OIL PRICE VOLATILITY MAY BE A CONTRIBUTING FACTOR IN RISING POLITICAL PARTISANSHIP IN THE UNITED STATES
by Tom Therramus 14 November 2010 (firstname.lastname@example.org)
Politics in the United States (US) has always been a hard-fought, as well as sometimes nasty business. This being said, the degree of electoral volatility and political partisanship have notably increased in the US over the last few years.
In this essay, it will be shown that the changeable moods and preferences of American voters may be increasingly influenced by rising oil market instability i.e., sharp increases or decreases in price occurring over relatively short time scales.
In what follows, data will be provided showing that from the mid-2000s onwards swings in polls measuring Presidential approval, Congressional approval and whether voters believe that the Direction of the Country is on the "right track" or the "wrong track" have begun to demonstrate an unusual level of entrainment with spikes in volatility in the price of oil.
This increasing correlation between changeability in oil price and subsequent movements in polling trends is relatively new. In the years prior to 2004, no such relationship was readily discernible.
Since the mid-2000s, more than half a dozen spikes in oil price volatility have occurred, each followed by a variance spike in political polls some 6 months later. The observed relationships are in line with jolts in oil price sparking downstream swings in the potential behavior of voters.
The strongest evidence for the relationship comes from Fourier Transform analysis of volatility trends between 2005 and 2010. During this time period, variance in oil price, Presidential approval and Direction of the Country shared the same rhythm in which spikes recurred at a dominant period of 32 months.
Auspiciously, a sharp rise and fall in oil price in the spring of 2011 conformed precisely to the schedule predicted by the Fourier analysis of the preceding decade. This new price spike in 2011 topped out ~$115 a barrel, exactly 32 months after the oil shock of mid-2008 reach its peak of ~$140.
According to the US Department of Energy, the global rate of oil production plateaued in 2005, indicating that the world may be at or approaching Peak-Oil. An autonomous pattern of repeating spikes in oil price variance would be an anticipated consequence of the teetering balance between supply and demand at Peak-Oil.
The initiation of the alignment between instabilities in oil price and polling trends corresponds to the aforementioned 2005 plateau in global in oil production. It is thus hypothesized that destabilization of oil markets resulting from geoplanetary limits to supply may be a factor in:
1. The increasing partisan animosity between Democrats and Republicans,
2. The splintering and destabilization of established political parties e.g., the Tea Party vs other parts of the longstanding Republican coalition
3. The increasingly unsettled moods and preferences of American voters.
The politically destabilizing effects of cycling volatility in global oil markets is probably not confined to the US. Recurring instabilities in the price of oil may be a shared instigating factor in other notable political disruptions that have occurred in other parts of the world in recent years - the "Arab Spring" being one example. ________________________________________________________________________________________
PUBLISHED ARTICLES BASED ON THIS WIKI
In late 2008 I began writing on whether the financial crisis of that year may have had an explanation rooted in instabilities in the oil markets.   At the core these articles was the identification of a distinctive, near decade-long signature in oil price volatility preceding the financial crisis. As shown in Figure 1 this distinct pattern initiated in the early 2000s and comprised a series of spikes in price variance. The largest of these spikes occurred in 2008 when oil jolted upwards to nearly $140 a barrel, before rapidly falling back to under $50 a barrel.
The signature of increasing oil price volatility that initiated after 2000 (i.e., Figure 1) was proposed to have acted as a portent of rising economic uncertainty for the financial markets. A long term signal of increased investment risk that pushed the industry into herding behaviors culminating in the expansion, looting and eventual collapse of the shadow banking system.
Conventional wisdom has settled on the US housing bubble and Wall street being at the root of the financial crisis. However, I made the case that these may have been secondary manifestations of precariousness in the investment environment. This increased investment risk was suggested to be ultimately traceable back to the aforementioned long term rise in oil market instability.
