The determinants of regime switching in the natural gas and crude oil cointegrating relationship

Matthew Brigida

In this analysis, we attempt to find the determinants of regime switching in the natural gas and crude oil cointegrating equation. Earlier research has found evidence for cointegration in the long-term relative pricing relationship between natural gas and crude oil prices (Bachmeier and Griffin 2006; Brown and Yücel 2008; Hartley et al 2008; Ramberg and Parsons 2012; Serletis and Herbert 1999; Villar and Joutz 2006). Many of these analyses, however, note that the cointegrating relationship likely exhibits structural breaks.

Further compelling evidence for structural breaks in the relationship was found by Brigida (2014a). This analysis found evidence for Markov regime switching in the cointegrating relationship. In Brigida (2014a), however, the regime-switching process was a first-order Markov process with constant transition probabilities. This means the transition probabilities are the same over the entire sample period, and they are unaffected by economic and other conditions. In this analysis, we will allow the transition probabilities in the first-order Markov process to be a function of exogenous variables. By doing so, we hope to find the determinants of the endogenous regime-switching process underlying the cointegrating relationship between natural gas and crude oil.

Moreover, since this and previous analyses have considered the cointegrating relationship over long time periods, it is an unlikely assumption that the transition probabilities in the Markov process have remained constant. For example, since natural gas price increases are driven by winter weather, but crude oil price increases are not, it is likely that temperature affects the state of the cointegrating relationship.

In our search for the determinants of regime switching, we will consider factors measuring natural gas and crude oil storage, temperature, fuel demand and macroeconomic variables. We will also investigate whether regime switching is, in fact, a part of the overall relationship between natural gas and oil, or if past regime switches were driven by the unique circumstances surrounding the rise, market power and fall of Enron.

2 Methods

In this section, we will discuss the empirical model, estimation technique and data used in this analysis. The model is an extension of the Hamilton (1989) case of constant transition probabilities. The extension was made by Diebold et al (1994) and Filardo (1994), who both assumed that the probability of switching may depend on a set of underlying economic fundamentals.

2.1 The two-state Markov regime-switching cointegrating equation with time-varying transition probabilities

Let $X_{t-1}$ be a stationary vector of variables that affect the likelihood of switches between regimes. The cointegrating equation with first-order, two-state, endogenous Markov-switching parameters with time-varying transition probabilities may be written as

$\displaystyle P_{\mathrm{HH}}$	$\displaystyle=\beta_{0,S_{t}}+\beta_{1,S_{t}}P_{\mathrm{WTI}}+e_{t},\quad e_{t% }\sim N(0,\sigma^{2}_{S_{t}}),$	(2.1)
$\displaystyle p_{ij,t}$	$\displaystyle=P(S_{t}=j\|S_{t-1}=i,X_{t-1})=\frac{\exp(\phi_{ij,0}+X^{\prime}_{% t-1}\phi_{ij,1})}{1+\exp(\phi_{ij,0}+X^{\prime}_{t-1}\phi_{ij,1})}\quad\text{% for~{}all~{}}i,j\in 1,2\text{~{}and~{}}\sum_{j=1}^{2}p_{ij}=1,$	(2.2)
$\displaystyle\beta_{0,S_{t}}$	$\displaystyle=\beta_{0,1}S_{1t}+\beta_{0,2}S_{2t},$	(2.3)
$\displaystyle\beta_{1,S_{t}}$	$\displaystyle=\beta_{1,1}S_{1t}+\beta_{1,2}S_{2t},$	(2.4)
$\displaystyle\sigma_{0,S_{t}}$	$\displaystyle=\sigma_{0,1}S_{1t}+\sigma_{0,2}S_{2t},$	(2.5)

where, for $m\in 1,2$ , if $S_{t}=m$ , then $S_{mt}=1$ , and $S_{mt}=0$ otherwise. The model is estimated by maximum likelihood, and state probabilities are calculated using the Hamilton filter.

