Since September 16, 2009 the readings of the headline CPI and its components for August 2009 are available (we retrieve all CPI data from http://www.bls.gov/data). We recalculate our model for selected stock prices from the S&P 500 list. First was ConocoPhillips since it provides a good example of a company, which share price has been leading defining components of the CPI. Here we present several companied from the “energy” subcategory of S&P 500. It is instructive that these companies are rather different than similar in the evolution of share price and thus in defining CPI components.

In the previous posts and articles [1,2] we introduced several models with varying number of CPI components. In our view, the best one, we call it 3-C model, is seeking those two CPI components from 34 pre-selected ones, which minimize the difference between observed (monthly closing price adjusted for dividends and splits) and predicted prices for the period between July 2003 and August 2009. This model also includes free term (constant) and linear time term [3-6], which compensates well know linear (time) trends between various CPI components.

In the previous post we reported the empirical 3-C model for COP:

COP(t)= 3.41CF(t+1) - 7.17EC(t-6) + 7.22*(t-2000) + 145.76

where t is the calendar time, CF is the headline CPI less food, which lags behind COP by one months, and EC is the index for education and communication leading COP by six months. Standard deviation between the curves is $3.96 for the period between July 2003 and August 2009. Figure 1 displays the observed and predicted prices.

In the previous posts and articles [1,2] we introduced several models with varying number of CPI components. In our view, the best one, we call it 3-C model, is seeking those two CPI components from 34 pre-selected ones, which minimize the difference between observed (monthly closing price adjusted for dividends and splits) and predicted prices for the period between July 2003 and August 2009. This model also includes free term (constant) and linear time term [3-6], which compensates well know linear (time) trends between various CPI components.

In the previous post we reported the empirical 3-C model for COP:

COP(t)= 3.41CF(t+1) - 7.17EC(t-6) + 7.22*(t-2000) + 145.76

where t is the calendar time, CF is the headline CPI less food, which lags behind COP by one months, and EC is the index for education and communication leading COP by six months. Standard deviation between the curves is $3.96 for the period between July 2003 and August 2009. Figure 1 displays the observed and predicted prices.

Figure 1. Observed and 3-C predicted COP’s share price.

Below we present analytic models and figures for several energy companies without comments. One can judge the accuracy of the predictions and the similarity/difference between the companies.

Figure 2. Observed and 3-C predicted Apache Corp.’s share price: APA(t) = 1.35*TPR(t+1) + 3.21*MCS(t-7) + 47.20*(t-2000) - 973, where TPR is the index of private transportation, MCS is the index of medical care services. Standard deviation is $6.36.

Figure 3. Observed and 3-C predicted Anadarko Petroleum Corp.’s share price: APC(t) = 3.31*EC(t+2) – 1.74*CSHF(t-5) + 5.49*(t-2000) + 58, where EC is the index of education and transportation, CSHF is the headline CPI less shelter and food. Standard deviation is $3.22.

Figure 4. Observed and 3-C predicted Baker Hughes’ share price: BHI(t) = 4.93*F(t-5) – 0.79*T(t+1) + 32.53*(t-2000) + 662, where F is the index of food and beverages, T is the index of transportation. Standard deviation is $5.30.

Figure 5. Observed and 3-C predicted Peabody Energy Corp.’s share price: BTU(t) = 0.64*FU(t-4) + 1.36*TPR(t+1) – 8.37*(t-2000) - 266, where FU is the index of (housing) fuels and utilities, TPR is the index of private transportation. Standard deviation is $4.35.

Figure 6. Observed and 3-C predicted Cameron Intl. CP share prices CAM(t) = 0.64*TPR(t+1) + 2.65*RENT(t-4) - 17.1*(t-2000) - 610, where FU is the index of (housing) fuels and utilities, TPR is the index of private transportation. Standard deviation is $3.38.

Figure 7. Observed and 3-C predicted Chesapeake Energy Corporation share price: CHK(t) = 0.41*E(t+1) - 1.50*ED(t-7) - 12.1*(t-2000) + 102.7, where E is the index of energy and ED is the index of education. Standard deviation is $2.70.

Figure 8. Observed and 3-C predicted Consol Energy share price: CNX(t) = 6.11*C(t+2) – 2.62*ED(t-5) – 2.81*(t-2000) - 767.5, where C is the headline CPI and ED is the index of education. Standard deviation is $5.65.

Figure 9. Observed and 3-C predicted Chevron share price: CVX(t) = 0.25*E(t+1) + 2.76*MCS(t+4) – 37.6*(t-2000) - 716.1, where E is the index of energy and MCS is the index of medical care services. Standard deviation is $3.26.

Figure 10. Observed and 3-C predicted Devon Energy Corp.’s share price: DVN(t) = 0.79*T(t-3) + 0.46*E(t+2) – 0.68*(t-2000) - 162.7, where E is the index of energy and T is the index of transportation. Standard deviation is $5.67.

Figure 11. Observed and 3-C predicted Ensco share prices: ESV(t) = 2.23*CSH(t+1) - 2.61*FB(t-5) + 8.89*(t-2000) + 65.9, where CSH is the headline CPI less shelter and FB is the index of food only. Standard deviation is $3.37.

[2] Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15862/01/MPRA_paper_15862.pdf

[3] 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.

[4] Kitov, I., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/13587/01/MPRA_paper_13587.pdf

[5] Kitov, I., Kitov, O., (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15039/01/MPRA_paper_15039.pdf

[6] Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, MPRA Paper 15194, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15194/01/MPRA_paper_15194.pdf

**References**

[1] Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: June-September 2009, MPRA Paper 15863, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15863/01/MPRA_paper_15863.pdf[2] Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15862/01/MPRA_paper_15862.pdf

[3] 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.

[4] Kitov, I., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/13587/01/MPRA_paper_13587.pdf

[5] Kitov, I., Kitov, O., (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15039/01/MPRA_paper_15039.pdf

[6] Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, MPRA Paper 15194, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15194/01/MPRA_paper_15194.pdf

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