Before going further something important needs to be emphasized. When phrases such as oil price volatility, variance or instability are used, not just sharp increases in oil price are being invoked. The effect of rapid declines in price also have to be considered. Thus, the rapid fall in gas prices to below $2.50 a gallon that occurred in February 2009 impacted price volatility just as certainly as its ascent to over $4.00 had some six months earlier. The point being that increased uncertainty about the future cost of energy resulting from rapid price changes profoundly destablizes the investment environment irrespective of the direction of the price change.
My previous work focused on the economic fallout of financial markets intuiting that Peak Oil was imminent from the increasing bumpiness of oil prices. However, I subsequently became curious as to whether politics might also be responding to the observed increased variance in the price oil that began after the turn of the new millenium. This idea is explored in the following essay.
Measuring Changeability in the Moods and Preferences of the US Electorate
An Alternate Way of Thinking About President Bush's "Cross-Over" in Popularity
The taking of political polls is a frequent habit of the American news media. As is the case with most things that the media does the focus is on the immediate - the results of a given poll for a given day. The gratification of the 24 hours news cycle usually gives short shrift to the interpretation of longer term trends. Nonetheless, this fixation on polling has conveniently generated vasts amounts of highly granular data on the American voter that spans many years.
Figure 2 provides an example of one of these long stretches of data. Here, Presidential job approval trends are shown over a ten year period that includes the tenure of both Presidents Bush and Obama. The monthly averages from 2000 to 2010 are based on data from multiple polling organizations that are archived at RealClearPolitics.com. 
A distinctive feature of figure 2 is the "cross-over" (marked by a black arrow) between "approval" (blue trend) and "disapproval" (red trend) in the center of the figure. This "cross-over" occurred between 2005 and 2006 during the tenure of President Bush.
Most readers would view the "cross-over" on Figure 2 as a product of the then growing voter dissatisfaction with President Bush. Certainly, mounting negativity toward President Bush must have been a big factor in him tipping from net approval to disapproval in 2005. But can we be sure that this was the only thing going on ?
This essay probes the case for an alternate explanation of patterns in political polling data in the US over the last five to ten years - including Presidential approval. Namely, that the fluctuating preferences of the US electorate has increasingly become a function of growing instability in oil pricing.
First, there are some considerations that should be outlined. According to the United States Department of Energy, global oil production reached an all time peak in 2005.  Production has remained stuck on a plateau since 2005. As a consequence many experts consider that this mid-decadal peak is close to the highest rate of production that oil will ever reach i.e., Peak-Oil.
Further support that Peak Oil may be at hand or already in the rear view mirror comes from leaked diplomatic cables published by the Guardian Newspaper concerning Saudi Arabia, the world's largest oil producer.  Among these official communiques the US Consul General gives a disturbing account of a conversation with Sadad al-Husseini, the geologist who formerly headed exploration at Aramco, the Saudi state oil company. Based on his unique access to the data, al-Husseini's assessment was that Saudi oil reserves may be over estimated by as much as 40 %.
More troubling still, these official cables, which were dated somewhere between 2007 and 2009, indicated that Saudi production would shortly move past recovery of 50 % of original proven reserves. Putting this another way, Saudi Arabia would soon reach the highest possible rate at which it could pump oil i.e., Peak Oil.
The second consideration key to the hypothesis is embodied in the volatility signature illustrated in Figure 1. Variation of this type is an expected by-product of the teetering balance between demand and supply for a finite resource once its availability begins to level off or decline.
Large changes in price of a non-renewable such as oil occur as part of a "baked-in" process after the most easily tapped reservoirs of that resource have been exploited. With maxed-out mega-producers such as Saudi Arabia unable to pick up production, demand exceeds supply and volatility ensues.
The phenomena that a sought-after, but declining resource will be subject to whipsaw changes in price (or supply) is predicted by theoretical models and has been observed in numerous real world studies of commodities other than oil.
Scarcity drove large fluctuations in the price of whale bone in the 19th century as baleen whales were harpooned to near extinction . A related story accompanied production declines in whale oil during the same historical period. In a more recent example, Atlantic cod numbers landed off New England have shown striking surges and falls over time in response to overfishing. 
Drawing on Chaos theory mathematics, Jeff Vail has pointed out that the potential for dramatic bumps up and down in oil price with dwindling supply following Peak-oil has parallels to boom-bust cycles in predator-prey numbers in the wild. 
