The Price of Crude Oil on the NYMEX
-
Upload
willhambly -
Category
Documents
-
view
227 -
download
0
Transcript of The Price of Crude Oil on the NYMEX
-
8/14/2019 The Price of Crude Oil on the NYMEX
1/28
Explaining the real price of crude oil on the NYMEX
Will C. Hambly
December 2, 2005Economics 272
Professor Studenmund
-
8/14/2019 The Price of Crude Oil on the NYMEX
2/28
Hambly
Background Information
Being the lifeblood of the worlds industrialized economies, crude oil is the most actively
traded commodity. The world consumes roughly 80 million barrels of crude oil per day and uses
petroleum products for a multitude of applications, including transportation, heating, and plastic
production. Because oil is such an essential input in the production process, its price is closely
followed and reported daily by the financial press. Also, most of the worlds heaviest consumers
of petroleum rely on imports from Middle Eastern oil-producing nations. Since the formation of
an international petroleum cartel, the Organization of Petroleum Exporting Countries (OPEC),
the political importance of oil has escalated. In an effort to insulate the American economy from
oil shocks, the U.S. government began stockpiling emergency oil reserves in 1977 as a national
security policy.
The question of whether the price of oil is high or low based on market fundamentals is a
contentious debate. Currently, oil is trading at about $60 per barrel in 2005 dollars, a relatively
high price compared to historical averages. Many justify this price and remain bullish, adhering
to the idea that the supply of petroleum is fixed and that increased demand from developing
countries will drive the price higher as they accelerate growth. Others dismiss the current price
as being irrational and the result of increased speculative activity by large alternative investment
funds. This paper seeks to explain what determines the price of oil.
Several different types of crude oil are produced and receive different market prices. For
instance, North Sea crude, generally known as Brent crude, commands about a $1 premium to
the OPEC Basket Price, which includes various blends of Dubai, Saharan, and Venezuelan
crudes. The price quoted on the New York Mercantile Exchange, however, is for light-sweet, or
West Texas Intermediate (WTI) crude. WTI is the most easily and widely refined crude in
2
-
8/14/2019 The Price of Crude Oil on the NYMEX
3/28
-
8/14/2019 The Price of Crude Oil on the NYMEX
4/28
Hambly
Much of the academic literature pertaining to the price of oil surrounds the impact of oil
prices on the macroeconomy. Understanding the Impact of Oil Shocks,published by the
Federal Reserve Bank of St. Louis, examines oil price shocks in the 1970s and shows
how they contributed to a drop in real GDP and an increase in the price level. This study,
however, analyzes oil prices as an independent variable and does not describe how oil
prices are set; nevertheless it confirms the correlation between economic growth and oil
prices. Another scholarly article, The Cyclical Behavior of NYMEX Energy Prices,
published in Energy Economics, explains that oil prices are procyclical. That is, an
expansion of real GDP is usually accompanied by an increase in the price of crude.
Besides a review of the scholarly literature, relevant commodities articles in both the Wall
Street Journal and the Financial Times offer daily insight into what may be moving the
market. Additionally, information provided by Phil Flynn, an oil trader with Alaron
Trading Co., offered a perspective on fundamental evaluators, such as real GDP, housing
starts, and industrial production. In the interview conducted, he stressed the importance
of commercial crude oil stocks and economic growth.
A Theoretical Model
A review of the literature pertaining to oil prices makes clear that as economic growth
increases, demand for oil increases. The economic theory behind the relationship between
economic growth and oil consumption is strong. In a model seeking to explain changes in price,
there is no question that a measure of demand is necessary. Another important aspect of the oil
market is the role of OPEC, the international petroleum cartel. While OPECs role in reducing
petroleum production has diminished over time, the cartel is still likely to have a significant
impact on the price of oil. Additionally, the role of stockpiles of crude oil should have an impact
4
-
8/14/2019 The Price of Crude Oil on the NYMEX
5/28
Hambly
on the price of crude. As stocks are depleted, there may be a fear that the commodity is in short
supply and traders will bid up the price. Also, a shock to the production of crude must have an
impact on the price. If there is a significant decline in oil production in a specific area, the
market will likely react to the prospect of reduced availability of oil by bidding up the price.
Lastly, to reflect current trends in the market for crude oil, a time-series model with very frequent
observations should be used. For practical reasons concerning the publishing of economic data,
a monthly model from January of 2002 through June of 2005 will be used.
Additionally, because crude oil on the NYMEX is measured in dollars, inflation must have an
effect on the price of oil. To measure real impacts on the price, inflation must be filtered out of
the dependent variable.
The Independent Variables, Functional Form, and Expected Signs of Coefficients
While it is clear that many variables affect the price of crude oil, determining the correct
variables for an equation is difficult because there are several ways to measure a single
phenomenon. Below are the independent variables and a detailed explanation of why each was
chosen and what it means:
Industrial Production Index: As the worlds economies grow, industrial production
expands and global demand for oil increases. Because the United States economy
consumes roughly 25% of the worlds crude oil, and meticulous monthly data is
collected by the government, the Industrial Production Index was chosen to explain
demand for oil in developed countries. The Industrial Production Index measures the
monthly physical output of the manufacturing, mining, gas, and electricity industries.
Other ways of measuring output, such as real GDP, are inferior to the Industrial
Production Index for this model because real GDP measures output in the service and
5
-
8/14/2019 The Price of Crude Oil on the NYMEX
6/28
Hambly
technology sectors, which consume less petroleum than heavy industries. Theory
suggests that the relationship between industrial output and crude prices should be
linear. Increases in industrial output should mean that oil demand has increased and
that the price should rise. A positive (+) sign is expected.
Non-OECD Consumption of Petroleum: This variable is a measure of oil
consumption in the developing world. As the developing world industrializes, the
world economys demand for petroleum accelerates. Both China and India are two of
the fastest growing nations and consume large amounts of oil. Almost all literature
concerning the price of oil cites Chinese demand as a driver of prices. The
relationship between non-OECD consumption and the price of oil should be linear as
well. As the consumption of a non-renewable resource increases, price should rise, so
the expected sign of this coefficient is positive (+).
Change in Crude Stocks: Changes in the commercial stocks of crude oil are an
important driver behind changes in price. Quantities of crude oil stocks are stocks of
oil held at refineries, in pipelines, in bulk terminals, or any quantities in transit to the
aforementioned destinations. If this variable were the absolute level of crude stocks,
an inverse function form would be theoretically accurate, because the impact of the
stock levels on price would diminish as they increased. Because it is the change in
stocks, only linear is appropriate. An increase in crude stocks should ease the
markets fear of a shortage, so the expected sign of this coefficient is negative (-).