2.2 Data

Crude oil and natural gas prices are continuous front-month New York Mercantile Exchange (NYMEX) futures prices. Crude oil (NYMEX ticker: CL) is for West Texas Intermediate crude oil deliverable in Cushing, OK. For robustness, we also use continuous front-month Intercontinental Exchange (ICE) Brent crude oil futures (ICE ticker: B). Brent crude oil is deliverable to Sullom Voe Terminal in the European North Sea. Natural gas (NYMEX ticker: NG) is deliverable to the Henry Hub in Louisiana. We fail to reject the null hypothesis of a unit root in all price series. Further, in testing for cointegration between crude oil and natural gas series, we are unable to reject the null of a unit root in the residuals of a regression of the log of natural gas on the log of crude oil. We conclude, similar to Brigida (2014a) and Ramberg and Parsons (2012), that the series are not cointegrated.

Note that in crude oil markets the front-month futures contract is often used as a proxy for the spot price. This is because pipeline nominations are made at the end of each month, for the following month. Nominations are where you schedule your crude oil’s passage through the pipeline network. So, given the time it takes to arrange shipment, spot transactions are effectively for delivery next month. The front-month futures contract, therefore, is nearly identical to the spot price, with the benefit of more accurate reporting.

The data used to explain regime switching is of four main types: storage, weather, macroeconomic and Enron indicator. All variables concern data from the United States. Storage variables represent supply for natural gas and crude oil. Weather variables mainly proxy for natural gas demand. Utilities will demand more natural gas as temperatures reach extremes (ie, colder in winter and hotter in summer). Macroeconomic variables are included because of the potential interplay between these variables and demand for crude oil and crude oil prices (Hamilton 1983). Last, we include an indicator for the six-month period in which Enron filed for bankruptcy. We reject a unit root in all explanatory variables at the 5% level of significance. A summary of the variables is given in Table 1.

Storage, heat rate and price data are gathered from the Application Programming Interface of the Energy Information Administration (part of the US Department of Energy), using the EIAdata (Brigida 2014b) wrapper for the R programming language. Temperature data is from the US National Weather Service’s Climate Prediction Center.¹¹URL: www.cpc.ncep.noaa.gov/products/analysis_monitoring/cdus/degree_days/. Macroeconomic variables are from the St Louis Federal Reserve Bank’s database.

Table 1: Summary of variables, by category, used to explain regime switching in the natural gas and crude oil cointegrating relationship. [HDD denotes heating degree day. CDD denotes cooling degree day.]

Storage

Working natural gas (lower 48): log difference from five-year average

Working natural gas (lower 48): log difference from two-year average

Ending stocks of crude oil, Cushing, OK: log difference from five-year average

Ending stocks of crude oil, Cushing, OK: log difference from two-year average

Temperature

HDD log deviation from norm

CDD log deviation from norm

Macroeconomic

Log differences in the broad trade-weighted US dollar index

Unexpected changes in three-month t-bill yield

Unexpected changes in ten-year t-note yield

Log difference of ten-year and three-month treasuries

Unexpected changes in thirty-year AAA-rated corporate debt yields

Unexpected changes in thirty-year ABB-rated corporate debt yields

Log difference in unemployment from two-year average

Log difference of the amount of commercial loans and leases from two-year average

Other

Enron indicator

First-difference of the relative heat rate of natural gas to oil (

\text{ln}(\mathrm{HR}_{\text{ng}}/\mathrm{HR}_{\text{oil}})

)

Percent changes in relative heat rate

2.3 Sampling frequency

We report results from weekly sampled data. Our main variables (natural gas storage and degree days) are released with a weekly frequency. However, because natural gas storage is released on Thursday, natural gas and crude oil prices are as of close of trading on Friday and degree days include the entire week, we have also repeated this analysis at the monthly frequency to ensure our results are robust to the influence of nonsynchronous data releases. The results at the monthly frequency are the same, and these are available upon request.

