to end-of-period observations (Benmoussa et al., 2020).A key contribution of this study is to systematically compare the relative forecast performance of end-of-period futures prices, , h t n F , and average futures prices, , h t a F , for the monthly average real price of oil, , t a R .
4. Technically, Alquist and Kilian (2010) average futures prices over the last 3-5 trading days of the month.However, we show that any averaging reduces the forecast accuracy of futures-based forecasts.Thus, our analysis focuses primarily on the closing price of the last trading day of the month.

F
F when documenting significant one-month-ahead forecasts of the real price of crude oil.We show that when closing prices are applied to the futures spread, these gains are measurable and statistically significant for up to 1 year ahead.

APPLICATION TO REAL-TIME FORECASTS
We construct monthly, recursive, real-time, and out-of-sample forecasts following Baumeister and Kilian (2012).Our baseline estimates are for West Texas Intermediate (WTI) crude oil.Forecasts for spot prices of alternative crude oil benchmarks, Brent and the U.S. refiners acquisition cost of imported crude oil, are considered in the robustness analysis.Monthly and daily spot prices for all crude oil series were obtained from the Energy Information Administration (EIA).Daily futures prices were collected from Haver.Contracts for different delivery months are traded with maturities up to 7 years.Contracts are used as continuous series, , h t i F , with = 1 h referring to the front contract, = 2 h referring to the second back contract, etc.Because trading for the front contract stops several days prior to the last business day of the month preceding delivery, the front contract rolls over to the next contract before the end of the month, typically around the 21st of the month. 6This means that the standard average futures price is based on prices for two adjacent contracts. 7 For forecast horizons of up to one year, our sample starts in 1992M1.For longer-term contracts, the sample starts when the contract values begin to be regularly reported: 1995M5 for the 2-year-contract, 2006M3 for the 3-year contract, and 2007M8 for the 5-year contract. 8For all forecasts, the sample period ends in 2021M1.
To construct real prices, monthly prices are deflated using real-time vintages of the seasonally adjusted U.S. consumer price index obtained from the FRASER database of the Federal Reserve Bank of St. Louis and the Philadelphia Federal Reserve.Expected inflation is derived from the CPI price index, which is projected using the historical average for CPI inflation from 1986M7 following Baumeister and Kilian (2012).
Forecast evaluation is conducted using the mean-squared prediction error (MSPE) ratio and the success ratio for directional accuracy.Consistent with the literature, both measures are compared against the no-change forecast constructed from the last available observation of the forecasted price series.Diebold and Mariano (1995) tests are used for the MSPE ratios to test the null hypothesis of equal predictability, whereas Pesaran and Timmermann (2009) tests are used to test the null hypothesis of random directional accuracy.

RESULTS
The results of the futures-based forecasts are presented in the following five sections.Section 4.1 presents the baseline results for WTI crude oil.Section 4.2 includes a discussion of how our findings relate to financialization and the competitive storage model.Section 4.3 considers the robustness of the WTI forecasts to alternative assumptions for constructing futures-based forecasts.Section 4.4 extends the results to alternative crude oil price series, and Section 4.5 compares the futures-based forecasts to alternative forecast models and benchmarks.
6. Trading terminates 3 business days prior to the 25th calendar day of the month prior to the contract month.If the 25th calendar day is not a business day, trading terminates 4 business days prior to the 25th calendar day of the month prior to the contract month.See https://www.cmegroup.com/markets/energy/crude-oil/light-sweet-crude.contractSpecs.html.
7. Forecasts based on average prices from a single contract are discussed in the robustness section.
8.An alternative approach to dealing with sparsely traded futures is to impute missing observations.However, while this approach extends the sample size, we found that it does not materially impact our results.

Futures-Based Forecasts of WTI Crude Oil Prices
Our main results focus on three different forecasting exercises, displayed in columns one to three in Table 1.The first column considers forecasts of the nominal end-of-month price of oil using end-of-month futures prices, as in Alquist and Kilian (2010).The futures-based forecasts exhibit lower MSPEs than the no-change forecasts at all forecast horizons.While the improvements are modest in magnitude and not statistically significant at short forecast horizons, they are large and significant for longer horizons.At the 1-year forecast horizon, the futures-based forecast reduces the MSPE of the no-change forecast by 13%, which is significant at the 5% significance level.Forecasts beyond one year are even better, with improvements close to 20% for the 2-and 6-year horizon.Improvements of more than 42% are observed at the 3-year horizon and are statistically significant at the 1% significance level.A similar pattern emerges from the success ratios, which indicate the directional accuracy of the futures-based forecast.The success ratio is slightly worse for short horizons, but both economically and statistically significantly more accurate than 50% for horizons of 1-year ahead and longer.For these forecasts, the directional accuracy is over 60%, peaking at 87% at the 3-year horizon.The brackets show the p-values for serial-dependence-robust tests of Diebold and Mariano (1995) for the null hypothesis of equal MSPEs and of Pesaran and Timmermann (2009) for the null of no directional accuracy.

