Oil price in 2012-2013

This is a revision to our oil price prediction as based on the difference between the overall PPI and the index of crude oil. Figure 1 compares our previous prediction in May 2011 with actual oil price in 2011 and 2012. In August 2011, the predicted price was a bit higher than the measured one. We expected the price to fall by approximately $5 per month to the level of ~$70 by December 2011. In reality, the price reflected from the high bound of the expected price (dashed line) and grew during the end of 2011. This effect reflects the high level of price volatility during short time intervals. Since February 2012, the price has been returning to the expected price range which expresses the slow fall through 2016, with the uncertainty bounds for the long-term trend in oil price shown in Figure 1. The level of oil price in 2016 is expected between $30 and $60 per barrel.

Here we confirm the oil price trend and its bounds. Red squares show our prediction of oil price through February 2013. Despite local fluctuations, the trend is negative and will bring the price to $45 (±$15) per barrel in 2016.  

Figure 1. The evolution of oil price since 2001 as estimated from the differnce of the overall PPI and the PPI of crude petroleum.

Time to buy SPY

A month ago, we predicted a drop in the S&P 500 to the level of 1300 by the end of May. We also suggested buying the index when it is 1300.  Both are done by now. We are waiting the level 1500 in October 2013 to sell and fix profit. The explanation from April is fully repeated below. The red segment in Figure 2 is now black since the prediction is realized.

We also expect oil price to drop further and force deflation by the end of 2012.

This repeats our previous postSeveral days ago we predicted the current fall in the S&P 500 index. For this reason, we did not enter the stock market and instead invested in a defensive portfolio. We are waiting the level of 1350.  The reason is explained below.

Figure 1 shows the evolution of the S&P 500 index since 1980. After 1995, the index behavior reveals some saw teeth with peaks in 2000 and 2007. The current growth resembles those between 1997 and 2000 and from 2003 and 2007.  There are two deep troughs in 2002 and 2009 which are marked by red and green lines, respectively.  For the current analysis we assume that the repeated shape of the teeth is likely induced by a degree of similarity in the evolution of macroeconomic variables. The intuition behind such an assumption is obvious – in the long run the market depends on the overall economic growth.

Having two peaks and troughs between 1995 and 2009, what can we say about the current growth in the S&P 500? Before making any statistical estimates, in Figure 2 we have shifted forward the original curve in Figure 1 in order to match the 2009 trough (blue line).  When the 2002 and 2009 troughs are matched, one can see that the current growth path closely repeats that after 2002. The first big deviation from the blues curve in Figure 2 started in 2011 and had amplitude of 150 units (from 1210 to 1360).  The black curve returned to the blue one in August/September 2011. A month ago, we observed a middle-size deviation of about 100 units and predicted that the index will have a negative correction down to the level of 1300 any time soon.  If the index will repeat the path of the previous rally one-to-one, one may expect the peak level of 1500 in the end of 2013.  In two to four weeks it might be a good time to invest for a 15% return cumulated to October 2013 (but not more than two months), when the negative correction is over. 

With the S&P 500 falling down to 1350, the prediction does not seem inappropriate. The next several weeks should decide on the new level. In Figure 2, we have drawn the fall we expect by the end of May 2012. We would wait by the end of April to decide on the following move in the S&P 500. If the current fall will reach 1300, it’s likely a good time to buy. Otherwise, the end of May is the horizon to wait the bottom.

Figure 1. The evolution of the S&P 500 market index between 1980 and 2012. 

Figure 2. The curve in Figure 1 peak is shifted forward to match the 2009 trough (blue line). Red line – expected fall in the S&P 500: from 1400 in Mach to 1300 in May.

Weird PPI of oil - illustration

Following our previous post on oil price we compare the price of oil futures (dark blue) and PPI of oil (BLS estimates) between 2007 and September 2011. Even simple visual inspection shows that the September's PPI estimate differs from its expected value when converted from oil price. Why?

Update 20.10.2011

I have replaced the Figure with not seasonally adjusted PPI and medium mon thly oil price between 2008 and September 2011. Now the difference in September is prominent.

Do not understand the growth in the producer price index of oil

It looks weird. Figure below shows daily change in oil price futures during the previous three months. There is no big difference between August and September 2011. I would estimate the change as negligible.  At the same time, the PPI of crude petroleum (not seasonally adjusted) grew from 241 to 275.9, which is approximately the level of June. It should be a mistake.