3 Results

First, we tested the regime-weighted residuals of our Markov regime-switching cointegrating equation, and we were able to reject the null hypothesis of a unit root (at the 5% level of significance). Therefore, like Brigida (2014a), we conclude that crude oil and natural gas are cointegrated once one controls for the effect of regime switching. Our filtered state probabilities (Figures 1 and 2) also coincide with the state probabilities estimated in Brigida (2014a).

The main results of the analysis are shown in Tables 2 and 3. Table 2 shows results without including the Enron indicator. In this case, deviation in heating degree day (HDD) from the norm significantly affects the transition probabilities, though our natural gas storage variable does not.

However, when including the Enron indicator, we see in Table 3 that the natural gas and storage variables are significant, and HDD deviations are insignificant (albeit with a $p$ -value of 0.1029).

We can consider the model in Table 2 to be a constrained version of the model in Table 3 (with the constraint being that the Enron (ENRN) coefficient is set to 0). Conducting a likelihood ratio test, we conclude that the unrestricted model is superior (with a $p$ -value less than $0.1\%$ ).

The macroeconomic variables were all insignificant. This result is consistent with Du et al (2010), who found evidence that oil prices affected macroeconomic variables in China, though macroeconomic variables did not affect oil prices.

Table 2: Parameter estimates of

P_{\text{HH}}=\beta_{0,S_{t}}+\beta_{\text{1},S_{t}}P_{\text{WTI}}+e_{S_{t}}

, where

S_{t}\in\{\text{1},\text{2}\}

, and the transition probabilities are time-varying functions of the deviation of the amount of working gas in storage from its five-year average (NG STOR) and the HDD percent deviation from its long-term norm (HDD DEV). [Data is sampled weekly and ranges from January 1, 1999 to June 20, 2014. The

p

-values are below the coefficients in parentheses. *, ** and *** denote significance at the 10%, 5% and 1% levels, respectively.]

(a) Cointegrating equation

	$S_{\textbf{1}}$	$S_{\textbf{2}}$
$\beta_{\text{0}}$	0.0978	$-$ 0.2547
	(0.1474)	(0.0173)**
$\beta_{\text{1}}$	0.2702	0.5308
	(0.0000)***	(0.0000)***
$\sigma$	0.1999	0.2077
	(0.0000)***	(0.0000)***

(b) Transition probabilities

	$S_{\textbf{1}}$	$S_{\textbf{2}}$
Intercept	$-$ 1.4360	$-$ 2.2829
	(0.0000)***	(0.0000)***
HDD DEV	2.5032
	(0.0027)***
NG STOR	$-$ 0.6330
	(0.2304)
Max loglikelihood	49.0685

Table 3: Parameter estimates of

P_{\text{HH}}=\beta_{0,S_{t}}+\beta_{\text{1},S_{t}}P_{\text{WTI}}+e_{S_{t}}

, where

S_{t}\in\{\text{1},\text{2}\}

, and the transition probabilities are time-varying functions of the deviation of the amount of working gas in storage from its five-year average (NG STOR), the HDD percent deviation from its long-term norm (HDD DEV) and an indicator for the collapse of Enron (ENRN). [Data is sampled weekly and ranges from January 1, 1999 to June 20, 2014. The

p

-values are below the coefficients in parentheses. *, ** and *** denote significance at the 10%, 5% and 1% levels, respectively.]