Table 1: Futures-based forecasts of monthly prices of WTI crude oil
These results differ from Alquist and Kilian (2010), who focused on forecasts of up to 1-year, but found that futures prices typically performed worse than no-change forecasts in terms of the MSPE and only marginally better for directional accuracy.We show that for a longer sample period that extends to 2021, futures prices are significantly (both economically and statistically) better predictors than the no-change forecast beginning at the 1-year horizon.
The results thus far apply to the full sample evaluations.To see how the forecast performance evolved, Figure 1 displays the evolution of the MSPE ratios and directional accuracy from recursively updated sample periods.Interestingly, the relative forecast performance at the one-year horizon started to improve considerably after 2007, just when the sample of Alquist and Kilian (2010) ended.By 2010, the gains were close to 10% and remained relatively stable.The p-values with the test for equal predictability associated with the recursively updated 1-year-ahead forecasts indicate that the null hypothesis of equal predictability can be rejected at the 5% confidence level for any estimation period that extends beyond December 2013.As discussed in more detail in the next section, one possible explanation for these results is that the liquidity and volume of future contracts-in particular of those with longer maturities-has gradually increased over the last decades.Qualitatively similar results are obtained for forecasts of the real price of oil when the forecasts are constructed with the average-futures price, as in Baumeister and Kilian (2012).The results are displayed in column 2 of Table 1.Except for very short forecast horizons up to 6 months, the futures based-forecasts outperform the no-change forecast, both in terms of the MSPE ratio and the success ratio.These improvements are statistically significant at conventional levels for all horizons of one year and beyond.For the 3-year and 5-year horizon, the futures-based forecasts reduce the MSPE by over 50% and have a directional accuracy of more than 80%.
Figure 1 shows that similar to the forecasts for nominal end-of-month prices, the standard futures-based forecasts for the real price of oil improved considerably after the mid-2000s.Using a sample period until 2010, Baumeister and Kilian (2012) found that at forecast horizons up to one year, futures-based forecast were only marginally, and generally insignificantly, better than the no-change forecast.For larger sample periods, however, these forecasts are economically and statistically significant at the one-year horizon.Our results show that the forecast performance of the standard futures-based forecast of the real price of oil steadily improved over the 2010 and became statistically significant for samples ending in June 2014, which explains more favorable results reported in recent studies at horizons of one-and two-years ahead (e.g., Baumeister and Kilian, 2016;Manescu et al., 2016;Funk, 2018;Garratt et al., 2019).
Finally, the 3rd column of Table 1 considers forecasts of the real price of oil that are constructed using end-of-month futures.Contrary to the standard futures-based forecast, which are constructed with the average price, forecasts based on end-of-month futures significantly outperform the no-change forecast at all forecasting horizons.For the one-month-ahead forecast, the MSPE reduction is 41% and the directional accuracy is 72%.These gains in forecast accuracy exceed gains typically found in studies advocating for introducing new models, predictor variables, or forecast combination techniques (see, e.g.Baumeister and Kilian, 2015;Funk, 2018;Garratt et al., 2019).
The short-run forecast accuracy of end-of-month futures-based forecasts is exceptionally robust across time.Figure 1 shows that at the one-month ahead horizon, the forecasting gains according to both criteria are large throughout the sample period.The MSPE gains are statistically significant at the 1 and 5 percent level for 97.2 and 100 percent of the sample, respectively.Moreover, the improvements in the MSPE and in the directional accuracy remained very stable throughout the COVID-19 episode.Figure 1 shows that the recursively estimated criteria remained close to pre-COVID-19 levels until the end of our sample period in 2021M1 for all forecasting horizons, indicating that futures continued to provide useful forecasts throughout this notable period.This degree of robustness is remarkable in a literature that is plagued with unstable forecast performances across different samples. 9nother important insight from these comparisons is that the forecast based on end-ofmonth futures is at least as good as the average-price futures-based forecast for all horizons.For the one-step ahead prediction, the improvements from introducing information from end-of-month prices are statistically significant at the 1% significance level for 93.6 percent of the sample, including the end of the sample.Likewise, for all forecast-horizons up to one year, the null hypothesis of equal forecast performance in terms of the MSPE and the success ratios can be rejected at the 10% significance level.Even though the improvements are somewhat weaker for longer-horizon fore-casts, our results show that futures-based forecasts should always be constructed with end-of-month futures prices rather than monthly average prices.