While accepting the "bumpy plateau" for pricing at Peak-Oil as a theoretical possibility, a number of knowledgeable folk would argue that increasing variance in the price of oil is actually a product of financialization of the markets over the last decade.  This is a satisfying explanation for many people as it puts the blame for energy price volatility on speculators, including the dastardly Goldman Sachs et al.
The amoral greed of the financial industry has appalled good people everywhere. However, it should be borne in mind that the factors determining the global supply of energy operate on planetary-geological scales that vastly outweigh even mighty Wall Street. The need to identify a villain has led us astray in the past and now again may be blinding us to recognizing a painful truth.
...And what is that painful truth as it pertains to the present instability of US politics. The evidence that will be laid out in this essay suggests that the increasing unpredictability, and indeed nastiness of our politics, may be being driven by impersonal geophysical factors associated with the onset of Peak Oil.
The Usefulness of "Spread" between Approval and Disapproval as a Measurement Tool
A device used to simplify two-part polling questions such as whether a potential voter "approves" or "disapproves" of the President is to subtract one trend from the other to obtain the "spread" between the two questions. This "spread" (black trend) between "approval" and disapproval is given in the lower panel of Figure 2.
There are advantages of using "spread" of trends in pollee sentiment as opposed to the "approval" and/or "dissapproval" numbers alone. "Spread" simplifies representation of the data. When "spread" is above zero (as indicated by the blue fill on the lower panel of Figure 2) the sitting President is generally in positive territory in the opinion of those polled. When "spread" falls below zero, a majority of those polled have a negative view. An appropro example of this is the aforementioned 2005 "cross-over" of President Bush when the "spread" trend penetrated the Y-axis zero line.
"Spread" is also advantageous in that it combines two responses into a single number. Moreover, this single index better incorporates useful aspects of the poll than "approval" or disapproval" do alone. For example, "spread" embodies within its trend contributions from those polled who are "not sure" and those who "have not heard of" the President.
Yes, even late into his 8 years of incumbency, an alarming one to two percent of American voters polled claimed that they had not heard of President Bush.
A Broad Snapshot of Electoral Sentiment in Three Distinct Polls
Presidential approval rating is one of the more important gauges of the mood of the American Electorate. Two other key political measurements are the "Approval or Disapproval of the US Congress" and the so-called "Direction of the Country". In the latter case, pollees are asked whether they think that the US is on the "right track or direction" or "the wrong track". As is the case for "Presidential approval", the two-part nature of the "congressional approval/disapproval" and the "right track/wrong track" questions enable spreads to be calculated.
Figure 3 consolidates representations of the monthly average of spreads from polls of "Presidential approval", "Congressional approval" and "Direction of the country" archived at the RealClearPolitics.com and PollingReport.com websites.
The alchemy of American Politics is reflected in fascinating ways by Figure 3. Presidential approval ratings are undoubtedly influenced by identification with or against the politician in question. However, a notable aspect of "Congressional" and "Direction" polls is that they address more abstract questions, being less grounded in personalities.
The congress is obviously made up of individual politicians. But it is likely that congressional approval ratings are more guided by the response to congress as an institution, as opposed to the individuals that comprise it. Indeed, it is often observed that voters tend to be more satisfied with their own local congressional representatives, than with the congress as a whole.
The "Direction of the Country" represents an even farther abstraction. It attempts to get at voter dissatisfaction at a visceral level - no doubt sometimes reflecting the worst of our insecurities and prejudices. "Direction of the country" is thus one of the more interesting polls sampled from the electorate. It is personal, stripped down and probably one of the more honest polls of voter sentiment. The "Direction" poll seems to be less susceptible to being confounded by empathy, sympathy or the demonization of individual politicians.
General observations on Figure 3 include that "Presidential", "Congressional" and "Direction" all climb to a peak in early 2003 corresponding to the aftermath of the 911 terrorist attacks. From here, the three plots undergo bumpy downward trends through to 2008. The "Congressional" and "Direction" spreads cross from positive into negative territory earlier than the "Presidential plot and also go more deeply negative.