Change in U.S. Field Production: A disruption in U.S. field production should have
a large impact on prices. Because the U.S. consumes more petroleum than it
produces, it is forced to import crude oil from abroad. As more oil is produced in the
6
-
8/14/2019 The Price of Crude Oil on the NYMEX
7/28
Hambly
United States, fears of a shortage will diminish and the price should fall. The
relationship between changes in field production and the price of oil should be linear.
The expected sign of this coefficient is negative (-).
Change in OPEC Output: By restricting output, OPEC has been able to raise the
price of oil. OPECs share of world oil production has decreased since the 1970s
because new oil fields have come on-line and market power has eroded; nevertheless,
OPECs pricing power still exists. Theory suggests that the relationship between
changes in OPEC output and the price of oil is linear. The expected sign of this
coefficient is negative (-) because as OPEC increases output, the price of oil should
fall.
For this model it is reasonable to assume a functional form in which the equation is linear
in both the coefficients and the variables. Theory does not suggest that the relationship between
the variables described above and the price of oil should be anything other than linear.
Discussion of the Data
Below is a discussion of the dependent variable and each independent variable. A
description of how the data is expressed, sources, and any irregularities found are offered.
Real Price of NYMEX Crude: Daily data on the price of crude oil is available from
the U.S. Energy Information Administration website. These prices are, however, in
nominal prices. Because there has been persistent inflation throughout the last three
years, prices quoted on the NYMEX were converted to January, 2002 dollars, when
the Consumer Price Index, Less Energy was equal to 186. Each monthly observation
is the real closing price (in January, 2002 dollars) of the contract of nearest expiration
on the first trading day of the month.
7
-
8/14/2019 The Price of Crude Oil on the NYMEX
8/28
Hambly
Industrial Production Index: Data was obtained from the Federal Reserve Bank of
St. Louis Federal Reserve Economic Data website. This data is seasonally adjusted,
of monthly frequency, and has a base year of 2002.
Non-OECD Consumption of Petroleum: Monthly time series data concerning
petroleum consumption and economic growth for countries not belonging to the
Organisation for Economic Co-operation and Development is not accessible.
Because data on oil consumption is not readily available, it was calculated as a
residual. Non-OECD consumption was calculated as the difference between total
world production per day per month of crude oil and OECD consumption per day per
month. Because a portion of the oil produced could enter stockpiles, this variable
may not be precise, however the theory behind the idea that developing countries
consume large amounts of oil as they industrialize is very strong, so this variable
must be included. It is expressed as the percentage change in consumption from the
same month in the previous year to adjust for seasonality. Data was obtained from
the U.S. Energy Information Administration websites section on international
petroleum.
Change in Crude Stocks: Changes in the crude oil stocks are measured as a
percentage change in the quantity of commercial crude oil stocks of the same month
from the previous year to eliminate any seasonal trends. This data is available on the
U.S. Energy Information Administrations website in the supply and disposition
section.
Change in U.S. Field Production: Data on U.S. field production of crude oil is
available at the U.S. Energy Information Administrations website as well. This
8
-
8/14/2019 The Price of Crude Oil on the NYMEX
9/28
Hambly
variable is calculated as the percentage change in field production from the same
month of the previous year to avoid seasonality.
Change in OPEC Output: This variable is measured as the percentage change in
output from the same month of the previous year to eliminate any seasonal patterns.
Statistics on OPEC production are also available from the U.S. Energy Information
Administration.
Estimation and Evaluation of the Equation
Using Ordinary Least Squares and the variables discussed above to estimate an equation
yields the following results (t-scores in parenthesis):
Equation 1:
NYMEX = -263.354 + 2.894 INDPROD + 0.061 NONOECD - 0.176 STOCKS
(11.600) (0.794) (-2.210)
+ 0.212 FIELDPROD + 0.062 OPEC
(0.9053) (0.676)
N = 42 Adjusted-R 2 = 0.8795 DW = 1.400
INDPROD = the Industrial Production Index
NONOECD = the percentage change in Non-OECD Consumption
STOCKS = the percentage change in commercial stocks
FIELDPROD = the percentage change in U.S. production
OPEC = the percentage change in OPEC output
Note: See Appendix Equation 1 for Regression Output, Correlation Matrix, Residuals,
and Data.Hypothesis Tests for Each of the Coefficients in Equation 1:
Degrees of Freedom = 36
5% One-Sided Test: tc = 1.697
9
-
8/14/2019 The Price of Crude Oil on the NYMEX
10/28
Hambly
HO: INDPROD 0 tINDPROD = 11.600 | tINDPROD| > tc and the sign is in the correct
direction. Reject HO.
HA: INDPROD > 0
HO: NONOECD 0 tNONOECD = 0.794 | tNONOECD| < tc even thought the sign is in the
correct direction.
HA: NONOECD > 0 Fail to Reject HO.
HO: STOCKS 0 tSTOCKS = -2.209 | tSTOCKS| > tc and the sign is in the correct
direction. Reject HO.
HA: STOCKS < 0
HO: FIELDPROD 0 tFIELDPROD = 0.905 | tFIELDPROD| < tc and the sign is in the wrong
direction. Fail to Reject HO.
HA: FIELDPROD < 0
HO: OPEC 0 tOPEC = 0.676 | tOPEC| < tc and the sign is in the wrong
direction. Fail to
Reject HO.
HA: OPEC < 0
Of the five coefficients, two are significant in the expected direction. INDPROD andSTOCKS
were significant and in the hypothesized directions. NONOECD had the expected positive sign,
however it was not significant. FIELDPROD andOPEC were insignificant in the unexpected direction.
Of the insignificant coefficients, the economic theory behind OPEC andNONOECD is indisputable.
10
-
8/14/2019 The Price of Crude Oil on the NYMEX
11/28
Hambly
The impact of OPECs output and the developing worlds demand for crude oil is well
documented and strongly supported by economic theory. By reducing output, OPEC is able to
increase the price of oil. Also, as countries not in the OECD, or the worlds developing
countries, industrialize they will increase demand for petroleum products and the price of oil will
rise. Both OPEC and NONOECD belong in the equation.
