Couple years ago we introduced a concept of deterministic and sustainable trends in the differences of consumer (and later on - producer) price indices [1,2]. One of the best examples was the difference between the overall (often called “headline”) CPI and the index of motor oil [3], both indices were seasonally adjusted ones. A year ago we revisited this difference [4] and found our predictions in good agreement with observations. Essentially, this difference approached the new trend and we expected the following evolution along this new trend, which assumes that the price index of motor fuel will decrease relative to the CPI.

The model 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).

This post displays the evolution of the difference in 2010 (see Figure 1). All in all, the prediction was good enough: the earlier positive deviation from the trend is now compensated by a negative one. Currently, the difference is below the trend and we expect it to reach the trend in the beginning of 2011. This recovery should be accompanied by a drop in the price index of motor fuel and likely in the index of crude oil.

*Figure 1. The difference between the headline CPI and the index for motor fuel. Solid diamonds represent the prediction given in March 2009 through December 2009 [1]. 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. In 2010, the difference has been fluctuating around the trend and thus should return to the trend in the beginning of 2011.*

**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). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany

4. Kitov, I.. Kitov, O. (2010). "Crude oil and motor fuel: Fair price revisited," Quantitative Finance Papers 1005.0051, arXiv.org.

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