There is a bounce in the popularity of the President in late 2008, with the election of Mr Obama. Similarly timed upswings coinciding with Mr Obama's election occur in the "Congressional" and "Direction" polls. However, neither of the lines goes positive in 2008/2009 and their curve dynamics tend to lag the sharp upstroke in the "Presidential" approval spread associated with Obama's election.
The plots of the three different "spread" indices show strongly related patterns over time - they are all essentially icebergs of very similar shape with more or less of their trends poking above a water-line marked by the Y axis zero. The President is somewhat more buoyant, but the mass of "Congress" and the "Direction of Country" trends are mostly sunken wrecks, in opinion of most of those polled.
Charting Relationships between Instability in Oil Markets and US Political Indexes
The "cross-over" of the "Congressional" and "Direction" trends into negative territory precedes the start of the 2005 oil production plateau, so in this respect they differ from the Presidential approval trend. However, as was just discussed, apart from where the poll lines cut the Y-axis, the general "gestalt" of the three plots over time is remarkably similar.
The next phase of the analysis goes into rhythms hidden within the "bergs and cols" of the three political polls - i.e., their respective volatility. Within this cryptic domain of trend variation much can be learned.
Cutting to the chase, it will be shown that the similarities do not end with the common "gestalt" of the 3 plots illustrated in Figure 3. Volatility of Presidential approval and "Direction" polls appear to share related patterns. These correlated patterns in turn appear to be entrained with the rhythm of the oil volatility signature illustrated in Figure 1.
Mr President, Ups and Downs in Your Popularity May be Partly Determined by Changes in Oil Price
Volatility in "Presidential approval/disapproval" spread was calculated from 2000 to 2010 using a method that has been described previously in my essay on oil price volatility and investment risk (reference 2). In brief, a rolling three month average was estimated from the "Presidential" spread data (Figure 4 - top panel). From this sequence, a rolling bi-monthly standard deviation was derived to generate the plot illustrated in the bottom panel of Figure 4.
It is important to note that while the equation for standard deviation was utilized to generate an index of volatility, this equation was not put to use for traditional statistical reasons. Standard deviation was employed to provide a "positive definitive" measure of changeability in "Presidential" spread month-to-month over time. For those interested, a discussion of the approach to estimating volatility, including remarks from professional statisticians and other numerati can be found at the "Oil Drum". 
In figure 5 variance in oil price (red line) and Presidential approval/disapproval (blue line) are plotted together. The spikes comprising the price volatility signature from figure 1 are identified by seven red arrows on the chart. Figure 1 was generated early in March 2009. Figure 5 now incorporates new oil price volatility data stretching into 2010.
There is a general similarity between the patterns revealed by the overlapping red and blue plots on Figure 5. One parallel that stands out is the coincidence between the spike in oil price in 2008 and the surge in Presidential popularity accompanying the election of Mr Obama.
To further assist with the comparison of the red and blue lines, spikes in volatility of the Presidential index have been identified (subjectively by me) on figure 5 by blue arrows located just below the red (oil) arrows. Comparing the location of the blue and red arrows shown, a limited, but not overly strong correlation between the timing of spikes in the oil and Presidential indices is seen.
However, this limited apparent correlation over time is not unexpected. The hypothesis proposes that changes in the preference of US voters will not be coincident with, but should occur downstream of volatility spikes in oil price.
Spikes in Fluidity of Presidential Popularity Align with Upstream Spikes in Oil Price Volatility
In Figure 6 the downstream alignment is examined. Here, the oil price index is moved ahead a number of months in order to examine how spikes in oil price volatility match up with prospective changes in Presidential approval ratings occurring half a year later.
The alignment, carried out based on eyeball-based judgment, suggested a best-fit between spikes on the two plots that occurred at around 5 to 6 months. As it turns out this, this subjectively optimized phase-shift was not too far off an alignment indicated by an objective method that will be described subsequently.