Interpretation
One potential explanation for our results is that oil futures have become more effective predictors of spot prices with the influx of additional market participants and increased trading activity over the last decades.Figure 2  Although the level of trading activity of longer dated contracts remains markedly lower than that of contracts with a closer delivery date, contracts with maturity of more than 24 months experienced some of the largest relative increases, as these contracts were hardly traded before 2005.As documented in previous studies, much of the elevated trading activity can be traced back to the influx of financial investors (see, e.g.Fattouh et al., 2013;Alquist and Gervais, 2013).To understand how this development could influence the predictive content of futures prices, it is useful to consider that the futures price of the h-month ahead contract, h t F , can be de- composed into an expectations component and a risk premium: where ( | )

E S I
+ is the conditional market expectation of the spot price in period t h + given time t information and h t RP is the futures risk premium (see, e.g., Hamilton, 2009; Baumeister and Kil- ian, 2016).Equation 3 highlights two potential channels through which investors could influence the forecast accuracy.First, investors might possess additional information over traditional market participants and improve market efficiency when they trade on this information (Goldstein and Yang, 2022).This would be reflected in a more precise conditional expectation, ( | )

E S I
+ , due to an increase in the information set.Second, as suggested by Hamilton and Wu (2014), the influx of investors might have contributed to a reduction in the risk premium.As seen from Equation 3, a reduction in the risk premium increases the signal about future expectations that is contained in futures prices.Although it is not possible to further disentangle these effects without additional evidence or assumptions, our results are supportive of the notion that financialization had, if anything, positive effects on market liquidity and information efficiency in the oil futures market (Boyd et al., 2018).Our results can also be interpreted through the lens of the competitive storage model (Working, 1948;Triantafyllou et al., 2020).According to this model, a negative commodity futures-spot price spread is associated with rising convenience yields for holding physical inventory and hence with rising commodity prices.To investigate the relationship between the spread and spot prices, we consider an extension to our baseline model, in which we use the futures-spot price spread as a predictor variable in forecast regressions.Forecasts are computed via the equation

Table 2: Regression-based forecasts of WTI crude oil prices using the futures-spot spread
where α and β are real-time, least-squares estimates from recursive regressions.Similar to Alquist and Kilian (2010), we consider three different cases: the first restricts β to zero and while α is es- timated (row "EoM, α" in Table 2); the second, restricts α to zero and β is estimated (row "EoM, β "); and a third were both parameters are estimated freely (row "EoM, α β ").
Our baseline results from the previous section (row "EoM") can be interpreted a special case of Equation 4 where α is restricted to zero and β is restricted to one.In this case, Equation 4becomes The forecast success of the baseline model suggest that a higher net convenience yield (defined as the difference between the spot price and the futures prices) is associated with higher current prices but lower growth and hence lower spot prices in the future.As such, our results are consistent with the competitive storage model, which postulates a positive relationship between the convenience yield and current prices.
Similar to the baseline model, we find that the point estimates of the slope parameter β are positive. 10This is again in line with the predictions of the competitive storage model.However, Table 2 shows that there is little evidence that recursive estimates of α and β improve upon the forecast accuracy of the baseline model.While some estimated models outperform the restricted, estimation-free model, the improvements are typically modest, inconsistent across the different evaluation criteria, and only apply to selected forecasting horizons.Thus, the relationship between the futures spread and prices imposed by our baseline model is not only consistent with the theory of storage, but also produces effective forecasts in practice.