(a) Cointegrating equation

	$S_{\textbf{1}}$	$S_{\textbf{2}}$
$\beta_{\text{0}}$	0.1269	$-$ 0.2590
	(0.3344)	(0.0024)***
$\beta_{\text{1}}$	0.3254	0.5485
	(0.0000)***	(0.0000)***
$\sigma$	0.4430	0.0843
	(0.0000)***	(0.0000)***

(b) Transition probabilities

	$S_{\textbf{1}}$	$S_{\textbf{2}}$
Intercept	$-$ 0.9534	$-$ 0.2775
	(0.0000)***	(0.0496)**
HDD DEV	0.2825
	(0.1029)
NG STOR	0.8694
	(0.0196)**
ENRN	0.6805
	(0.0114)**
Max loglikelihood	238.4117

Figure 1: (a) Filtered probability of being in state 2. Filtered probability of being in state 2 when estimating the cointegrating equation $P_{\text{HH}}=\beta_{\text{0},S_{t}}+\beta_{\text{1},S_{t}}P_{\text{WTI}}+e_{S% _{t}}$ , where $S_{t}\in\{\text{1},\text{2}\}$ , and the transition probabilities are time-varying functions of the deviation of the amount of working gas in storage from its two-year average (NG STOR) and the HDD percent deviation from its long-term norm (HDD DEV). Data is sampled weekly and ranges from January 1, 1999 to June 20, 2014.

Hartley and Medlock (2014) found evidence that the value of the US dollar affects the natural gas and crude oil cointegrating relationship. We estimated the model including changes in the US dollar (as measured by the nominal broad trade-weighted US dollar index, available from the Federal Reserve Board of Governors).²²The time series is available from the St Louis Federal Reserve’s economic database (FRED) here: https://research.stlouisfed.org/fred2/data/TWEXB.txt. We found no evidence that the value of the US dollar determines regime changes in the cointegrating relationship. The results are summarized in a table in the online appendix.

Last, we estimated whether the first-difference in the relative heat rate of natural gas to oil (defined as $\ln(\mathrm{HR}_{\text{ng}}/\mathrm{HR}_{\text{oil}})$ ) affects regime switching in the cointegrating relationship. Since heat rate data is only available for the years 2001 through 2013, we estimated the model on this subsample. From the resulting estimates, we conclude that neither variable affects the state of the cointegrating relationship. These results are available from the author upon request.

4 Discussion

The results are evidence that regime switching in the natural gas and crude oil price cointegrating process is not driven by the macroeconomy. That is, overall demand for energy and currency effects do not cause shifts in the cointegrating relationship.

Further, our measure of the efficiency of natural gas-fired electricity generation relative to heating oil generation has no effect on the cointegrating relationship. This may reflect that small changes in the relative efficiency will not affect the substantial efficiency advantage of natural gas generation.

Ultimately, we find that the cointegrating process is largely a function of factors specific to energy markets and, in particular, factors affecting supply and demand for natural gas. For instance, when natural gas in storage has a negative deviation from its five-year average, the cointegrating relationship is more likely to switch to a state in which natural gas is less sensitive to crude oil prices (state 1). This is consistent with natural gas being more driven by factors in its own market when supplies are relatively low. Similarly, during the collapse of Enron, natural gas was less sensitive to crude oil prices. That natural gas is less sensitive to crude oil prices can be seen in both the smaller slope coefficient and the much larger standard deviation of the error term in state 1.

5 Conclusions and policy implications

This analysis has found evidence for the importance of the amount of natural gas in storage in the relationship between gas and oil prices. When the amount of gas in storage is lower than its five-year average, this causes gas prices to be somewhat less sensitive to oil prices. Conversely, if there are ample natural gas supplies, there will be a closer relationship between gas and oil prices. To the extent that a closer relationship allows easier relative natural gas pricing for producers and consumers, it may make sense for policy to encourage ample natural gas supplies.

This analysis has also shown that the collapse of Enron was a significant determinant of the relationship between natural gas and crude oil prices. The collapse caused a shift to a regime in which natural gas prices are less sensitive and also underperform relative to crude oil prices. The introduction of policies that do not allow such a dominant participant in an energy market would lessen this effect. Further, policies aimed at lowering financing costs for competing firms during such a collapse may also mitigate this effect on energy market prices.

Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

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