Another chance to sell oil futures

Two weeks ago, when oil was at $84,  I recommended  to sell oil futures before oil price falls to $79 and even lower. After this recommendation, oil actually fell down to $76 and could bring a 10% return. Today, oil is approaching $83, as we predicted five days ago. Therefore, a good time to sell oil futures is coming again. Below I reproduce some details of the model predicting oil price.

In May 2011, we predicted oil (WTI) price to fall to the level of $70 per barrel by the end of 2011. This is a monthly revision for September 2011. We consider the average oil price of $84 per barrel what is equivalent to the producer price index of 244 in September. (Actual estimate will be published by the Bureau of Labor Statistics in the middle of October.)
        Figure 1 compares our prediction with actual oil price in 2011. In August 2011, the predicted price is a bit higher than the measured one. In any case, we expect the price to fall by approximately $5 per month to the level of ~$70 in December 2011. We also expect the price to slowly fall through 2016 and put the uncertainty bounds for the long-term trend in oil price. The level of oil price in 2016 is between $30 and $60 per barrel. These bounds are also shown in Figure 1.

       

This part is the prediction of the current growth in oil price given days ago.

 A week ago, when oil price was at ~$79 per barrel, we recommended buying oil futures. The intuition behind this idea was that $79 is approximately $5 below the expected price for September. This is a disequilibrium which should be recovered in the short run. Today, oil price is at the level of ~84. This is the equilibrium level for September. A small hike in oil price is possible during the next few days. However, at a two-week horizon, oil price should fall again. Therefore, I recommend selling now and buying in approximately two weeks or when the price will be around $75. It will grow to the level of ~$82 to $85 in October or November.

Figure 1. Oil price prediction in 2011. The price is expected to fall by $5 per month between June and December 2011. The price level is ~$70 in December 2011. We also show the range of expected price evolution by 2016.

Oil falls - attractive to buy

Today, oil price has been declining since early morning. It looks more and more attractive to buy. For $78 per barrel one cac obtain between 3% and  5% return in a week or so with the price at $82 to $84. Two weeks ago we proposed the same thing and the return was around 10% with back and forth oscillations between $84 and $79.

Time to buy oil futures. Again

Ten days ago the price of oil was very low relative to its expected level in September. We concluded that it was a good time to buy oil futures because the price had to bounce back to $84. It did happen several days later and we proposed to sell at $84. Now it is a good time again to buy oil futures since the current price is below the expected equilibrium level for October, which is between $80 and  $82. The expected return at a two-week horizon is about 3%.

Good time to sell oil futures

In May 2011, we predicted oil (WTI) price to fall to the level of $70 per barrel by the end of 2011. This is a monthly revision for September 2011. We consider the average oil price of $84 per barrel what is equivalent to the producer price index of 244 in September. (Actual estimate will be published by the Bureau of Labor Statistics in the middle of October.)


Figure 1 compares our prediction with actual oil price in 2011. In August 2011, the predicted price is a bit higher than the measured one. In any case, we expect the price to fall by approximately $5 per month to the level of ~$70 in December 2011. We also expect the price to slowly fall through 2016 and put the uncertainty bounds for the long-term trend in oil price. The level of oil price in 2016 is between $30 and $60 per barrel. These bounds are also shown in Figure 1.

A week ago, when oil price was at ~$79 per barrel, we recommended buying oil futures. The intuition behind this idea was that $79 is approximately $5 below the expected price for September. This is a disequilibrium which should be recovered in the short run. Today, oil price is at the level of ~84. This is the equilibrium level for September. A small hike in oil price is possible during the next few days. However, at a two-week horizon, oil price should fall again. Therefore, I recommend selling now and buying in approximately two weeks or when the price will be around $75. It will grow to the level of ~$82 to $85 in October or November.

Figure 1. Oil price prediction in 2011. The price is expected to fall by $5 per month between June and December 2011. The price level is ~$70 in December 2011. We also show the range of expected price evolution by 2016.

Time to buy oil futures

Several day ago I showed that oil price had fallen below expectation in August. Today oil price has been falling since the very morning  and now  is approaching $80 per barrel. We predicted $70 in December 2011.  Thus, oil price has to grow again and it's good time to buy futures.

Oil price in August

In May 2011, we predicted oil (WTI) price to fall to the level of $70 per barrel by the end of 2011.  This is a monthly revision for August 2011. We consider the average oil price of $86 per barrel what is equivalent to the producer price index of 240 in August.  (Actual estimate will be published by the Bureau of Labor Statistics in the middle of September.)