Alternative Futures Curves
This section examines the robustness of our results to alternative ways of constructing the futures-based forecast.In the first exercise, futures-based forecasts are constructed as direct forecasts using the deflated end-of-month futures prices: where | t h t p + is the expected consumer price index in period 1 t + .As for the spread model of Equa- tion 2, expected values of the CPI index are constructed by applying real-time estimates of the average historical inflation rate to the nowcasted real-time CPI data.Forecasts constructed in this way are similar to the spread model, but do not rely on log-approximations.Because the futures spread typically increases with the forecast horizon, one might expect differences in forecast performance at longer horizons.However, as shown in row "EoM, Direct" in Table 3, direct forecasts yield almost identical results to those obtained from the futures spread model.
The second robustness exercise investigates how averaging over end-of-month daily closing prices affects the futures-based forecasts.Averaging daily futures prices could be helpful if prices are distorted by random noise arising from measurement error or from market-microstructure dynamics.However, we find that introducing any averaging over daily futures prices decreases the performance of the futures-based forecasts.For example, the forecast based on the average price over the last three trading days, which is similar to the averaging used by Alquist and Kilian (2010), yields slightly worse MSPE ratios and does not improve on the Success Ratio (rows "EoM 3 Day Ave." in Table 3).Moreover, averaging over additional days is found to systematically worsen forecasts.The forecast improvements we obtain from end-of-period observations instead of averaged observations indicate that random noise in daily futures prices is largely irrelevant in practice.The result is not unexpected, given that oil futures prices are determined in liquid markets.It suggests that similar to other assets, market-microstructure noise in oil futures prices can generally be ignored at the daily frequency (see, e.g., Hansen and Lunde, 2006).
10. Details can be found in the online appendix, which reports recursive estimates for β over the sample period.

Table 3: Robustness to alternative ways of constructing futures curves for WTI crude oil
Notes: EoM stands for the baseline spread model using end-of-month closing prices, the other models are described in the text.The sample period is 1992M1 to 2021M1, except for the 36-months-ahead forecasts, which begin in 2006M3.MSPE ratios are expressed relative to the no-change forecast.Bold values indicate improvements over the no-change forecast.The brackets show the p-values for serial-dependence-robust tests of Diebold and Mariano (1995) for the null hypothesis of equal MSPEs and of Pesaran and Timmermann (2009) for the null of no directional accuracy.
The remaining exercises consider different alignments between futures prices and the forecasting horizon.Because the front month contract changes over the course of the month (and hence the th h contract more generally), the standard monthly average futures price used in the literature involves contracts from two distinct delivery months.As such, the front month contract in time t refers to the delivery in month 1 t + in the earlier days of month t, while the front month contract refers to a delivery in month 2 t + in the later days of the month, after the rollover.We now investigate forecasts that are based on the available information from a single contract before the rollover.Using the closing price or the average monthly price for a contract based on the information on the date when the front contact rolls over (rows "End of Contract" and "Contract Average", respectively) significantly deteriorates the short run forecasts.This is consistent with the idea that the closing price on the last trading day of the month contains significant additional information that is not available on the roll-over date.
Finally, we investigate whether the baseline spread model relying on end-of-month futures prices can be further improved by realigning the forecast horizon with the closest delivery date of the contract.By the end of the month, the front contract has rolled over and pertains to delivery dates that are appropriately 7 weeks out from the last trading day of the month.We therefore examine the possibility that the front month contract at the end of the month is a better predictor of the twomonth-ahead forecast and shift the forecasts at all horizons one month ahead.For the missing onestep-ahead forecast, we rely on a simple imputation that exploits the curvature of the futures curve.In particular, we apply the average curvature over the first 12 contracts to the first contract to create an artificial futures price for the 1-month-ahead contract.
The adjustment yields small but robust forecast improvements for forecasts up to ninemonths-ahead (row "EoM, Adjusted" in Table 3).For example, the one-month ahead MSPE ratio is reduced to 0.58 compared to 0.59 from the baseline specification and the three-month-ahead MSPE ratio is reduced to 0.86 from 0.87.Despite being small, the MSPE improvements at horizons less than one year are quite robust, as we find them to hold for over 92 percent of potential end points of the evaluation sample.These results suggest that some forecast gains can be realized by aligning the front month contract with the two-month ahead forecast.The futures-based forecasts of the remaining sections are therefore based on the adjusted futures curve model.