After rethinking the theory behind the regression, FIELDPROD, which was insignificant in
the wrong direction, could be an irrelevant variable. Although there is some theory behind the
idea that as U.S. field production increases, the price of oil should fall, this variable may not
belong because U.S. production is a small fraction of the world total. In fact, increases in field
production may be highly correlated with increases in the price of oil. As the price rises, it
becomes economically viable to drill in harsh environments, therefore increasing the production
of crude oil. In other words, field production does not have a significant impact on the price of
crude oil. The possibility of it being irrelevant must be investigated. It is now dropped from the
model based on theory and the coefficients are re-estimated.
The following is Equation 2 (t-scores in parenthesis):
NYMEX = - 262.886 + 2.889 INDPROD + 0.057 NONOECD - 0.169 STOCKS
(11.612) (0.737) (-2.139)
+ 0.064 OPEC
(0.702)
N = 42 Adjusted-R 2 = .8801 DW = 1.368
INDPROD = the Industrial Production Index
NONOECD = the percentage change in Non-OECD Consumption
STOCKS = the percentage change in commercial stocks
OPEC = the percentage change in OPEC output
11
-
8/14/2019 The Price of Crude Oil on the NYMEX
12/28
Hambly
Note: See Appendix Equation 2 for Regression Output, Correlation Matrix, Residuals,
and Data.
Hypothesis Tests for Each of the Coefficients in Equation 2:
Degrees of Freedom = 37
5% One-Sided Test: tc = 1.697
HO: INDPROD 0 tINDPROD = 11.612 | tINDPROD| > tc and the sign is in the correct
direction. Reject HO.
HA: INDPROD > 0
HO: NONOECD 0 tNONOECD = 0.737 | tNONOECD| < tc even thought the sign is in the
correct direction. Fail to
HA: NONOECD > 0 Reject HO.
HO: STOCKS 0 tSTOCKS = -2.139 | tSTOCKS| > tc and the sign is in the correct
direction. Reject HO.
HA: STOCKS < 0
HO: OPEC 0 tOPEC = 0.702 | tOPEC| < tc and the sign is in the wrong
direction. Fail to
Reject HO.
HA: OPEC < 0
After re-estimating the equation excluding the suspected irrelevant variable, the four
specification criteria must be applied to the results.
12
-
8/14/2019 The Price of Crude Oil on the NYMEX
13/28
Hambly
Theory: The theory behind the idea that U.S. field production affects the price of
crude oil is valid, however the United States only produces a small fraction of the
worlds oil, so this variable may not be belong. Additionally, field production may
not be affecting the price, but the price may be inducing producers to produce more.
Also, U.S. oil supplies may be insulated from periodic disruptions in field production
because of the Strategic Petroleum Reserves held by the government.
T-test: The t-score for the coefficient of field production was insignificant in
Equation 1. Two out of the four coefficients became more significant, but only one
became more significant in the expected direction. This is a relatively weak sign that
field production may be an irrelevant variable.
Adjusted-R2: Adjusted-R2 increased from 0.8795 to 0.8801. This is a small change in
adjusted-R2, nevertheless it increased. This is further evidence that field production
was an irrelevant variable.
Changes in the Coefficients: None of the coefficients changed significantly. This is
evidence that that field production is an irrelevant variable and its exclusion is not
causing any bias.
Based on the specification criteria, field production is removed from the model. Moving
forward with Equation 2, the equation must be tested to determine if any econometric maladies
afflict it.
Omitted Variables
The equation almost certainly has an omitted variable. A variable for political concern
over future oil supply should be included, however, political tension is not easily quantified. A
dummy variable for political events concerning the oil market would also be appropriate,
13
-
8/14/2019 The Price of Crude Oil on the NYMEX
14/28
Hambly
however observations of this variable would indicate that in each month there was a political
event, which would prove useless for the model. Also, since every month has a political event in
the oil market, deciding which event should be considered important injects human error and the
psychological phenomenon of confirmation bias into the equation.
Another possible omitted variable is a gauge of the developing worlds economic growth.
The Non-OECD Consumption of Petroleum variable contains imperfect data. Data on the
developing worlds economic growth or expectations of growth would enhance the accuracy of
the model and may result in a significant t-score for NONOECD.
Irrelevant Variables
Based on the four specification criteria, the field production variable was eliminated from
the model. The economic theory behind the existing variables is strong and in two of the four
coefficients, it is supported by significant t-scores. Because the variables included are supported
by strong theory, none is irrelevant. The regression results show that NONOECD andOPEC have a
very small impact on the price of oil and the coefficients are insignificant. Despite this
weakness, theory is strong and both variables must be included.
Functional Form
There is no reason to suspect that any functional form besides linear in the coefficients as
well as in the variables is appropriate. Including an intercept dummy or slope dummy for
political events may be theoretically appropriate, however, in every month there are several
political events of importance involving oil supply, so determining which events to include
would be of dangerously subjective nature.
Multicollinearity
14
-
8/14/2019 The Price of Crude Oil on the NYMEX
15/28
Hambly
Because the t-scores for NONOECD andOPEC are insignificant, and OPEC has an unexpected
sign, the equation could be afflicted with multicollinearity, which would result in high standard
errors and low t-scores. The Equation 2 Correlation Matrix included in the Appendix shows
the simple correlation coefficients between the independent variables.
All simple correlation coefficients are below 0.80. This is evidence that the equation does not
have multicollinearity. To further investigate multicollinearity in the equation, calculating the
variance inflation factors is necessary. Computer output for each estimated auxiliary equation
used to compute the VIF is included in the Appendix. Each VIF is presented below:
INDPROD NONOECD STOCKS OPEC
R-squared 0.5879 0.0147 0.4586 0.4736
VIF 2.43 1.01 1.85 1.90
None of the variables have a variance inflation factor above the threshold of 5. This is
further evidence that the equation does not have multicollinearity.
Serial Correlation
Being a time-series model, there is a high probability that the equation may have pure
positive serial correlation. This would bias the estimates of the standard errors negative and
increase the probability of a Type I error, making hypothesis testing unreliable.
The Durbin-Watson statistic for the equation is 1.368. A 5% one-sided Durbin-Watson
Test requires the appropriate critical values for an equation in which K = 4 and N = 42. These
values are as follows: dL = 1.29, dU = 1.72.