Figure 1 compares our prediction with actual oil price in 2011. In August 2011, the predicted price is a bit higher than the predicted one. However, we still expect the price to fall by approximately $6 per month to the level of ~$70 in December 2011. We also expect the price to slowly fall through 2016 and put the uncertainty bounds for the long-term trend in oil price. The level of oil price in 2016 is between $30 and $60 per barrel. 

Figure 1. Oil price prediction in 2011. The price is expected to fall by $6 per month between June and December 2011. The price level is ~$70 in December 2011. We also show the range of expected price evolution by 2016.

ConocoPhillips share price to fall

Our original pricing model states that a share price, for example, that of ConocoPhillips, COP(t), can be approximated by a linear function of the difference between the core CPI, coreCPI, and headline CPI:

COP(t) = A + B (coreCPI - CPI(t))                          (1)

where A and B are empirical constants; t is the elapsed time.  Here we extend the set of defining indices by the consumer price index of energy, eCPI, and the producer price index of crude petroleum, pPPI, together with the overall PPI. Thus, we test the following models for the period between 2001 and 2011:

COP(t) = A1 + B1(coreCPI - eCPI(t))  (2)   

COP(t) = A2 + B2(pPPI - PPI(t))         (3) 

Figures 1 through 3 compare the original and new predictions for COP. Coefficients in (1) through (3) are given in Figure captions. The best model for the period between 2001 and July 2011 is based on the index of energy and core CPI. Practically the same accuracy is associated with the original model as based on the core and headline CPI. At the same time, model (3) based on the producer price indices is the worst and has failed to predict the amplitude of the largest oscillation in 2008.  

We have predicted oil price to fall through 2016. In 2011, we expect oil price to fall down to $70 per barrel. Considering these short- and mid-term predictions one can conclude that ConocoPhillips share price will be falling as well. 

Figure 1.  The observed COP price and that predicted from the core and headline CPI.  A=75, B=-5.5.

Figure 2.  The observed COP price and that predicted from the core CPI and the consumer price index of energy.  A1=58, B1=-0.54.

Figure 3.  The observed COP price and that predicted from the overall PPI and the producer price index of crude petroleum (domestic production).  A2=45, B2=-0.3.

Oil price and deflation

The current turbulence in financial markets and the expectation of a poor economic performance (i.e. recession) in the biggest economies has been accompanied by a dramatic fall in oil price. We have predicted this drop several months ago and expect the price to fall to the level of $70 per barrel by the end of 2011.  We will address this prediction when the Bureau of Labor Statistics publishes the PPI and CPI estimates for July 2011. Here we would like to highlight the influence of oil price on the PPI and headline CPI.

            The price index of energy comprises approximately 10% of the headline CPI is highly correlated with oil price. The surge in oil price observed since the beginning of 2011 (Figure 1) has been the most important driver of the elevated consumer price inflation. Accordingly, many economic and financial experts expect a period of hyperinflation in the near future. However, oil price has been falling. This fall resulted in a negative rate of monthly inflation in June 2011. In July, the monthly rate of inflation is likely to be positive because the price index of energy (oil) did not fall much relative to June.  

            The monthly rate of inflation is an important but only a transient indicator of the overall price change. Therefore, we have calculated the annual rate from the curves in Figure 1, where red line is the original price index (black line) shifted by one year ahead. The ratio of black and red line is the rate of oil price inflation, as shown in Figure 2.  The rate of inflation is characterized by two peaks in 2008 and 2010. Obviously, the rate of inflation is defined by two factors: the current level of oil price and that one year ago. The difference between black and red line can be considered as a crude estimate of the inflation rate. When red line is above black line, the rate of inflation is negative. Otherwise, the rate is positive. What can we expect in 2012 with the price index of oil falling through the third and fourth quarters of 2011?  Almost inevitably, the rate of (oil price) inflation will be negative through 2012. Since other components of the headline CPI also demonstrate the tendency to fall one can expect a period of deflation in 2012.

Figure 3 presents our estimate of the oil price evolution in 2011. We expect the price to fall by $6 per month to the level of $70 in December 2011. We also expect the price to fall through 2016 and put the uncertainty bounds for the long-term trend in oil price. The level of oil price in 2016 is between $30 and $60 per barrel.

Figure 1. The (producer) price index of oil (domestic crude petroleum). Red line is the original price index shifted one year ahead. The ratio of black and red line is the rate of oil price inflation shown in Figure 2.    

 Figure 2. The annual rate of oil price growth.  

Figure 3. Oil price prediction in 2011. The price is expected to fall by $6 per month between June and December 2011. The price level is $70 in December 2011. We also show the range of expected price evolution by 2016.