Alternative Crude Oil Prices
This section shows that our results are very robust across alternative oil price series.In a first set of exercises, we examine forecasts for alternative crude oil benchmarks.As shown in Table 4, the adjusted futures spread based on end-of-month prices performs similarly well for real prices of Brent (row "Brent").As for WTI, the forecasts of Brent prices result in over 40 percent gains in directional accuracy at the one-step-ahead and gains of over 55 percent at longer horizons.Again, we find that for horizons less than one year, there are small but robust gains from assuming that the first front contact refers to the two-month-ahead forecast.

Table 4: Futures-based forecasts for alternative crude oil benchmarks
Notes: RAC (WTI) and RAC (Brent) stands for forecasts of US refiner acquisition costs of imported crude oil using WTI and Brent spreads, respectively.The sample period is 1992M1 to 2021M1, except for the 36-months-ahead forecasts, which begin in 2006M3.MSPE ratios are expressed relative to the no-change forecast.Bold values indicate improvements over the no-change forecast.The brackets show the p-values for serial-dependence-robust tests of Diebold and Mariano (1995) for the null hypothesis of equal MSPEs and of Pesaran and Timmermann (2009) for the null of no directional accuracy.
Another oil price benchmark that is widely used in applied work is the U.S. refiner acquisition costs of imported crude oil (RAC). 11RAC is obtained through a monthly survey of refiners, for which no futures contracts exist.To circumvent this issue, we now investigate whether information from the WTI or Brent futures spread is useful to forecast this series.
The most straightforward way of applying the futures spread model for forecasts of RAC, where B refers to WTI or Brent crude oil.Since RAC is a monthly survey, no end-of-period spot prices, , RAC t n R , exist.However, following Benmoussa et al. (2020), a series of nominal end-of-period RAC observations can be constructed by applying the growth rate of the end-of-month WTI price over the average price of WTI to the nowcast of the monthly average RAC, , , 11.This series is often used in forecasting and structural analysis since it tends to be highly correlated with WTI and Brent prices and exhibits a longer history (see, e.g., Alquist et al., 2013).
. Real end-of-period RAC observations are then obtained by deflating the nominal series in the standard way.
The results from these forecasts, displayed in rows "RAC (WTI)" and "RAC (Brent)" of Table 4, show that futures-based forecasts of RAC perform remarkably well.For all horizons, the forecasts significantly outperform the no-change forecast and often yield economically large forecast gains.Except for the MSPE ratio for the one-step-ahead forecasts, the gains are of similar magnitude to those found for WTI and Brent crude oil.Table 4 also shows that the RAC forecasts using the WTI futures spread are consistently better than those using the Brent futures spread.One possible explanation for this result is that the WTI futures are more actively traded.For example, the trading volume of the front month contract for WTI crude oil was on average almost twice as large as that of Brent.Again, this provides suggestive evidence that increased volume is associated with improved forecast accuracy.
Next, we show that our results are robust to alternative assumptions about expected inflation.The rows "Nominal" and "Real, Ex-post" in Table 5 show that we obtain significant forecast improvements also for nominal crude oil prices and ex-post revised data instead of real-time data.Similarly, computing the growth rate of the CPI index based on historical data in starting in 1973M1 or 1990M1 rather than in 1986M7 (the baseline model) has little effect on the qualitative findings (rows "Real, 1973" and"Real, 1990" in Table 5).Overall, the price deflator plays a minor role, which is unsurprising given the relatively low variability of US inflation compared to that of nominal oil prices.Diebold and Mariano (1995) for the null hypothesis of equal MSPEs and of Pesaran and Timmermann (2009) for the null of no directional accuracy.

Table 5: Futures-based forecasts for alternative measures of expected inflation
Finally, futures-based forecasts perform similarly well for quarterly and annual data.These frequencies are of primary interest to policymakers (Baumeister andKilian, 2014, 2015).Mimicking the monthly forecasts, we construct quarterly forecast using the closing price on the last trading day of the quarter.Table 6 displays the results for real quarterly prices of WTI and Brent crude oil as well as the RAC.The one-quarter-ahead MSPE and success ratios for WTI crude oil prices are 0.56 and 0.74, respectively, which is slightly better than the one-step ahead forecasts for monthly data.For all series and forecast horizons, the MSPE and the success ratios indicate forecast improvements over the no-change forecast.For the success ratio, all improvements are significant at the 5 percent level and, in many cases, also at the 1 percent significance level.These results show that futures-based forecasts are also useful for lower-frequency data.

