Download Observing the Changing Relationship Between

Observing the Changing Relationship
Between Natural Gas Prices and Power
Prices
The research views expressed herein are those of the author and do
not necessarily represent the views of the CME Group or its affiliates.
All examples in this presentation are hypothetical interpretations of
situations and are used for explanation purposes only.
This report and the information herein should not be considered
investment advice or the results of actual market experience.
Samantha Azzarello
Economist, CME Group
April 2013
Risk Disclosures
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The information within this presentation has been compiled by CME Group for general purposes
only. CME Group assumes no responsibility for any errors or omissions. Additionally, all
examples in this presentation are hypothetical situations, used for explanation purposes only,
and should not be considered investment advice or the results of actual market experience.
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© 2011 CME Group. All rights reserved
2
Objective and Scope of Analysis
• To better understand the changing
relationship between Power and Natural Gas.
• Analyzing the seasonal effect and trend of
natural gas price on power price.
• Completed analysis for multiple ISOs – MISO,
PJM, ISO NE and ERCOT.
• Used a Bayesian Statistical model to complete
analysis.
© 2011 CME Group. All rights reserved
3
Why use Bayesian Statistics with this
Analysis?
• Simply, the relationship between power and
natural gas has been changing.
• A major strength of this type of Bayesian
statistical model is that it captures changing
dynamics between variables.
© 2011 CME Group. All rights reserved
4
MISO Analysis
Dynamic Linear Model Regression
Parameter representing the influence of Natural Gas
price on Power price is unknown.
Estimation Equation
Powert= Constant + Natural Gast + errort
© 2011 CME Group. All rights reserved
5
Dynamic Linear Model (DLM)
• Dynamic models allow time varying coefficient
estimates.
• Sequential analysis allows for updating of coefficients
as new information is observed.
• Compare:
OLS Regression - One set of coefficient estimates for
whole time period.
DLM – Relationship of variable X on Y can change and
vary over time. DLM estimates capture this change.
© 2011 CME Group. All rights reserved
6
Data
Natural Gas
• ANR Gas Daily Prices (Platts).
Power
• Cinergy Average LMP data (until Feb-28-2011).
• Indiana Hub (Mar-1-2011).
• Data from April 2005 to April 2013.
• Model uses Daily Price Percent Change series for
both Power and Natural Gas.
© 2011 CME Group. All rights reserved
7
Seasonal Trend Decomposition (STL)
• Breaks a time series into Trend and Seasonal
components.
• Done by LOESS (Locally Weighted Regression).
• Smoothing algorithm which fits a locally weighted
polynomial – linear or quadratic.
• Decomposed the Total Effect of Natural Gas Price
on Power Price (Coefficient – βt) into
components.
βt = Trendt + Seasonalt + Remaindert
© 2011 CME Group. All rights reserved
8
MISO: Seasonal Effect
Seasonal Effect of Natural Gas Price in Influencing Power Price
Seasonal Component of Beta Coefficient
0.4
0.3
Summer
Winter
0.2
0.1
0.0
‐0.1
‐0.2
‐0.3
‐0.4
Source: ANR Gas prices and Indiana Hub data from NrgStream.
Bayesian DLM Model by CME Economics.
© 2011 CME Group. All rights reserved
9
MISO: Varying Effect of Natural Gas Price
Trend Line of Natural Gas Price Affecting Power Price
Trend Component of Beta Coefficient 1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Source: ANR Gas prices and Indiana Hub data from NrgStream.
Bayesian DLM Model by CME Economics.
© 2011 CME Group. All rights reserved
10
MISO: Remainder
Remainder Effect
Remainder Component of Beta Coefficient
1.0
0.8
0.6
0.4
0.2
0.0
‐0.2
‐0.4
‐0.6
‐0.8
‐1.0
Source: ANR Gas prices and Indiana Hub data from NrgStream.
Bayesian DLM Model by CME Economics.
© 2011 CME Group. All rights reserved
11
Results
Seasonal
•
Seasonal pattern shows strong summer peak and weaker winter peak.
Trend
•
Shows varying but overall increasing influence of Natural Gas price on
Power price.
•
Trend is disturbed due to financial crisis turmoil (many correlations fell
to zero in that period).
Remainder
•
Appears to be white noise - implying seasonal and trend breakdown fit
data.