The IEA projection for oil

The International Energy Agency has issued a new oil price projection through 2016:
For oil, the projections are based on prevailing futures prices, which form an assumption as opposed to a price forecast. The crude price assumption used in the outlook averages $103 per barrel, or around $20 more than in last year’s MTOGM.

We also presented a projection for oil price through 2016 which is based on the presence of a sustainable linear trend in the difference between the core and headline CPI in the USA. This price will be progressively decerasing to the level of $35 to $50 per barrel in 2016. It would be interesting to compare these prejections in, say, 3 years.

Does crude drive the price index of steel and iron?

This is a quarterly update.

In September 2009, we reported that the price index of crude oil had been likely evolving in sync with that of iron and steel, but with a lag of two months. In order to present both indices in a comparable form, the difference between a given index, iPPI, and the overall PPI was normalized to the PPI: (iPPI(t)-PPI(t))/PPI(t). The normalized differences represent the evolution of the rate of deviation from the PPI over years.

Figure 1 depicts the corresponding time histories of the normalized deviations from the PPI, including the most recent period since June 2010. Simple visual inspection reveals the following feature: the (normalized deviation from the PPI of the) index of iron and steel lags by two months behind the (normalized) index of crude oil.

Figure 1. The deviation of the iron and steel price index and the index of crude oil from the PPI, normalized to the PPI.

In order to reduce both deviations to the same scale we additionally normalized the curves in Figure 1 to their peak values between 2005 and 2009:

(iPPI(t)-PPI(t))/[PPI(t)*max{iPPI-PPI)}]

This scaling allows a direct comparison of corresponding shapes. In Figure 2, we display the normalized index of iron and steel shifted by two months ahead to synchronize its peak with that observed in the normalized index for crude petroleum. (The period between May and July 2010 is included.) The scaled index of crude demonstrates just minor discrepancies from the index of iron and steel in the overall shape and timing of the peak and trough. Simple smoothing with MA(3) makes the curves resemblance even better. As an invaluable benefit of the resemblance, one can use the two-month lag to predict the future of the iron and steel price index.

Figure 2. Deviation of the iron and steel price index from the PPI, normalized to the PPI and the peak value after 2005 as compared to the deviations of the index for crude petroleum normalized in the same way. The normalized index for iron and steel is shifted two months ahead.

Conclusion

Between 2006 and 2010, the deviation of the price index of iron and steel from the PPI in the USA repeats the trajectory of the deviation of the index of crude petroleum (domestic production) with a two-month lag. Therefore, the prediction of iron and steel price for at this horizon is a straightforward one. It is likely that in the fourth quarter of 2010 the index of iron and steel will be decreasing following the observed fall in the index for crude petroleum.

References

Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, Journal of Applied Research in Finance, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. I(1(1)_ Summ), pp. 43-51

Crude in 2010

Three months ago we presented a forecast for the PPI for crude oil and oil price in August 2010. Tentatively, we put the index at the level between 160 and 180 in August 2010. Crude oil price corresponding to this level of index should be between $62 and $70 per barrel. It’s time to revisit the price.

All our estimates are based on the existence of long-term sustainable trends in the differences between various subcategories of the producer price index (PPI). The concept is illustrated in Figure 1, where the difference between the overall PPI and that for crude petroleum is approximated by three linear trends. The most recent trend started in the beginning of 2010 and has been strengthening since then. Without loss of generality, we consider that the new developing trend will be a mirror reflection (opposite but equal slope) of the previous trend observed between 2002 and 20008. This is the long-term prediction for oil price with the PPI of crude at the level of 75 point in 2016.

Figure 2 presents the short term view elaborating on the most recent transition period from July 2008 to August 2009 and the details of the new trend. In March 2009, we presented two predictions. In (1) we presumed that, when reached the trend, the price would follow along it. Second prediction was based on a “dynamic overshoot” with oil price dropping much below the new trend, as shown by solid diamonds in Figure 2. From these two predictions, the first was right.

Figure 3 details our prediction made in June 2010 on the evolution of the oil price index between June and August 2010. We expected that the price would fall and the predicted curve rise above the trend, as shown by red circles. This is a consequence of the fluctuation around the trend: the price can not be retained just on one side of the trend line. The measured price did not touch the trend line, however. So, our prediction was not fully right despite the price actually has fallen significantly. The Augusts’ estimates of the producer price index for crude petroleum will be published in the middle of September. It will definitely show a decrease relative to July, but the price will not drop to $70 per barrel.

