We have revealed long term sustainable trends in the difference between producer price index for oil and the overall PPI. In the long run, one can foresee the direction of oil price trend which is crucial for investments. Moreover, there are many short-term price fluctuations around the trend which have large amplitudes and thus allow active speculations.

In the beginning of 2009, we developed a model [1, 2] predicting the long-term price evolution for various subcategories of consumer and producer price indices as well as major commodities: gold, crude oil, metals, etc. The model was based on one prominent feature of the difference between consumer (producer) prices of individual components and the overall consumer (producer) price index. These differences are characterized by the presence of sustainable long-term (quasi-) linear trends. For many producer price indices, these trends are slightly nonlinear but still robust. They are observed in subcategories with varying weights in the CPI and PPI: meats, gold ores, durables and non-durables, jewelry and jewelry related products, and motor fuel.

For major CPI and PPI subcategories, these trends last from five to 20 years and then turn to trends with opposite slopes. The transition to new trends lasted three years at most. We have not revealed any clear turns after 2009 and the current transition period might last longer. There are also several subcategories without slope changes since the start of the relevant measurement as reported by the Bureau of Labor Statistics. All CPI and PPI time series (in this study we use seasonally adjusted CPIs and not seasonally adjusted PPIs) were retrieved from the BLS. The best example of such a one-leg trend since 1980 is the consumer price index of medical care. The index of communication has been linearly deviating from the headline CPI since 1998; before 1998 it had been reported as an indistinguishable part of the index of education and communication.

In the short run, actual prices oscillate around the long-term trends with varying amplitudes. In a sense, the trends represent the lines of gravity centers for given prices and any large deviation from the trends must be compensated promptly. As a result, both short- and long-term predictions of commodity prices are feasible. In the long run, the prices follow up the trends. In the short-run, the next move in a given price depends on the current position relative to the corresponding trend. When far from the trend, the price is more likely to start returning. When approaching the trend, the price may choose any direction for the further evolution, i.e. it should not inevitably go the other side of the trend. In this article, we focus on crude oil and motor fuel.

For the price index of motor fuel, we developed a similar model as based on the deviation from the core CPI, i.e. the headline CPI less food and energy. Using this model, we predicted the evolution of oil price as well. The overall performance of the model between March and December 2009 was reported before. Here we also revise the long-term prediction of crude petroleum and motor fuel price and make necessary corrections to the model as related to the observations since March 2009.

The model derived in [1, 2] implies that the difference between the overall CPI (same for the PPI), *CPI (PPI)*, and a given individual price index iCPI (iPPI)*,* can be described by a linear time function over time intervals of several years:

*CPI(t) - iCPI(t) = A + Bt* (1)

, where *A* and *B* are the regression coefficients, and *t* is the elapsed time. Therefore, the "distance" between the CPI and the studied index is a linear function of time, with a positive or negative slope *B*. Free term *A* compensates the difference related to the start levels for a given year. For example, the index of communication was started from the level of 100 in December 1997 when the overall CPI was already at the level of 161.8 (base period 1982-84 =100).

Figure 1 displays examples of linear trends in the two differences related to the scope of this article. In the left panel, the evolution of the index of motor fuel relative to the headline CPI is shown. Notice that in the original paper we referred the index of motor fuel to the core CPI, but the discrepancy between the headline and core CPI is negligible relative to the change in the index of motor fuel. There are two distinct periods of linear dependence on time: from 1980 to 1999 and from 2001 to 2008. Apparently, there is one finished transition period between 1999 and 2001, where the trend with a positive slope (*B*=+4.2) changed to a negative one (*B*=-21.1), in both cases the determination coefficient being very high: R2~0.89. The first transition period is characterized by elevated price volatility. Since 2008, the negative trend in the difference has been suffering a transition to a positive one, which is shown in Figure 1 by a dashed line. This transition is characterized by a much higher volatility and has been fading away since the end of 2009. Without prejudice, we have drawn the new trend as increasing from -110 in 2009 to -60 in 2016. (Notice that we made a different tentative assumption in [3] since we had no actual data after 2009.) This defines the long-term prediction of the motor fuel index and fits observations since 2010.

In the right panel, the difference between the PPI and the index of crude petroleum (domestic production) is shown between 1985 and 2012. There are two distinct periods of linear dependence on time: from 1988 to 1999 and from 2001 to 2008. The slopes of regression lines in both periods are different from those for the index of motor fuel: +2.9 and -17.9, respectively. There was one transition period between 1999 and 2001, where the original positive trend was turned down. We expect the difference to grow (the oil price index has to rise slower than the PPI) from -80 in 2009 to +20 in 2016; the growth rate is ~14 point per year.

Figure 1. Illustration of linear trends. *Left panel*: the difference between the headline CPI and the index of motor fuel between 1980 and 2012. *Right panel*: The difference between the overall PPI and the (producer price) index of crude petroleum (domestic production). In both panels: there are two quasi-linear segments with a turning period between 1998 and 2001. Since the end of 2008, both differences have been passing a transition. Linear trends with relevant linear regression lines and corresponding slopes are also shown.

From Figure 1, one can conclude that the presence of linear trends is a basic feature of the CPI and PPI components which is likely to be repeated in the future. Another fundamental characteristic of the differences consists in the fact that all deviations from the trends were only short-term ones. This implies that any current or future deviations from the new trends in Figure 1, which have been under development since 2008, must be compensated promptly. This feature allows short-term (months) price predictions.

Simple visual inspection of the transition period in Figure 2 shows that the difference in timing and amplitude between motor fuel and crude oil is not too big. The amplitude of oil price fluctuations is higher since 2007 and especially during 2011 and 2012. In turn, the fluctuations in motor fuel price were slightly higher between 2000 and 2007.

Figure 2. Comparison of two differences.

Figure 3 presents both differences after 2007. Overall, the evolution of the difference between the CPI and the index of motor fuel follows the new trend since 2011. One may expect that after a few months below the trend (say, through October -December 2012) the next move will return the difference above the trend, i.e. the price of motor fuel will fall a bit relative to the CPI. In the long run motor fuel will be losing its pricing power relative to the CPI. The oil price prediction for 2013 is similar. The difference in Figure 3 will reach the new (dashed) trend line and the oil price has to fall below $80 per barrel.

Figure 3. *Left panel*: The difference between the headline CPI and the index for motor fuel. *Right panel*: Evolution of the difference between the PPI and the index for crude petroleum (domestic production). Notice oscillations around the new trends.

The forces behind the observed long- and short-term behavior are not accessible yet but very powerful. We may assume that they are fundamental and affect the economy to its roots. These forces retain equilibrium among all economic agents and originate the sustainable trends in the differences between consumer (producer) price indices. At some point, the forces meet their limits and should be re-balanced in order not to harm the economy. As a result, the trends in the CPI and PPI turn.

Meanwhile, it is instructive to revise our long-term prediction of oil price shown in Figure 1. After a few minor adjustments to the initial and final levels of the PPI and the index of crude petroleum, Figure 4 depicts the revised prediction after 2010. It is slightly different from our previous prediction with oil price in 2016 set between $30 and $60 per barrel. Short-term fluctuations cannot be predicted at a horizon of several years. However, the larger is a given deviation from the trend the larger is the returning force.

Figure 4. The evolution of crude oil price. Open circles represent the evolution of (monthly average) oil price for the period between 2001 and 2012. Dashed lines - the upper and lower limits of the new trend between 2009 and 2016. According to the prediction, the price should fall to the level between $60 and $30 per barrel by 2017

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