HO: 0 (no positive serial correlation)
HA: > 0 (positive serial correlation)
Because dL 1.368 dU, the resultsof the Durbin-Watson Test are inconclusive. The
existence of positive impure serial correlation cannot be detected. Even though a time series
15
-
8/14/2019 The Price of Crude Oil on the NYMEX
16/28
Hambly
model suggests serial correlation, because the Durbin-Watson test is inconclusive no remedy
should be applied.
Heteroskedasticity
Because this is a time-series model and there are not huge differences in size of the
dependent variable, heteroskedasticity is not extremely likely. Nevertheless, having
heteroskedasticity could lead to unreliable hypothesis testing because standard errors will be
biased negative, inflating the t-scores, and increasing the probability of a Type I error. The
existence of heteroskedasticity should be investigated. Running a Park Test requires a
proportionality factor, Z. It is reasonable to choose the Industrial Production Index as the
proportionality factor for this equation. The Industrial Production Index measures the physical
output of U.S. industry, and serves as a measure of the United States oil demand. As industrial
output increases, it is reasonable to assume that there may be a higher variance in the price of
crude oil. Thus, the Industrial Production Index is an appropriate proportionality factor.
Running the Park Test requires the generation of three new variables: the squared residuals, the
natural logarithm of the squared residuals, and the natural logarithm of the proportionality factor
Z, which is the Industrial Production Index. These variables are included in the Appendix. An
estimation of the regression to be used in the Park Test is as follows (t-scores in parenthesis):
LNRESIDSQ = -78.974 + 17.255 LNZ
(1.448)
N = 42 Adjusted-R 2 =0.026
LNZ = the natural logarithm of the Industrial Production Index
LNRESIDSQ = the natural logarithm of the residuals squared
Note: Regression output is included in the Appendix.
16
-
8/14/2019 The Price of Crude Oil on the NYMEX
17/28
Hambly
To run two-sided 1% t-test on the estimated coefficient of LNZ, the critical value of 2.704 is
needed.
HO: lnZ = 0 tlnZ = 1.448 | tlnZ| < tc
HA: lnZ 0 Fail to Reject the Null Hypothesis.
Because the Null Hypothesis cannot be rejected, there is no evidence of heteroskedasticity.
Results
Of the six major econometric diseases investigated, the only outstanding possibility of a
problem with the equation is the existence of an omitted variable. The quality of the equation
should not be judged by the adjusted-R2 statistic, but being able to explain approximately 88% of
the variation in oil prices with the independent variables used is satisfying. Although OPEC and
NONOECD have insignificant coefficients and the sign of OPEC is inthe unexpected direction, the
theory behind these variables commands that they must be included. The tests performed above
also show that the equation is not afflicted with multicollinearity or heteroskedasticity, however
the existence of serial correlation is inconclusive. The final equation (Equation 2) is presented
below:
NYMEX = - 262.886 + 2.889 INDPROD + 0.057 NONOECD - 0.169 STOCKS
(11.612) (0.737) (-2.139)
+ 0.064 OPEC
(0.702)
N = 42 Adjusted-R 2 = .8801 DW = 1.368
INDPROD = the Industrial Production Index
NONOECD = the percentage change in Non-OECD Consumption
STOCKS = the percentage change in commercial stocks
17
-
8/14/2019 The Price of Crude Oil on the NYMEX
18/28
Hambly
FIELDPROD = the percentage change in U.S. production
OPEC = the percentage change in OPEC output
Note: See Appendix Equation 2 for Data, Regression Output, Residuals, and Correlation
Matrix
Discussion and Conclusions
The equation shows that industrial output and the change in crude stocks have
significantly large impacts on the price of crude oil traded on the NYMEX. For each one-unit
increase in the Industrial Production Index, the price of crude should rise almost $3, holding all
other independent variables in the equation constant. Also, for each 1% increase in crude stocks
compared to the same month of the previous year, the price of crude should fall nearly $0.17,
holding constant all other variables in the equation. OPEC output and oil consumption in the
developing countries are also likely to be important drivers behind the price of crude, but in this
equation they are insignificant. The model can be used for judging the markets response to
changes in oil fundamentals, assessing the current price of oil, and creating an oil trading
strategy. Because the financial press devotes thousands of pages each year to covering the price
of oil, the equation above can be used to evaluate analysts interpretations of what moves the
market. Further research on possible proxies for political tension should be examined because
political concern is likely to have a positive impact on oil prices. Also, finding more accurate
and extensive monthly data on the developing worlds economic growth would increase the
precision of the model. As the developing worlds economic growth accelerates in the future and
data becomes available, another estimation of the equation with an increased sample size should
generate more robust results.
18
-
8/14/2019 The Price of Crude Oil on the NYMEX
19/28
Hambly
Bibliography
Augilar-Conraria, Luis. Understanding the Impact of Oil Shocks. Federal Reserve Bank of St.
Louis. Jun. 2005.
Coimbra, Carlos. Oil Price Assumptions in Macroeconomic Forecasts. OPEC Review 28
(1976): 87-107.
Farivar, Maswood. Crude-Oil Futures Edge Higher As Inventories Post Sharp Drop. Wall
Street Journal, 1 Dec. 2005.
Flynn, Phil. Alaron Trading Company. Personal Interview. 20 Oct. 2005.
Goodman, Leah. Crude Drops Below $57 a Barrel. Wall Street Journal, 18 Nov. 2005.
Hoyos, Carola. IEA Urges Calm Over Energy Prices. Financial Times, 10 Nov. 2005.
McKay, Peter. Energy Prices Finally Calm Down. Wall Street Journal, 22 Nov. 2005.
McNutty, Sheila. US Grapples with The Age of Energy Insecurity. Financial Times, 21 Nov.
2005.
Padgett, Gary. Great Pacific Trading Company. Personal Interview. 3 Aug. 2005.
Petroleum. Worldbook Encyclopedia. 2000.
Pindyck, Robert. Volatility and Commodity Price Dynamics. Journal of Futures Markets 24
(1981): 1029-1047.
Serletis, Apostolos. The Cyclical Behavior of Monthly NYMEX Energy Prices. Energy
Economics 20 (1998): 265-270.
Studenmund, A.H. Using Econometrics: A Practical Guide. New York: Addison Wesley, 2006.
United States Energy Information Administration. Monthly Energy Review. Nov. 2005.
19
-
8/14/2019 The Price of Crude Oil on the NYMEX
20/28
Hambly
United States Energy Information Administration. This Week in Petroleum. Sept-Dec. 2005.
Appendix
Equation 1.
Regression Results for Equation 1.