Therefore, we foresee two possible scenarios. A more likely one supposes that the price in September will fall below $70 per barrel and the measured difference (open circles) in Figure 3 will intercept the trend line. This scenario will be in line with our prediction of the S&P 500 level below 1000 in September.

We can not exclude that the price (and the S&P 500) will not drop in September cumulating more potential relative to the trends. Then, this must happen in October-November and the potential drop will just increase in time as the deviation between the actual curve and the trend. The trend itself seems to be well-established already since the price goes along the trend since August 2009. It might also happen that the true trend is different form the predicted one. It may have lower slope than during the previous period. Then the price will be decreasing a lower rate into the second half of the 2000s. One can better estimate the trend slope in couple years, but before actual data are available we will retain our hypothesis on the slope value.

All in all, we expect the price index of crude petroleum to follow the new trend in the long run with short-term fluctuations of various amplitude and period.

Figure 1. Sustainable linear trends in the difference between the overall PPI and that for crude oil between 1987 and 2010. Currently, we observe the emergence of a new trend, which supposedly is a mirror reflection of the previous one.

Figure 2. The evolution of the difference between the overall (all commodities) PPI and that for crude oil.

Figure 3. The measured and predicted difference between the overall PPI and the index for crude petroleum.

1. Crude Oil And Motor Fuel: Fair Price Revisited

Does crude drive the price index of steel and iron?

In September 2009, we reported that the price index of crude oil had been likely evolving in sync with that of iron and steel, but with a lag of two months. In order to present both indices in a comparable form, the difference between a given index, iPPI, and the overall PPI was normalized to the PPI: (iPPI(t)-PPI(t))/PPI(t). The normalized differences represent the evolution of the rate of deviation from the PPI over years.

Figure 1 depicts corresponding time histories of the normalized deviations from the PPI. Simple visual inspection reveals the following feature: the (normalized deviation from the PPI of the) index of iron and steel lags by two months behind the (normalized) index of crude oil.

Figure 1. The deviation of the iron and steel price index and the index of crude oil from the PPI, normalized to the PPI.

In order to reduce both deviations to the same scale we additionally normalized the curves in Figure 1 to their peak values between 2005 and 2009:

(iPPI(t)-PPI(t))/[PPI(t)*max{iPPI-PPI)}]

This scaling allows a direct comparison of corresponding shapes. In Figure 2, we display the normalized index of iron and steel shifted by two months ahead to synchronize its peak with that observed in the normalized index for crude petroleum. The scaled index of crude demonstrates just minor discrepancies from the index of iron and steel in the overall shape and timing of the peak and trough. Simple smoothing with MA(3) makes the curves resemblance even better. As an invaluable benefit of the resemblance, one can use the two-month lag to predict the future of the iron and steel price index.

Figure 2. Deviation of the iron and steel price index from the PPI, normalized to the PPI and the peak value after 2005 as compared to the deviations of the index for crude petroleum normalized in the same way. The normalized index for iron and steel is shifted two months ahead.

Conclusion

Between 2006 and 2010, the deviation of the price index of iron and steel from the PPI in the USA repeats the trajectory of the deviation of the index of crude petroleum (domestic production) with a two-month lag. Therefore, the prediction of iron and steel price for at this horizon is a straightforward one. It is likely that in 2010 the index of iron and steel will approach closely the level attained in August 2008. From this level, it will be declining in the long run following the new trend of oil price, as shown in our previous post.

References

Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, Journal of Applied Research in Finance, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. I(1(1)_ Summ), pp. 43-51

Crude price in August 2010

A month ago we presented a forecast for oil price. It’s time to revisit the price. All our estimates are based on the existence of long-term sustainable trends in the differences between various subcategories of the producer price index (PPI). The concept and numerous forecasts is published in this paper. The dry residual is that the producer price indices evolve along straight lines, with all deviations from the trend cancelling themselves out over relatively short periods of several months.

Figure 1 present the case of crude petroleum (domestic production) for the period between 2007 and 2012. We have predicted that the difference between the overall PPI and the index for oil will be on a upward trend since 2009. This means than the PPI will grow faster than the index of oil, the latter likely to fall into 2016 down to the level of ~75.

In March and April 2010, the index of crude petroleum had a bigger deviation out of the trend in Figure 1. Therefore, the most likely next movement in the price will be the return to the trend. Moreover, the difference will likely to break the trend line and go into the other side for several months. This would mean the price of oil falling in May 2010 and during the summer months, as shown in Figure 1 by red circles. Tentatively, we put the index at the level between 160 and 180 in August 2010. Relevant crude oil price will be between $62 and $70 per barrel.

