**Introduction**

The change in producer and consumer prices has been always a concern for all stock market participants. Lately, we have demonstrated that the evolution of various components of CPI and PPI in the United States is not a random process but rather a predetermined one with long-term sustainable trends [1-4]. Using these trends, one can predict consumer and producer price indices for various goods, services and commodities [5-7]. Moreover, share prices for selected S&P 500 companies are also well described in the past by the differences in the PPI and CPI [8,9]. The near future will test the predictive power of our model.

In [1,3], we gave a prediction of the index for energy as a proxy of crude petroleum price. In [5-7], we developed a technique to describe the evolution of producer prices for gold, jewelry, durable and nondurable goods. So, there was no direct prediction of crude oil price. This paper fills this gap.

**1. The model**

The model derived in [4] implies that the difference between the headline PPI, *PPI*, and the index for crude petroleum, *cpPPI*, can be described by a linear time function over time intervals of several years:

*PPI(t) – cpPPI(t) = A + Bt* (1)

where *A* and *B *are empirical constants, and *t* is the elapsed time. Therefore, the “distance” between the PPI and the studied index is a linear function of time, with a positive or negative slope *B*. Figure 1 displays this difference between 1985 and 2009. There are two distinct periods of linear dependence on time: from 1988 to 2000, from 2001 to 2008. There was one transition period between 2000 and 2001, where the trends undergo changes. This turning point was characterized by an elevated volatility. Since 2008, the difference has been also passing a turning point with very high volatility caused by the uncertainty in the characteristics of the following trend.

Figure 1 presents quantitative parameters of the linear trends. Between 1988 and 2000, the difference was growing at a rate of *B*=+2.0 units per year. Between 2001 and 2008, the difference underwent a rapid fall at a rate of *B*=-21 units per year. Both trends are reliable ones with a high goodness-of-fit.

A fundamental feature of the difference consists in the fact that all deviations from the trends were only short-term ones. This implies that the current or future deviations from the new trend, which has been under development since 2008, must be rapidly compensated. This feature allows a short-term (months) price prediction.

Figure 1. Illustration of linear trends in the difference between the headline PPI and the producer price index for crude petroleum (domestic production) in the U.S. There are two quasi-linear segments with a turning point near 2000. Currently, the difference passes second transition period. Two linear trends with relevant linear regression lines and corresponding slopes are also shown.

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**2. Price prediction **

Having relationship (1) which describes the evolution of the studied difference one can easily predict its short- and long-term evolution. Figure 2 depicts the time history of the PPI and the index for crude petroleum. The PPI curve is smoother because it represents a weighted average of all commodities. The curve for crude petroleum has several peaks, but that in 2008 is by far the largest in absolute terms. Our purpose is to continue both curves in line with their long-term and short-term behavior in the past.

Since 2008, the new linear trend has been emerging. At this point, it is difficult to accurately estimate the rate of future growth. A naive assumption is that the following period will be a “mirror reflection” of the previous one. Therefore, the new slope should be the same as the old one but with opposite sign. Figure 1 shows the new trend by solid green line – the difference will grow from -55 in 2008 to +80 in 2016. In Figure 2, we split the difference into its component: the PPI will be growing with an annual increment of +2 units [10-12] and the index of crude petroleum will be decreasing by 19 units per year. This makes the slope *B*=+21. Therefore, the price for crude oil will be falling between 2010 and 2016. The start level is 190 units for both indices. Similar prediction has been already done for the index of motor fuel [3].

Figure 2. Evolution of the price index for crude petroleum and the PPI.

The difference curve in Figure 1 is not a straight line, however. Both observed trends are the gravity lines for the actual curve, but deviations from the trends have large amplitudes. Good news is that they are also back to the trends. This property allows a short-term prediction. Figure 3 displays the past five years. The largest ever deviation from the trend started in the beginning of 2008. One would guess that the uncertainty of the future behavior of crude price caused an euphoria among market players …, which quickly mutated into panic in the end of 2008. Accordingly, the price high-rocketed to ~$150 and then did not returned to the new trend but dropped to ~$40. In physics, such process would be called “dynamic overshoot”. One can also use the term *rebound*.

What can we say about the near future of the difference after May 2009, i.e. the last point currently available? A reasonable assumption of the next move in the difference is shows by red diamond – the curve will follow its natural motion down to the new trend and, after intersection of the red line, the difference will continue its way down. What will be the rate of rise in the index of crude petroleum? This is a big question. We assumed +20 units per month till the end of 2009, i.e. the index will grow from 157 in May to 297 in December. It is worth noting, that there is a trade-off between the rate of growth and the duration of the growth – if the rate is higher the duration is shorter. One can draw own line between June and December.

Figure 3. The difference between the PPI and the index for crude petroleum. Red diamonds predict the evolution of the difference between June and December 2009. Total increase in the difference is -140 units of index Solid red line represents the “mirror” trend for that between 2002 and 2008, which is shown by solid black line.

Finally, what will be crude petroleum price by the end of 2009? One can easily convert price indices into real prices. We used a conversion factor of 2.65, which corresponds to $145 per barrel in July 2008 and the index of 384.3. The price for June 2009 is $66.8 with the index of 177. Crude price in December is at $112. This is our best prediction using the assumption of the index growth. The price might be reached earlier or later depending of rate of growth. The absolute value of $112 also can also be higher or lower depending on the amplitude of the overshoot in the second part of 2009.

Figure 4. The evolution of crude petroleum (domestic production) price. Between June and December 2009 the price will rise from $66 to $112 per barrel.

** ****Conclusion**

The price index for crude petroleum (domestic production) in the USA should grow by ~45% between June and December 2009 – from $66 to $112. Our simple model suggests a constant price increment over months, but actual monthly growth might not be even. In any case, the total price increase in 2009 should compensate the fall in 2008 and demonstrate some price “overshoot” relative to the trend line, i.e. the price will rise above the trend.

It is likely that the price index for crude petroleum will be decreasing in absolute terms approaching the level of 60 units in 2016. This corresponds to $22 per barrel.

**References**

1. Kitov, I., Kitov, O., (2008). Long-Term Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ), pp. 101-112.

2. Kitov, I., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany.

3. Kitov, I., Kitov, O., (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany,

4. Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, Journal of Applied Research in Finance, v. 1, (in press)

5. Kitov, I., Kitov, O., (2009). PPI of durable and nondurable goods: 1985-2016, MPRA Paper 15874, University Library of Munich, Germany

6. Kitov, I., (2009). Predicting gold ores price, MPRA Paper 15873, University Library of Munich, Germany

7. Kitov, I., (2009). Predicting the price index for jewelry and jewelry products: 2009-2016, MPRA Paper 15875, University Library of Munich, Germany

8. Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: June-September 2009, MPRA Paper 15863, University Library of Munich, Germany

9. Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany

10. Kitov, I. (2006). Inflation, unemployment, labor force change in the USA, Working Papers 28, ECINEQ, Society for the Study of Economic Inequality

11. Kitov, I., (2006). Exact prediction of inflation in the USA, MPRA Paper 2735, University Library of Munich, Germany

12. Kitov, I., Kitov, O., Dolinskaya, S., (2007). Inflation as a function of labor force change rate: cointegration test for the USA, MPRA Paper 2734, University Library of Munich, Germany

**Disclosure: no positions**