Dependent Variable: NYMEXMethod: Least SquaresDate: 11/30/05 Time: 20:41Sample: 2002:01 2005:06Included observations: 42
Variable Coefficient Std. Error t-Statistic Prob.
C -263.3541 25.45925 -10.34414 0.0000INDPROD 2.894178 0.249490 11.60038 0.0000NONOECD 0.061189 0.077049 0.794155 0.4323
STOCKS -0.176052 0.079707 -2.208745 0.0336OPEC 0.061559 0.091025 0.676293 0.5032
FIELDPROD 0.211721 0.233857 0.905347 0.3713
R-squared 0.894220 Mean dependent var 33.83429Adjusted R-squared 0.879529 S.D. dependent var 8.689565S.E. of regression 3.016061 Akaike info criterion 5.177344Sum squared resid 327.4785 Schwarz criterion 5.425583Log likelihood -102.7242 F-statistic 60.86590Durbin-Watson stat 1.400394 Prob(F-statistic) 0.000000
Correlation Matrix for Equation 1.
STOCKS OPEC NONOECD INDPROD FIELDPRODSTOCKS 1.000000 -0.153512 -0.100230 0.487337 0.111060
OPEC -0.153512 1.000000 0.083053 0.510144 -0.006444NONOECD -0.100230 0.083053 1.000000 -0.006297 -0.076037INDPROD 0.487337 0.510144 -0.006297 1.000000 0.046509
FIELDPROD 0.111060 -0.006444 -0.076037 0.046509 1.000000
Residuals for Equation 1.
obs Actual Fitted Residual Residual Plot
2002:01 21.0100 19.2563 1.75370 | . | * . |
2002:02 20.3400 18.0703 2.26971 | . | *. |2002:03 22.3300 22.3629 -0.03290 | . * . |2002:04 26.7400 24.7487 1.99125 | . | *. |2002:05 26.5800 26.5426 0.03737 | . * . |2002:06 24.8900 27.7317 -2.84168 | * | . |2002:07 26.5700 27.1877 -0.61772 | . *| . |2002:08 26.1600 28.4176 -2.25762 | .* | . |2002:09 27.4200 28.7411 -1.32105 | . * | . |2002:10 30.4000 28.0324 2.36763 | . | *. |
20
-
8/14/2019 The Price of Crude Oil on the NYMEX
21/28
Hambly
2002:11 26.7100 29.6928 -2.98283 | * | . |2002:12 26.7900 27.6288 -0.83877 | . *| . |2003:01 31.2800 31.1533 0.12668 | . * . |2003:02 32.1200 31.0965 1.02351 | . |* . |2003:03 35.1800 31.6285 3.55152 | . | .* |2003:04 29.2000 27.1463 2.05366 | . | *. |2003:05 25.4700 27.5295 -2.05954 | .* | . |2003:06 30.0200 27.1727 2.84728 | . | * |2003:07 29.6500 27.5438 2.10619 | . | *. |2003:08 31.4600 28.9880 2.47200 | . | *. |2003:09 28.6300 28.4652 0.16475 | . * . |2003:10 28.5500 29.1924 -0.64236 | . *| . |2003:11 28.0400 32.5991 -4.55914 | * . | . |2003:12 29.0100 33.5845 -4.57450 | * . | . |2004:01 32.6700 35.0387 -2.36866 | .* | . |2004:02 33.7800 35.2113 -1.43131 | . * | . |2004:03 35.4900 34.7842 0.70581 | . |* . |2004:04 32.9200 37.3893 -4.46929 | * . | . |2004:05 36.6200 40.0361 -3.41605 | *. | . |2004:06 40.5000 37.5816 2.91837 | . | * |
2004:07 37.0100 40.9628 -3.95281 | *. | . |2004:08 41.8400 41.4789 0.36113 | . |* . |2004:09 41.9000 41.1784 0.72161 | . |* . |2004:10 47.6100 44.4186 3.19142 | . | * |2004:11 47.5200 44.2003 3.31972 | . | .* |2004:12 43.0800 44.3408 -1.26079 | . * | . |2005:01 39.8100 45.9339 -6.12389 | * . | . |2005:02 44.4700 46.4533 -1.98332 | .* | . |2005:03 48.6000 46.7094 1.89056 | . | *. |2005:04 53.7700 46.1458 7.62417 | . | . *2005:05 47.7400 46.7030 1.03704 | . |* . |2005:06 51.1600 47.9609 3.19914 | . | * |
Data for Equation 1.
obs FIELDPROD NONOECD NYMEX OPEC STOCKS2002:01 -0.677000 -4.470000 21.01000 -11.20200 8.8250002002:02 0.406000 -2.408000 20.34000 -10.01400 15.892002002:03 0.206000 5.127000 22.33000 -11.19300 8.0900002002:04 -0.421000 1.528000 26.74000 -13.02000 -1.7930002002:05 1.110000 9.017000 26.58000 -9.268000 -0.4070002002:06 -0.141000 -5.182000 24.89000 -5.321000 3.0190002002:07 -2.452000 -4.453000 26.57000 -7.312000 -2.7520002002:08 0.709000 0.852000 26.16000 -9.498000 -3.8050002002:09 -6.880000 3.367000 27.42000 -3.703000 -12.493002002:10 -0.889000 3.549000 30.40000 -0.538000 -6.948000
2002:11 4.350000 -3.619000 26.71000 0.526000 -7.7270002002:12 1.834000 -12.92300 26.79000 -2.691000 -11.015002003:01 1.501000 8.131000 31.28000 2.508000 -14.442002003:02 0.100000 -1.827000 32.12000 7.787000 -17.189002003:03 0.449000 17.59900 35.18000 9.162000 -15.567002003:04 -0.733000 -1.495000 29.20000 10.80600 -10.249002003:05 -0.703000 4.311000 25.47000 7.320000 -12.692002003:06 -0.565000 -6.310000 30.02000 5.339000 -10.379002003:07 -3.063000 -0.112000 29.65000 3.430000 -6.360000
21
-
8/14/2019 The Price of Crude Oil on the NYMEX
22/28
Hambly
2003:08 1.244000 4.409000 31.46000 6.149000 -5.6450002003:09 1.579000 -1.316000 28.63000 4.132000 5.9150002003:10 -0.858000 1.179000 28.55000 3.248000 1.0890002003:11 -1.316000 5.370000 28.04000 2.745000 -2.3750002003:12 0.327000 -6.411000 29.01000 12.30400 -3.1480002004:01 -0.150000 7.504000 32.67000 10.35300 -0.8900002004:02 -0.258000 -5.883000 33.78000 4.832000 4.8800002004:03 0.928000 1.212000 35.49000 2.306000 5.5970002004:04 -1.444000 7.039000 32.92000 5.407000 4.0930002004:05 0.389000 7.190000 36.62000 4.500000 6.6490002004:06 -2.698000 -0.989000 40.50000 11.93300 7.1160002004:07 1.099000 -0.059000 37.01000 13.00700 3.3350002004:08 -2.283000 -2.749000 41.84000 10.15000 -0.3040002004:09 -5.078000 0.778000 41.90000 10.56100 -4.7810002004:10 1.861000 1.878000 47.61000 8.388000 -2.7080002004:11 4.648000 -4.525000 47.52000 6.528000 2.4930002004:12 0.321000 -8.431000 43.08000 5.099000 6.2730002005:01 -0.359000 11.11200 39.81000 4.242000 6.2690002005:02 1.383000 -5.102000 44.47000 4.881000 6.7910002005:03 0.530000 4.556000 48.60000 5.843000 7.198000
2005:04 -0.175000 8.464000 53.77000 6.379000 8.9930002005:05 0.118000 5.156000 47.74000 6.631000 9.2290002005:06 -1.214000 -9.968000 51.16000 2.897000 7.992000
Sources: Energy Information Administration website, Federal Reserve Economic Data website
Equation 2.