Comparison to Other Forecasts
Thus far, our results have shown that futures prices are useful predictors relative to the standard no-change forecast, which uses the last observation of the respective price series as a predictor of future prices at all horizons.This section compares the effectiveness of the futures-based forecast to that of other model-based and model-free forecasts.Specifically, we consider the autoregressive and vector autoregressive models of Baumeister and Kilian (2012), the judgement-based EIA forecasts, and the real end-of-month no-change forecast proposed by Ellwanger and Snudden (2021).
The EIA publishes monthly forecasts for the nominal price of WTI consistently since 2000M9 in their Short-Term Energy Outlook (STEO).Similar to the futures-based forecast, we compute forecasts for real prices by deflating the forecasts using the historical average growth rate of inflation between 1986M7 and the forecast date.The forecasts end in December of the following calendar year, which limits our analysis to horizons of up to 12 months.The STEO reports are published sometime between the end of the first and second week of each month and use information up to a couple of days before publication.Thus, the forecast for the first month is actually a nowcast that uses information that is not available at the end of the previous month.However, despite the informational advantage, row "EIA" in Table 7 shows that the EIA forecasts are inferior to the futures-based forecast at all horizons.
For the model-based forecasts, we replicate the real-time forecasts from the autoregressive (AR) and vector autoregressive (VAR) models of Baumeister and Kilian (2012).The vector autoregressive model is a 4-variable model that includes the real price of oil, a real economic activity index (Kilian, 2019), a proxy for changes in global crude oil inventories, and the growth rate of global crude oil production. 12Both models are estimated with 12 lags, but similar results are obtained for models with 24 lags.
12. The online appendix provides a detailed description and access to the data.Rows "AR" and "VAR" in Table 7 show that neither the AR nor the VAR forecasts significantly improve upon the MSPE of the no-change forecast at any horizon up to one year.This is consistent with evidence from other recent studies showing a deterioration in forecast accuracy of these models beginning in the late 2000s (Funk, 2018;Snudden, 2018;Baumeister et al., 2022).Although both models show forecasting gains relative to the no-change forecasts at the 36-month-horizon, these gains are not statistically significant for the MSPE ratio and smaller than those obtained from the futures-based forecast.More generally, the forecast improvements of the futures-based model displayed in Table 7 are larger than improvements reported from other, recently proposed VAR-based forecasts of the real price of oil (see, e.g., Funk, 2018;Snudden, 2018;Garratt et al., 2019;Baumeister et al., 2022).This suggests that futures prices are also useful relative to forecasts obtained from economic models.
Finally, Table 7 also displays the accuracy of the alternative no-change forecast recently proposed by Ellwanger and Snudden (2021).The authors argue that for real prices, the no-change forecast implied by the random walk model should be based on the real end-of-month price rather than the standard real monthly average price.Ellwanger and Snudden (2021) further document that the performance of the alternative no-change forecast often dominates that of the conventional no-change forecasts, especially at shorter forecast horizons.The results (row "No Change, EoM") show that this is indeed the case for the real price of WTI crude oil.Despite these improvements in the no-change forecast, however, the futures-based forecast remains more accurate at all forecasting horizons, with particularly large improvements observed for longer horizon forecasts.Taken together, the results from this section corroborate the evidence for the practical usefulness of futures prices for forecasting the price of oil.

DISCUSSION
Contrary to established views, futures prices are useful predictors of the spot price of crude oil.Futures curves constructed with end-of-month prices have always been able to generate robust one-step-ahead forecast accuracy improvements of over 40 percent for the average spot price.Moreover, the predictive content of longer horizon forecasts has improved considerably since the mid-2000s.Long-horizon forecasts perform particularly well, with reductions in the MSPE relative to the no-change forecast of over 55 percent at the 3-year horizons.
A potential explanation for this result is that oil futures have become more effective predictors with the influx of investors over the 2000s.This might occur either through additional information brought in by these investors (Goldstein and Yang, 2022), or through the associated decrease in the risk premium component of futures prices (Hamilton and Wu, 2014).Consistent with this view, we find that the relative increase in trading volume and open interest was largest for longer dated contracts.
In light of these results, previous recommendations against futures-based forecasts seem outdated.Futures-based forecast are easy to implement in real-time, offering policymakers, investors, and market participants straightforward forecasts of average crude oil prices that are significantly better than no-change forecasts.As such, they also provide a natural point of comparison to evaluate the usefulness of model-based forecasts of the price of crude oil, which have become increasingly popular over the last decade.
Our results also raise the question if similar improvements could be found for futures-based forecasts of other commodity prices.While historically, futures-based forecasts have proven to perform quite differently across different commodities (Chinn and Coibion, 2014), there is reason to believe that the insights of our paper apply more broadly.First, as suggested by Ellwanger and Snudden (2021), the gains from using end-of-period prices instead of average should apply to any persistent series, including the prices of other commodities.Second, many futures markets of other assets have experienced a similar process of financialization as the oil futures markets, which could, in principle, have contributed to similar changes in the predictive content of futures in these markets.Revisiting the predictive content of futures for other applications in the light of these findings opens up a promising avenue for future research.