With the 6 month phase-shift in the oil plot, the trends of the red and blue lines in Figure 6 again suggest a general relationship between the oil and Presidential measurements. However, a notably stronger co-localization between the red and blue arrows marking volatility spikes is now evident. In particular, each of the seven spikes in the volatility signature in Figure 1 show reasonable alignment with matching upward pulses in changeability of the Presidential approval/disapproval spread.
There are caveats. That "Presidential" approval and oil price share alignment between multiple surges in volatility is provocative. It goes beyond arguments based on the monumental year of 2008 and general similarity of spiking frequency in Figures 5 and 6. Nonetheless, the spiking over time of the Presidential index, excepting 2008, is of modest amplitude.
Also, there is one period in which the correlation between the oil and Presidential plots is unremarkable. Prior to 2005 there appears to be lower correlations between the trends traced by the red and blue lines. It is only after 2004 that volatility in the price of oil appears to become predictive of changes in pollee satisfaction with the performance of the sitting Commander-in-Chief.
This feature of the chart will be returned to subsequently in the essay. But to give the heads-up on where this is going, the mid-decadal onset of this change in the correlation coincides with the timing of the Bush "cross-over" and marks the 2005 onset of the plateau in global oil production.
Spikes in Volatility of Congressional Approval and "Direction of the Country" Show Good Alignments with Upstream Spikes in Oil Price Volatility
The next step in the analysis is taken in Figure 7. Here, the volatility trends for "Congressional approval" and "Direction of the country" are plotted with that of oil - again, with the oil volatility plot phase shifted forward 6 months with respect to the political indices.
To my eyes, the level of agreement between these two polling indices and the oil plot was more persuasive than that shown in Figure 6 for Presidential approval. The confluence of red and blue lines on Figure 7 were frequently matched "bump-by-bump". The data suggested that the rhythms political life in the US were becoming entrained to movements in energy pricing. Nearly every spike in changeability in both the "Congressional" and "Direction" indices was preceded by a major peak in oil price volatility.
Moreover, unlike the "Presidential" volatility plot, the height or amplitude of "spikes" in the other two polls were relatively even over time. In other words, the correlations of the "Congressional" and "Direction" indices with oil price volatility could not as easily be discounted on the basis of the unusual events of 2008.
Objectively Measuring Spikes, Spike Patterns and their Relationships
The relationships between the oil price and the variables measured from US political polls appeared to be so strong that I wondered if I was fooling myself. Re-checking data confirmed that the numbers were in order. Nonetheless, I decided that a more objective approach was required to probe the relationship between oil price and political instability. To do this analysis the problem was divided up into three tasks as follows.
First, an approach was developed to objectively identify a volatility spike from the 2000 to 2010 data series.
Second an approach to determining a "best-fit" between patterns of spiking variability in oil price and polling data was devised.
Third, a method of testing whether the relationships were real and meaningful was developed.
At this point I am going to apologize for what is about to come. Unfortunately, a certain amount of excruciating detail is required. If it is any consolation this math does not come easily to me either. In fact, friends helped with some of the more specialized calculations.
What are Volatility Spikes
The magnitude or threshold at which an oil price shock becomes sufficient to trigger downstream effects on the economy or our politics is an important aspect of the hypothesis. Not all up-ticks in variance may have the required oomph.
The issue of volatility spike definition goes beyond mathematical abstraction. Spikes appear to be unitary phenomena that emerge autonomously above the background variance, in some respects appearing to take on a life of their own.
One way I draw a mental picture of a spike comes from my background in biology. Spikes resemble the electrical impulses that propagate along nerves or stimulate the heart to contract.
The bioelectricity found in neural tissues and the heart are spontaneous, self-organizing phenomena. Electrical instabilities in cell membranes that reach a critical threshold and then surge outward in waves to power our thoughts, actions and beating hearts.
To continue the analogy, as with a nerve impulse that sparks a muscle contraction, the assumed cause and effect linkage between oil shocks and untoward economic developments is a widely accepted concept. For example, media economists can often be heard hedging prognostications on economic recovery with intonations on the dangers of oil surging over $140 a barrel again, as it did in the price shock of 2008.
The use of the word "price shock" is interesting in itself - with its metaphoric invocation of the startle and injury caused by an unexpected jolt of electricity.