Figure 1. The difference between the overall PPI and the index for crude petroleum. The new predicted trend is shown by dashed line. In May and likely in summer 2010, the index for oil will be decreasing. The difference will be growing as shown by red circles.

P.S. Apparently, oil price lost several dollars in May 2010, and one could say that this post is a bit late and just declares known facts. This is the Bureau of Labor Statistics who reports the PPI and its components in the middle of the next month. Our concept would fail to predict that this is exactly May 2010 when oil price should stop to grow. However, the currently observed level of price is not viable. The price must fall at some point, the larger is the deviation the faster and more violent is the recovery.

CRUDE OIL AND MOTOR FUEL: FAIR PRICE REVISITED

CRUDE OIL AND MOTOR FUEL: FAIR PRICE REVISITED
Ivan O. Kitov, Oleg I. Kitov
Institute for the Geospheres’ Dynamics, Russian Academy of Sciences

Abstract
In April 2009, we introduced a model representing the evolution of motor fuel price (a subcategory of the consumer price index of transportation) relative to the overall CPI as a linear function of time. Under our framework, all price deviations from the linear trend are transient and the price must promptly return to the trend. Specifically, the model predicted that “the price for motor fuel in the US will also grow by 50% by the end of 2009. Oil price is expected to rise by ~50% as well, from its current value of ~$50 per barrel.” The behavior of actual price has shown that this prediction is accurate in both amplitude and trajectory shape. Hence, one can conclude that the concept of price decomposition into a short-term (oscillating) and long-term (linear trend) components is valid. According to the model, the price of motor fuel and crude oil will be falling to the level of $30 per barrel during the next 5 to 8 years.

Key words: CPI, PPI, crude oil, motor fuel, price, prediction, USA
JEL Classification: E31, E37

Introduction
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 [3], gold ores [4], durables and nondurables [5], jewelry and jewelry related products [6], and motor fuel [7].

For major subcategories these trends last between five and twenty years and then turn to trends with opposite slopes. The transition to new trends lasts three years at most. However, there are subcategories without slope changes as reported by the Bureau of Labor Statistics [8], where all CPI and PPI time series were retrieved from. The best example of such a one-leg trend since 1980 is the price index of medical care [1]. The index of communication has been linearly deviating from the headline CPI since 1998 (in this study we use seasonally adjusted CPIs and not seasonally adjusted PPIs), i.e. since the beginning of reporting; before 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 corresponding trend. When very 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. Using long-term trends and short-term deviations we predicted the evolution of prices for gold, durables and nondurables, jewelry and a number of consumer price indices. These predictions will be revisited in due course. In this paper, we focus on crude oil and motor fuel.

For the price index of motor fuel, Kitov and Kitov [7] 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 in [9]. 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
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 paper. 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 [7] 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 goodness-of-fit being very high: R2~0.9. 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. A new trend has been emerging since the beginning of 2010. Without prejudice, we drew the new trend as a mirror reflection to the previous one. Supposedly, it will last seven years. As a result, the difference will increase from -50 in 2009 to +75 in 2016 since the index of motor fuel will be falling at a rate of 17.9 units per year relative to the headline CPI. This casts the long-term prediction of the motor fuel index.

In the right panel, the difference between the PPI and the index of crude petroleum (domestic production) is shown between 1985 and 2010. Expectedly, there are two distinct periods of linear dependence on time: from 1988 to 1999 and from 2001 to 2008. The regression coefficients in both periods are different from those for the index of motor fuel: +2.9 and -17.1, respectively. In other words, the motor fuel index magnifies the change in oil price. There was one transition period between 1999 and 2001, where the original positive trend was turned down. Even a simple visual inspection of the transition period reveals several differences in timing and amplitude between motor fuel and crude oil: the former started to fall three months later and came to the level of 1999 in the end of 2001. The index of crude oil fell by ~15 units relative to its level in 1999.

Figure 1. Illustration of linear trends. Left panel: the difference between the headline CPI and the index of motor fuel between 1980 and 2010. 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 point near 2000. 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 (and many others published before), one can conclude that the presence of linear trends is a basic feature of the CPI and PPI. 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.