Regression Results for Equation 2.
Dependent Variable: NYMEXMethod: Least Squares
Date: 11/30/05 Time: 21:43Sample: 2002:01 2005:06Included observations: 42
Variable Coefficient Std. Error t-Statistic Prob.
C -262.8857 25.39188 -10.35314 0.0000INDPROD 2.889269 0.248822 11.61177 0.0000
NONOECD 0.056550 0.076691 0.737384 0.4655STOCKS -0.169321 0.079166 -2.138824 0.0391
OPEC 0.063705 0.090772 0.701815 0.4872
R-squared 0.891812 Mean dependent var 33.83429Adjusted R-squared 0.880116 S.D. dependent var 8.689565S.E. of regression 3.008702 Akaike info criterion 5.152238Sum squared resid 334.9346 Schwarz criterion 5.359103
Log likelihood -103.1970 F-statistic 76.24912Durbin-Watson stat 1.367571 Prob(F-statistic) 0.000000
Correlation Matrix for Equation 2.
STOCKS OPEC NONOECD INDPRODSTOCKS 1.000000 -0.153512 -0.100230 0.487337
OPEC -0.153512 1.000000 0.083053 0.510144NONOECD -0.100230 0.083053 1.000000 -0.006297
22
-
8/14/2019 The Price of Crude Oil on the NYMEX
23/28
Hambly
INDPROD 0.487337 0.510144 -0.006297 1.000000
Residuals for Equation 2.
obs Actual Fitted Residual Residual Plot
2002:01 21.0100 19.4402 1.56979 | . | * . |2002:02 20.3400 18.0661 2.27392 | . | *. |2002:03 22.3300 22.3067 0.02332 | . * . |2002:04 26.7400 24.7696 1.97035 | . | *. |2002:05 26.5800 26.2203 0.35970 | . |* . |2002:06 24.8900 27.7670 -2.87704 | * | . |2002:07 26.5700 27.6676 -1.09756 | . * | . |2002:08 26.1600 28.1915 -2.03151 | .* | . |2002:09 27.4200 30.0642 -2.64418 | * | . |2002:10 30.4000 28.1324 2.26762 | . | *. |2002:11 26.7100 28.7126 -2.00259 | .* | . |2002:12 26.7900 27.1976 -0.40762 | . *| . |2003:01 31.2800 30.6808 0.59923 | . |* . |
2003:02 32.1200 30.9595 1.16049 | . | * . |2003:03 35.1800 31.3423 3.83772 | . | .* |2003:04 29.2000 27.2420 1.95795 | . | *. |2003:05 25.4700 27.5684 -2.09838 | .* | . |2003:06 30.0200 27.2416 2.77843 | . | * |2003:07 29.6500 28.1335 1.51653 | . | * . |2003:08 31.4600 28.6551 2.80491 | . | * |2003:09 28.6300 28.1582 0.47181 | . |* . |2003:10 28.5500 29.3548 -0.80482 | . *| . |2003:11 28.0400 32.8102 -4.77021 | * . | . |2003:12 29.0100 33.5166 -4.50658 | * . | . |2004:01 32.6700 35.0161 -2.34613 | .* | . |2004:02 33.7800 35.2967 -1.51671 | . * | . |
2004:03 35.4900 34.5864 0.90361 | . |* . |2004:04 32.9200 37.6593 -4.73931 | * . | . |2004:05 36.6200 39.9279 -3.30787 | *. | . |2004:06 40.5000 38.1869 2.31310 | . | *. |2004:07 37.0100 40.7337 -3.72368 | *. | . |2004:08 41.8400 41.9461 -0.10606 | . * . |2004:09 41.9000 42.1930 -0.29298 | . * . |2004:10 47.6100 43.9645 3.64551 | . | .* |2004:11 47.5200 43.2158 4.30421 | . | . * |2004:12 43.0800 44.3094 -1.22944 | . * | . |2005:01 39.8100 45.9530 -6.14299 | * . | . |2005:02 44.4700 46.1817 -1.71167 | . * | . |2005:03 48.6000 46.5786 2.02137 | . | *. |
2005:04 53.7700 46.1600 7.60998 | . | . *2005:05 47.7400 46.6714 1.06864 | . |* . |2005:06 51.1600 48.2609 2.89912 | . | * |
Data for Equation 2.