Setting a Spike Threshold Spike
So what is the threshold for a spontaneously generated volatility spike in oil price that has sufficient oomph ?
Fortunately, determining the precise level of this hypothetical threshold is probably not necessary and probably not even possible. For practical purposes a workable approach is to set an arbitrary, but consistent bar high enough that spikes exceeding this level are captured, but not so low that "signal" is overwhelmed by noise.
The rigor in the approach comes from sticking to the threshold. If a value for a given month falls below the bar it is excluded, if the monthly volatility number exceeds the bar, then it makes the grade and is accepted as a spike.
The first step in "thresholding" spikes from the total population of volatility measurements is to generate a broad survey of the entire population of volatility estimates. This is done on Figure 8. In the top part of this figure, all monthly volatility estimates for oil from January 2000 until July 2010 have been plotted in a histogram according to the frequency at which they occur during the 10 year period.
It is notable that the frequency histogram does not conform to the symmetric bell-shaped curve that characterizes a normal or Gaussian distribution. Volatility frequencies distribute in an asymmetric distribution, with most values clustered near the Y axis and a long tail that extends to the right.
Now.... Where to set the threshold on the histogram ? The red arrow near the center of the frequency distribution at which half values fall below (black lines) and half above (red lines) is the median or 50th percentile of the distribution.
The median resembles the mean or average of a normal curve in that it provides a balance point in the middle of the frequency distribution. The median is a commonly used measure of this central tendency for non-normal distributions (e.g. figure 8).
The lower left hand graph of figure 8 repeats the graph first seen in figure 5 except that this time red and pink fill marks those months on the plot that are above the median (i.e., the 50th percentile) of the distribution and black indicates those below the median. Inspection of this graph indicates those red colored spikes that penetrate a bar set at the median include those that were identified earlier by eye-balling in figure 5.
However, setting the threshold at the median also seems to bring to light numerous and disparate months that are not obviously part of spikes. As such the 50th percentile may be to low, in that it admits too much noise into the spike discrimination process.
In a normal distribution one standard deviation to the right along the x axis falls at ~67th percentile. Approximately one third of all values will occur at the 67th percentile or above for normally distributed variables. The histogram on figure 8 shows that we are not dealing with a Gaussian distribution, so segmentation of the volatility frequency distribution by standard deviation is not optimal. All the same, we can use the 67th percentile as our threshold to segment out the top third of monthly values; as has been done in the histogram at the top of figure 9.
One notable outcome of setting threshold at the 67th percentile is that the "long fat tail" segment of the histogram is captured, without significant inclusion of "noisy" monthly values near the broader more central part of the frequency distribution.
The middle graph on figure 9 again uses red outlining and pink fill to mark those months that fall above the new, higher threshold. Spikes seem to be relatively well discriminated above background noise by a threshold set at the 67th percentile. Based on this, the 67th percentile is adopted as the arbitrary, but hard and fast bar for defining the level that a monthly volatility level in oil price must reach before it is defined as a spike.
In the lower graph on figure 9 the tops of 16 spikes in oil price volatility that exceed the 67th percentile have been plotted as red bars along a timeline from January 2000 to December 2009. Above the oil spike locators (red bars), smaller blue bars mark the tops of 21 volatility spikes that exceed the 67th percentile in Presidential approval/disapproval spread.
From 2004 to the 2010 there is good agreement in the frequency and spacing of oil and presidential spikes. However, the red and blue bars in this time frame do not line up well, suggesting that the sequences for the presidential and oil indices may be out of phase with respect to each other.
In the next section the first of two unbiased methods for determining whether the two spike patterns show relationships in time will be described. The question of most interest remains whether oil spikes occur in a manner that is consistent with a causal relationship with (i.e., upstream of) spikes in volatility of the political polls?
Determining the "Best-Fit" Alignment Between Volatility Spikes in Oil Price and Presidential Approval
To objectively determine whether spike tops for the Oil and Presidential approval share a common cycle length, albeit a different phase, a simple computational approach was taken.