Predicted vs. actual
Originally, we presented a model for the price evolution for motor fuel and crude oil from March to December 2009. For the motor fuel index, we drew a straight line shown in the left panel of Figure 2. This line said that motor fuel price would be growing faster than the price of all goods and services. Specifically, we predicted that:

In March 2009, the difference was at the level of +45, i.e. much higher than the level predicted by the new trend. As happened in the past with numerous individual price indices [9,10], such a strong deviation (one might call it “dynamic overshoot”) should be compensated in the near future. Without loss of generality, we have restricted the recovery to the trend by the end of 2009. As a result the index for motor fuel should growth by 90 units during the next 9 months, or by 10 units per month. Red filled circles represent the evolution of the difference from April to December 2009. In 2010, the difference may undergo an overshoot in the opposite direction with additional rise in the index for motor fuel.
Translating indices into prices, the rise in the difference by 90 units (from 173 in March to 263 in December) means an increase in price by 50%. Therefore, it is very likely that the price for motor fuel in the beginning of 2010 will be 60% to 70% larger than in March 2009 due to the overshoot.

We have been also tracking the evolution of crude oil price, which obviously affects the price index of motor fuel. As Figure 1 demonstrates, these prices have no one-to-one correspondence and it might be instructive to model them separately. So, for oil price we used an alternative approach and assumed that the price trajectory would continue the pendulum-like motion observed since 2008. This implied the difference between the PPI and the index of crude petroleum should sink below the new trend and stop at the level of -120, which roughly corresponds to $120 per barrel.

So, there were two approaches: 1) motor fuel (oil) price would to be stopped at the new trend and then be evolving along it; 2) oil (motor fuel) price should follow up the observed free pendulum oscillation and penetrate deep below the trend line in a dynamic overshoot. The second approach implies that the price will rebound above the trend. Both predictions are shown in Figure 2 by solid diamonds for the period between March and December 2009.

Figure 2 also presents actual prices for the predicted period. Overall, the evolution of the difference between the CPI and the index of motor fuel follows the predetermined path: from its peak in February 2009 to the new trend line, which was reached in December 2009. In January 2010, the actual time series likely started to align along the new trend. One may expect the next move will be below the trend with small-amplitude short-term (few months) oscillations around the trend in 2010 and 2011. In the long run motor fuel will be losing its pricing power relative to the CPI.

Obviously, the assumption behind the oil price prediction was wrong. There was no free pendulum motion observed beyond June 2009. When reached the new (dashed) trend line, the difference started the alignment along the line. Instead of $120 per barrel oil price has been hovering around $75, as was predicted by the motor fuel model. There is no sign that petroleum price will significantly deviate from the trend in the near future. In March and April 2010, we expect the price to rise above the new trend. It must return below the line by the third quarter, however.

Figure 2. Left panel: The difference between the headline CPI and the index for motor fuel. Solid diamonds represent the prediction given in March 2009 through December 2009. The total increase in the difference is +60 units of index or +35%: from 173 in March to 233 in December. Dashed line represents the new trend, which is a mirror reflection to that between 2001 and 2008 shown by solid black line. Right panel: Evolution of the difference between the PPI and the index for crude petroleum (domestic production). Solid diamonds represent the predicted values between March and December 2009, as anticipated in April 2009 with a dynamic overshoot below the new trend. Open circles – the observed difference between September and December 2009. Dashed line represents the new trend as described in the text.

From Figure 2, it is clear that the oil price differnce leads that of motor fuel by six to eight months. It is likely that the index of motor fuel will follow up the trajectory drawn by oil price and fluctuate around its trend with slightly larger amplitude. The predictive power of this assumption will be tested by the end of 2010. We are going to track and report on actual behavior. Our model needs further validation in both short- and long run.

Discussion
All in all, our prediction of the price index of motor fuel was based on a sound assumption and thus is accurate. The forces behind the observed long- and short-term behavior are not accessible yet but very powerful. We dare say they are fundamental and affect the economy to its deepest 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 sustainable 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 3 depicts the revised prediction after 2010. It is very similar to the previous prediction with oil price in 2016 set at $30 per barrel. The index of motor fuel will follow up the trend with a delay and larger amplitude. Short-term fluctuations can not 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 3. The evolution of crude oil price. Solid line – oil price for the period between 2001 and 2010. Dashed line – the new developed trend between 2009 and 2016. According to the prediction, the price should fall to the level of $30 per barrel by 2016.