obs FIELDPROD INDPROD NONOECD NYMEX OPEC STOCKS2002:01 -0.677000 98.56700 -4.470000 21.01000 -11.20200 8.8250002002:02 0.406000 98.43900 -2.408000 20.34000 -10.01400 15.89200
23
-
8/14/2019 The Price of Crude Oil on the NYMEX
24/28
Hambly
2002:03 0.206000 99.32800 5.127000 22.33000 -11.19300 8.0900002002:04 -0.421000 99.71200 1.528000 26.74000 -13.02000 -1.7930002002:05 1.110000 100.0660 9.017000 26.58000 -9.268000 -0.4070002002:06 -0.141000 100.9930 -5.182000 24.89000 -5.321000 3.0190002002:07 -2.452000 100.6500 -4.453000 26.57000 -7.312000 -2.7520002002:08 0.709000 100.7140 0.852000 26.16000 -9.498000 -3.8050002002:09 -6.880000 100.6760 3.367000 27.42000 -3.703000 -12.493002002:10 -0.889000 100.2590 3.549000 30.40000 -0.538000 -6.9480002002:11 4.350000 100.5310 -3.619000 26.71000 0.526000 -7.7270002002:12 1.834000 100.0670 -12.92300 26.79000 -2.691000 -11.015002003:01 1.501000 100.5450 8.131000 31.28000 2.508000 -14.442002003:02 0.100000 100.5590 -1.827000 32.12000 7.787000 -17.189002003:03 0.449000 100.3760 17.59900 35.18000 9.162000 -15.567002003:04 -0.733000 99.60600 -1.495000 29.20000 10.80600 -10.249002003:05 -0.703000 99.53900 4.311000 25.47000 7.320000 -12.692002003:06 -0.565000 99.81300 -6.310000 30.02000 5.339000 -10.379002003:07 -3.063000 100.2780 -0.112000 29.65000 3.430000 -6.3600002003:08 1.244000 100.3520 4.409000 31.46000 6.149000 -5.6450002003:09 1.579000 101.0140 -1.316000 28.63000 4.132000 5.9150002003:10 -0.858000 101.1160 1.179000 28.55000 3.248000 1.089000
2003:11 -1.316000 102.0380 5.370000 28.04000 2.745000 -2.3750002003:12 0.327000 102.2570 -6.411000 29.01000 12.30400 -3.1480002004:01 -0.150000 102.6790 7.504000 32.67000 10.35300 -0.8900002004:02 -0.258000 103.4980 -5.883000 33.78000 4.832000 4.8800002004:03 0.928000 103.2110 1.212000 35.49000 2.306000 5.5970002004:04 -1.444000 104.0040 7.039000 32.92000 5.407000 4.0930002004:05 0.389000 104.9560 7.190000 36.62000 4.500000 6.6490002004:06 -2.698000 104.3770 -0.989000 40.50000 11.93300 7.1160002004:07 1.099000 104.9950 -0.059000 37.01000 13.00700 3.3350002004:08 -2.283000 105.3170 -2.749000 41.84000 10.15000 -0.3040002004:09 -5.078000 105.0620 0.778000 41.90000 10.56100 -4.7810002004:10 1.861000 105.8230 1.878000 47.61000 8.388000 -2.7080002004:11 4.648000 106.0350 -4.525000 47.52000 6.528000 2.493000
2004:12 0.321000 106.7430 -8.431000 43.08000 5.099000 6.2730002005:01 -0.359000 106.9480 11.11200 39.81000 4.242000 6.2690002005:02 1.383000 107.3610 -5.102000 44.47000 4.881000 6.7910002005:03 0.530000 107.3120 4.556000 48.60000 5.843000 7.1980002005:04 -0.175000 107.1840 8.464000 53.77000 6.379000 8.9930002005:05 0.118000 107.4340 5.156000 47.74000 6.631000 9.2290002005:06 -1.214000 108.2900 -9.968000 51.16000 2.897000 7.992000
Sources: Energy Information Administration website, Federal Reserve Economic Data website
Auxiliary Equations Used in Calculating VIFs.
Dependent Variable: INDPRODMethod: Least SquaresDate: 11/30/05 Time: 22:27Sample: 2002:01 2005:06Included observations: 42
Variable Coefficient Std. Error t-Statistic Prob.
C 102.0284 0.326063 312.9100 0.0000NONOECD 0.000973 0.049999 0.019461 0.9846
STOCKS 0.211323 0.038583 5.477105 0.0000
24
-
8/14/2019 The Price of Crude Oil on the NYMEX
25/28
Hambly
OPEC 0.246962 0.043557 5.669907 0.0000
R-squared 0.587933 Mean dependent var 102.5887Adjusted R-squared 0.555401 S.D. dependent var 2.941805S.E. of regression 1.961543 Akaike info criterion 4.275733Sum squared resid 146.2108 Schwarz criterion 4.441225Log likelihood -85.79040 F-statistic 18.07268
Durbin-Watson stat 0.472237 Prob(F-statistic) 0.000000
Dependent Variable: NONOECDMethod: Least SquaresDate: 11/30/05 Time: 22:28Sample: 2002:01 2005:06Included observations: 42
Variable Coefficient Std. Error t-Statistic Prob.
C -0.508813 53.71062 -0.009473 0.9925INDPROD 0.010243 0.526324 0.019461 0.9846STOCKS -0.070717 0.167063 -0.423296 0.6745OPEC 0.057427 0.191781 0.299439 0.7662
R-squared 0.014745 Mean dependent var 0.740381
Adjusted R-squared -0.063038 S.D. dependent var 6.172633S.E. of regression 6.364216 Akaike info criterion 6.629652Sum squared resid 1539.123 Schwarz criterion 6.795144Log likelihood -135.2227 F-statistic 0.189566Durbin-Watson stat 2.432060 Prob(F-statistic) 0.902852
Dependent Variable: STOCKSMethod: Least SquaresDate: 11/30/05 Time: 22:29Sample: 2002:01 2005:06Included observations: 42
Variable Coefficient Std. Error t-Statistic Prob.
C -213.0143 38.89989 -5.475960 0.0000
INDPROD 2.087632 0.381156 5.477105 0.0000NONOECD -0.066365 0.156781 -0.423296 0.6745OPEC -0.607943 0.157707 -3.854900 0.0004
R-squared 0.458641 Mean dependent var -0.569786Adjusted R-squared 0.415903 S.D. dependent var 8.066933S.E. of regression 6.165256 Akaike info criterion 6.566129Sum squared resid 1444.394 Schwarz criterion 6.731621Log likelihood -133.8887 F-statistic 10.73125Durbin-Watson stat 0.619896 Prob(F-statistic) 0.000030
Dependent Variable: OPECMethod: Least SquaresDate: 11/30/05 Time: 22:30
Sample: 2002:01 2005:06Included observations: 42
Variable Coefficient Std. Error t-Statistic Prob.