•
Any large spike in remainder implies influence of different factor than
Gas price in greatly affecting Power price.
© 2011 CME Group. All rights reserved
12
Comparisons to other ISOs
ERCOT
•
ERCOT Power Houston Hun (NrgStream)
•
Houston Ship Channel Gas (Platts)
•
Data from Nov 2008 – Dec 2012
PJM
•
PJM Monthly Peak Futures Contract (DM1 Bloomberg)
•
Henry Hub Gas Futures (NG1 Bloomberg)
•
Data from May 2003 – Aug 2012
ISO NE
•
ISO NE Internal Hub Daily Average Peak Day Ahead Price (NrgStream)
•
Algonquin Daily Next Day Natural Gas Prices (Platts)
•
Data from Jan 2004 – Aug 2012
© 2011 CME Group. All rights reserved
13
ERCOT Seasonal Effect:
Strong Summer Peak
Seasonal Effect of Natural Gas Price in Influencing Power Price
Seasonal Component of Beta Coefficient
1
Summer
0.8
0.6
0.4
0.2
0
‐0.2
‐0.4
‐0.6
‐0.8
Source: Houston Ship Channel Gas prices from Platts and ERCOT Power Houston Hub from NrgStream. Bayesian DLM Model by CME Economics.
© 2011 CME Group. All rights reserved
14
PJM Seasonal Effect:
Strong Summer Peak
Seasonal Effect of Natural Gas Price in Influencing Power Price
Seasonal Component of Beta Coefficient
0.25
Summer
0.20
0.15
0.10
0.05
0.00
‐0.05
‐0.10
Spring ‐0.15
4/2003 4/2004 4/2005 4/2006 4/2007 4/2008 4/2009 4/2010 4/2011 4/2012
Source: Data from Bloomberg Professional. Bayesian DLM Model by CME Economics.
Note: Seasonal Analysis used PJM Power Futures and Henry Hub Gas Futures
© 2011 CME Group. All rights reserved
15
ISO New England Seasonal Effect:
Natural Gas Influence Heightened in Summer and Winter
2.0
Seasonal Effect of Natural Gas Price in Influencing Power Price ‐ ISO NE
Seasonal Component of Beta Coefficient
Winter
Summer
1.5
1.0
0.5
0.0
‐0.5
‐1.0
‐1.5
3/2009
9/2009
3/2010
9/2010
3/2011
9/2011
3/2012
Source: Data from Bloomberg Professional. Bayesian DLM Model by CME Economics.
© 2011 CME Group. All rights reserved
16
ERCOT: Increasing Influence of Natural Gas Price since
2008
Trend Line of Natural Gas Price Affecting Power Price
Trend Component of Beta Coefficient 2.0
1.5
1.0
0.5
0.0
‐0.5
‐1.0
Source: Data from Platts and NrgStream.
Bayesian DLM Model by CME Economics.
© 2011 CME Group. All rights reserved
17
PJM: Increasing Influence of Natural Gas Price since 2009
Trend Line of Natural Gas Price Affecting Power Price
Trend Component of Beta Coefficient
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
‐0.1
4/2003
4/2004
4/2005
4/2006
4/2007
4/2008
4/2009
4/2010
4/2011
4/2012
Source: Data from Bloomberg Professional. Bayesian DLM Model by CME Economics.
Note: Seasonal Analysis used PJM Power Futures and Henry Hub Gas Futures
© 2011 CME Group. All rights reserved
18
ISO NE: Increasing Influence of Natural Gas Price since
2005
Trend Line of Natural Gas Price Affecting Power Price
Trend Component of Beta Coefficient
0.45
0.35
0.25
0.15
0.05
‐0.05
‐0.15
Source: Data from Platts and NRG Stream. Bayesian DLM Model by CME Economics.
© 2011 CME Group. All rights reserved
19
ERCOT Remainder Component:
Remainder Component of Beta Coefficient
2.0
Remainder Effect
1.0
0.0
‐1.0
‐2.0
Source: Data from Platts and NrgStream.
Bayesian DLM Model by CME Economics.
© 2011 CME Group. All rights reserved
20
Comparison among ISOs
Seasonal
•
Seasonal pattern is distinct to each ISO:
• ERCOT exhibits a strong seasonal peak for summer.
• MISO and ISO NE exhibits seasonal peaks for Winter AND Summer.