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. III(2(4)_Summ), pp. 101-112.
2. Kitov, I., Kitov, O. (2009). Sustainable trends in producer price indices, Journal of Applied Research in Finance, vol. I(1(1)_ Summ), pp. 43-51.
3. Kitov, I., Kitov, O., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany
4. Kitov, I. (2009). Predicting gold ores price, MPRA Paper 15873, University Library of Munich, Germany
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 the price index for jewelry and jewelry products: 2009-2016, MPRA Paper 15875, University Library of Munich, Germany
7. Kitov, I., Kitov, O. (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany
8. Bureau of Labor Statistics. (2010). Databases, Tables & Calculators by Subject, retrieved 30.03.2010 from http://www.bls.gov/data/
9. Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing

Goldman Sachs on oil in 2009 and 2010

Reuters cites an updated forecast on oil demand and price just issued by GS: $85 per barrel by the end of 2009. Currently, oil price is down to $66-67, but it should reach $100 in 2009.

Share price of select energy companies. Part 2

Figure 12. Observed and 3-C predicted Halliburton share prices: HAL(t) = -3.66*EC(t-6) +2.42*CF(t+1) - 0.41*(t-2000) - 37, where EC is the index of education and communication and CF is the headline CPI less food. Standard deviation is $2.35.

Figure 13. Observed and 3-C predicted Hess CP share prices: HES(t) = 0.61*E(t+1) + 4.1*RENT(t-7) – 26.4*(t-2000) - 865.7, where EC is the index of education and communication and CF is the headline CPI less food. Standard deviation is $5.92.

Figure 14. Observed and 3-C predicted Massey Energy CP share prices: MEE(t) = 3.25*CSH(t+1) - 6.37*CFSHE(t-11) + 2.33*(t-2000) + 592.9, where CSH is the headline CPI less shelter and CFSHE is the headline CPI less food, shelter and energy. Standard deviation is $6.30.

Figure 15. Observed and 3-C predicted Murphy Oil CP share prices: MUR(t) = 0.83*T(t+1) – 6.25*HFO(t) + 6.20*(t-2000) + 655.9, where T is the index of transportation and HFO is the index of household furnishing and operations. Standard deviation is $4.27.

Figure 16. Observed and 3-C predicted Noble Energy share prices: NBL(t) = 0.86*T(t+2) + 2.88*RENT(t-3) - 15.8*(t-2000) - 694.4, where T is the index of transportation and RENT is the index of rent. Standard deviation is $3.97.

Figure 17. Observed and 3-C predicted National Oilwell Varco share prices: NOV(t) = 4.13*C(t+1) – 10.87*HFO(t+1) - 9.26*(t-2000) + 641.5, where C is the headline CPI and HFO is the index of household furnishing and operations. Standard deviation is $5.28.

Figure 18. Observed and 3-C predicted Occidental Petroleum share prices: OXY(t) = 0.73*T(t+1) + 1.17*MCS(t-5) - 12.36*(t-2000) - 405.5, where T is the index of transportation and MCS is the index of medical care services. Standard deviation is $3.25.

Figure 19. Observed and 3-C predicted Pioneer Natural Resources share prices: PXD(t) = - 3.24*EC(t-6) + 0.43*E(t+1) + 4.08*(t-2000) + 305.6, where EC is the index of education and communication and E is the index of energy. Standard deviation is $3.73.

Figure 20. Observed and 3-C predicted Rowan Companies share prices: RDC(t) = - 1.74*F(t-5) + 0.49*TPR(t+1) + 9.59*(t-2000) + 222.5, where F is the index of food and beverages and TPR is the index of private transportation. Standard deviation is $2.85.

Figure 21. Observed and 3-C predicted Schlumberger share prices: SLB(t) = - 5.47*F(t-11) + 0.93*T(t+1) + 36.9*(t-2000) + 695.9, where F is the index of food and beverages and T is the index of transportation. Standard deviation is $7.24.

Figure 22. Observed and 3-C predicted Sunoco share prices: SUN(t) = - 15.9*CO(t-8) + 10.17*HFO(t-8) - 19.8*(t-2000) + 257.7, where CO is the index of communication and HFO is the index of household furnishing and operations. Standard deviation is $6.12.

Figure 23. Observed and 3-C predicted Tesoro share prices: TSO(t) = -2.85*F(t+2) - 5.44*FB(t-11) + 54.4*(t-2000) + 1273, where F is the index of food and beverages and FB is the index of food only. Standard deviation is $6.12.

Figure 24. Observed and 3-C predicted XTO Energy share prices: XTO(t) = 1.49*CSH(t+2) – 1.73*FB(t-6) + 9.87*(t-2000) + 18.1, where CSH is the headline CPI less shelter and FB is the index of food only. Standard deviation is $3.29.