C -187.9143 33.61505 -5.590184 0.0000INDPROD 1.855699 0.327289 5.669907 0.0000NONOECD 0.040992 0.136895 0.299439 0.7662STOCKS -0.462417 0.119956 -3.854900 0.0004
R-squared 0.473559 Mean dependent var 2.753167Adjusted R-squared 0.431997 S.D. dependent var 7.134466
25
-
8/14/2019 The Price of Crude Oil on the NYMEX
26/28
Hambly
S.E. of regression 5.376958 Akaike info criterion 6.292515Sum squared resid 1098.644 Schwarz criterion 6.458008Log likelihood -128.1428 F-statistic 11.39425Durbin-Watson stat 0.571854 Prob(F-statistic) 0.000018
Park Test Data.
obs RESIDSQ LNZ LNRESIDSQ2002:01 2.464240 4.590737 0.9018832002:02 5.170714 4.589437 1.6430112002:03 0.000544 4.598428 -7.5171332002:04 3.882282 4.602286 1.3564232002:05 0.129385 4.605830 -2.0449622002:06 8.277362 4.615051 2.1135242002:07 1.204643 4.611649 0.1861832002:08 4.127040 4.612285 1.4175602002:09 6.991669 4.611907 1.9447192002:10 5.142083 4.607757 1.6374582002:11 4.010386 4.610466 1.388887
2002:12 0.166152 4.605840 -1.7948502003:01 0.359080 4.610605 -1.0242102003:02 1.346734 4.610745 0.2976822003:03 14.72810 4.608923 2.6897572003:04 3.833571 4.601222 1.3437972003:05 4.403182 4.600550 1.4823282003:06 7.719650 4.603298 2.0437692003:07 2.299865 4.607946 0.8328512003:08 7.867526 4.608684 2.0627442003:09 0.222607 4.615259 -1.5023502003:10 0.647728 4.616268 -0.4342842003:11 22.75490 4.625345 3.1247802003:12 20.30926 4.627489 3.011077
2004:01 5.504349 4.631608 1.7055382004:02 2.300400 4.639552 0.8330832004:03 0.816511 4.636775 -0.2027152004:04 22.46104 4.644429 3.1117822004:05 10.94198 4.653541 2.3926062004:06 5.350435 4.648009 1.6771782004:07 13.86581 4.653913 2.6294262004:08 0.011249 4.656975 -4.4874942004:09 0.085839 4.654551 -2.4552762004:10 13.28975 4.661768 2.5869932004:11 18.52621 4.663769 2.9191872004:12 1.511521 4.670424 0.4131162005:01 37.73628 4.672343 3.6306222005:02 2.929806 4.676197 1.0749362005:03 4.085945 4.675740 1.4075532005:04 57.91187 4.674547 4.0589222005:05 1.141997 4.676877 0.1327792005:06 8.404904 4.684813 2.128815
26
-
8/14/2019 The Price of Crude Oil on the NYMEX
27/28
Hambly
Regression Results for Park Test
Dependent Variable: LNRESIDSQMethod: Least Squares
Date: 12/05/05 Time: 11:06Sample: 2002:01 2005:06Included observations: 42
Variable Coefficient Std. Error t-Statistic Prob.
C -78.97407 55.17128 -1.431435 0.1601LNZ 17.25491 11.91497 1.448170 0.1554
R-squared 0.049818 Mean dependent var 0.921850Adjusted R-squared 0.026063 S.D. dependent var 2.202682S.E. of regression 2.173788 Akaike info criterion 4.437268Sum squared resid 189.0142 Schwarz criterion 4.520014Log likelihood -91.18262 F-statistic 2.097197Durbin-Watson stat 2.081217 Prob(F-statistic) 0.155363
Park Test Residuals
obs Actual Fitted Residual Residual Plot
2002:01 0.90188 0.23868 0.66321 | . |* . |2002:02 1.64301 0.21625 1.42676 | . | *. |2002:03 -7.51713 0.37138 -7.88852 |* . | . |2002:04 1.35642 0.43796 0.91846 | . |* . |2002:05 -2.04496 0.49911 -2.54407 | * | . |2002:06 2.11352 0.65822 1.45530 | . | *. |2002:07 0.18618 0.59952 -0.41334 | . *| . |2002:08 1.41756 0.61049 0.80707 | . |* . |2002:09 1.94472 0.60398 1.34074 | . | *. |
2002:10 1.63746 0.53236 1.10510 | . |* . |2002:11 1.38889 0.57911 0.80978 | . |* . |2002:12 -1.79485 0.49928 -2.29414 | * | . |2003:01 -1.02421 0.58151 -1.60572 | .* | . |2003:02 0.29768 0.58391 -0.28623 | . * . |2003:03 2.68976 0.55248 2.13727 | . | * |2003:04 1.34380 0.41961 0.92419 | . |* . |2003:05 1.48233 0.40800 1.07433 | . |* . |2003:06 2.04377 0.45543 1.58834 | . | *. |2003:07 0.83285 0.53563 0.29722 | . * . |2003:08 2.06274 0.54836 1.51439 | . | *. |2003:09 -1.50235 0.66181 -2.16416 | * | . |2003:10 -0.43428 0.67923 -1.11351 | . *| . |
2003:11 3.12478 0.83585 2.28893 | . | * |2003:12 3.01108 0.87284 2.13824 | . | * |2004:01 1.70554 0.94390 0.76164 | . |* . |2004:02 0.83308 1.08099 -0.24790 | . * . |2004:03 -0.20272 1.03307 -1.23579 | .* | . |2004:04 3.11178 1.16514 1.94664 | . | * |2004:05 2.39261 1.32237 1.07024 | . |* . |2004:06 1.67718 1.22691 0.45026 | . |* . |2004:07 2.62943 1.32878 1.30065 | . | *. |2004:08 -4.48749 1.38161 -5.86911 | * . | . |
27
-
8/14/2019 The Price of Crude Oil on the NYMEX
28/28
Hambly
2004:09 -2.45528 1.33978 -3.79506 | * . | . |2004:10 2.58699 1.46432 1.12268 | . | *. |2004:11 2.91919 1.49885 1.42034 | . | *. |2004:12 0.41312 1.61368 -1.20056 | .* | . |2005:01 3.63062 1.64678 1.98384 | . | * |2005:02 1.07494 1.71329 -0.63835 | . *| . |2005:03 1.40755 1.70541 -0.29786 | . * . |2005:04 4.05892 1.68482 2.37410 | . | * |2005:05 0.13278 1.72502 -1.59224 | .* | . |2005:06 2.12882 1.86195 0.26686 | . * . |
28