Notes:
Futures-based forecasts of the monthly price of WTI crude oil.EoM stands for end-of-month prices, Average for average prices.Horizon stands for the forecast horizon in months.The start of the sample is 1992M1, or the month when futures prices for that contract are regularly observed; the end of the sample is 2021M1.MSPE ratios are expressed relative to the no-change forecast.Bold values indicate improvements over the no-change forecast.

Figure 1 :
Figure 1: Recursive MSPEs and success ratios for futures-based forecasts of WTI crude oil prices displays the evolution of two different indicators of market activity, namely trading volume and open interest, for WTI and Brent.The figure shows that, for both markets, volume and open interest have increased considerably since the early 2000s.

Figure 2 :
Figure 2: Trading volume and open interest for WTI and Brent crude oil

Notes:
Forecast performance of forecasting regressions using the futures-spot spread.EoM stands for the baseline futures spread model, EoM, α stands for a model with intercept, EoM, β for a model with slope coefficient, and EoM, α β for an unrestricted regression model.The sample period is 1992M1 to 2021M1, except for the 36-months-ahead forecasts, which begin in 2006M3.MSPE ratios are expressed relative to the no-change forecast.Bold values indicate improvements over the no-change forecast.The brackets show the p-values for serial-dependence-robust tests ofDiebold and Mariano (1995) for the null hypothesis of equal MSPEs and ofPesaran and Timmermann (2009) for the null of no directional accuracy.
Notes: Futures-based forecasts for the monthly price of WTI crude oil."Nominal" stands for forecasts of nominal WTI prices, "Real, Ex-post" stands for forecasts from the futures-based model that relies on ex-post revised instead of nowcasted inflation data.The dates in column CPI refer to the starting date used for the computation of average CPI inflation during the nowcasts.The sample period is 1992M1 to 2021M1, except for the 36-months-ahead forecasts, which begin in 2006M3.MSPE ratios are expressed relative to the no-change forecast.Bold values indicate improvements over the no-change forecast.The brackets show the p-values for serial-dependence-robust tests of

Table 6 :
Futures-based forecasts of the quarterly real price of crude oilNotes: Futures-based forecasts of the quarterly real price of WTI, Brent, and RAC crude oil.RAC (WTI) stands for forecasts of RAC using the WTI spread.The sample period is 1992Q1 to 2021Q1, except for the 8-and 12-quarter-ahead forecasts, which begin in 1995Q2 and 2006Q1, respectively.MSPE ratios are expressed relative to the no-change forecast.Bold values indicate improvements over the no-change forecast.The brackets show the p-values for serial-dependence-robust tests ofDiebold and Mariano (1995) for the null hypothesis of equal MSPEs and ofPesaran and Timmermann (2009) for the null of no directional accuracy.

Table 7 :
Comparison with alternative forecasting approaches for the real price of WTI crude oilNotes: Futures, EoM stands for the adjusted futures-based forecast using end-of-month futures prices; EIA stands for forecasts provided by the EIA; AR and VAR stands for forecasts from the autoregressive and the vector-autoregressive models ofBaumeister and Kilian (2012), respectively; No Change, EoM stands for the no-change forecast based on real end-of-month spot prices as proposed byEllwanger and Snudden (2021).The sample period is 2000M9-2021M1, except for the 36-months-ahead forecasts, which begin in 2006M3.MSPE ratios are expressed relative to the no-change forecast.Bold values indicate improvements over the no-change forecast.The brackets show the p-values for serial-dependence-robust tests ofDiebold and Mariano (1995) for the null hypothesis of equal MSPEs and ofPesaran and Timmermann (2009) for the null of no directional accuracy.
forecast the end-of-month nominal spot price, , who used monthly average real spot prices, , )