• PJM exhibits slight seasonal summer peak.
Trend
•
ISO NE and PJM show an increasing influence of Natural Gas price on
Power price starting in 2005.
•
MISO and PJM shows the effect of the financial panic in 2008, causing
correlations to move temporarily to zero – ISO NE and ERCOT do not.
Remainder
•
ISO NE: Remainder is generally white noise, but with large spikes.
•
PJM: Remainder is purely white noise.
© 2011 CME Group. All rights reserved
21
Next Steps
ISO
•
Analyze additional ISOs.
Addressing Other Fuel Sources
•
Coal
•
Method to capture impact of Wind? (Relevant to MISO)
Level of Review
•
Analysis addressed most visible price relationship in ISO
•
Potential sub-regions within ISOs
• Most relevant sub-regions?
© 2011 CME Group. All rights reserved
22
Appendix
Bayesian Statistics and Model Equations
Frequentist vs. Bayesian Statistics
Key Difference: The way “Uncertainty” is treated
Frequentist:
Uncertainty about quantities or parameters
estimated is captured by looking at how estimates
would change in repeated sampling from the
same population (or data set).
Bayesian:
Uncertainty is addressed by updating prior
opinions about quantities and parameters
estimated as NEW data is observed.
© 2011 CME Group. All rights reserved
24
Bayesian Statistics
Bayes’ Theorem
© 2011 CME Group. All rights reserved
25
Bayesian Analysis
PRIOR x LIKELIHOOD  POSTERIOR
• Prior – Initial probability distribution of parameters
• Likelihood – Joint probability of observing the data
given the parameters estimated
• Posterior - Probability of parameters given the data
• The process of moving from Prior to Posterior is
called Bayesian Learning
© 2011 CME Group. All rights reserved
26
Model General
The DLM is a two equation system estimated as:
Estimation Equation
Yt=(Ft)’ βt + vt
•
vt ~ N[0,Vt]
Where F are the explanatory factors and β are the Beta
parameter estimates
State Equation
βt =Gt βt-1 + wt
•
wt ~N[0,Wt]
Governs the path of Beta Estimates changing over time
© 2011 CME Group. All rights reserved
27
Model – MISO Analysis
Estimation Equation
1.
Powert= β0t * Constant + β1t * Natural_Gast + et
• β is a vector of the estimated Beta coefficients
et is the error term
•
State Equation
2.
βt =Gt βt-1 + gt
•
Estimated beta coefficients may change over time as
allowed by the State Equation
•
gt is the error term
© 2011 CME Group. All rights reserved
28
DLM Code
Part I – Initial Information
• Set mean and variance of the Prior Distribution for
Period 0, this information acts as starting values for
model.
Part II – Create Placeholders
• Create “placeholder” vectors and matrices for all the
components of the function. The placeholders are
filled in as the function runs and repeats the steps for
each time period.
© 2011 CME Group. All rights reserved
29
DLM Code II
Part III –Loop
• Loop repeats the steps of the function for every time
period
Steps
1. Posterior at t-1 (βt-1|Dt-1)~N[mt-1,Ct-1]
2. Prior at t (βt|Dt-1)~N[at,Rt]
3. Next-step ahead forecast (Yt|Dt-1)~N[ft,Qt]
4. Posterior at t (βt|Dt)~N[mt,Ct]
© 2011 CME Group. All rights reserved
30
DLM Code III
• Steps 1 - 4 of the loop update the Distribution of
parameters, hence the 2 moments which
characterize each Normal distribution are
calculated and updated.
• The Mean and Standard Deviation estimate from
the Posterior distribution at time t are used as the
final output of Beta coefficients and Standard
Errors of the model.
© 2011 CME Group. All rights reserved
31
Other Applications
• Federal Reserve Policy
• Dynamic Volatility Estimation
• Natural Gas Price and Power Price
• Brazilian GDP Forecasting
• FX Models
© 2011 CME Group. All rights reserved
32
Observing the Changing Relationship
Between Natural Gas Prices and Power
Prices
The research views expressed herein are those of the author and do
not necessarily represent the views of the CME Group or its affiliates.
All examples in this presentation are hypothetical interpretations of
situations and are used for explanation purposes only.
This report and the information herein should not be considered
investment advice or the results of actual market experience.
Samantha Azzarello
Economist, CME Group
April 2013