The pain of reading the specifics of what was done can be saved by telling the reader that good alignment could be achieved when Presidential spike tops where translated 7 months back in time with respect to spike tops in the oil price volatility index.
Those readers who require details on the approach, are invited to scrutinize the following 8 or so paragraphs.
Using an Excel spreadsheet, the Presidential approval spike top sequence was shifted forward plus 12 months with respect to that of oil and then the distance in months (+/- 1, 2, 3...) was recorded from each spike top in the series to the nearest oil spike top.
This process was repeated for a shift of plus 11 months, plus 10 months and so on all the way down to 0 months in which no shift in phase is imposed i.e., as shown in the lower panel of figure 9.
The iterated calculation was then repeated again for shifts of the Presidential spike top sequence back minus 1 month from the alignment at 0 months and so on month-by-month all the way down to a phase shift of minus 12 months.
In the end, a matrix of 400 numbers was generated composed of 25 columns representing the alignments in one month steps from minus 12 months to plus 12 months and rows for each of the 16 oil spike tops occurring between January 2000 and December 2009.
Each number in the matrix was then squared and a mean square for each of the 25 columns was calculated. In this way the alignment with the smallest average (squared) displacement between oil and Presidential Spike tops was identified.
This is shown graphically by the blue line line on the graph at top of Figure 10, where it can be seen that the column with the least mean square occurs when the sequence of Presidential spike tops is moved back minus 7 months (light red bar) with respect to the sequence of oil spike tops.
Figure 10 tells us that volatility in Presidential approval is unlikely to precede variance in oil price, as mean square increases sharply as we move forward from the nadir at minus 7 months representing the optimal alignment of phase. To put this another way, figure 10 teaches that oil spikes have occurred downstream from spikes in the Presidential volatility index in a manner that is consistent with a causal relationship.
Recalculating mean squares for alignments restricted to the years between 2005 and 2010 yielded the same result, confirming that oil spike tops have preceded spike tops in the Presidential index by minus 7 months, over the more recent 5 year stretch (green line top graph figure 10). Amazingly, after minus 7 months shift in phase, the timing of Presidential spikes on average differed from oil spikes by only a single month!
In other words, with the 7 month shift in phase, the wavelengths for oil price and Presidential approval sit more or less "balls-on" on top of each other. For the 6 year period between 2004 and 2010, spikes in Presidential approval pop up after spikes in oil price volatility in a more or less predictable sequence.
A few more notes on methodology. Calculating mean square is a tried and trued method in statistics. The advantages include that squaring gives each number in the matrix a positive sign - simplifying calculations. A squared transformation also weights the analysis against those oil and Presidential spike tops that show large displacements from another. Not using a squared transformation on the data does not change the outcome, but does improve the confidence that the relationship under scrutiny is meaningful. For example, the square of a displacement between nearest-neighbor spikes of 0 and 1 months is 0 and 1 respectively. But if the distance between nearest spike tops is 3, then the penalty for misalignment is geometrically much larger at 9, increasing the mean square value for a given column. The transformational weighting thus makes the close, one-month difference found in spike phase even more remarkable.
In the lower chart on figure 10 spike tops in the Presidential index (blue bars) have been shifted back minus 7 months with respect to oil spike tops (red bars), to illustrate the optimal alignment of phase indicated by the least mean square method.
Similar to the conclusions reached earlier using the subjective alignment of volatility spikes, agreement from mid-2004 to 2010 is excellent. Prior to 2004, the relationship between oil and Presidential approval volatility is not all that strong.
"Best-Fit" Alignments Between Volatility Spikes in Oil with those of Congressional Approval and Direction of the Country
Using the same least mean square approach as just described, the optimal alignments for volatility in Congressional approval and the Direction of Country with oil were also calculated to be minus 7 months. Indicating that spikes in oil volatility tended to occur some half a year before the emergence of a corresponding variance spike in each of the 3 political indices.
This confluence in spiking can be seen in Figure 11 where the "best-fit" alignments of Presidential approval, Congressional approval and Direction of the Country volatility spike tops are plotted together against those of oil.
In my opinion, figure 11 is remarkable. It shows that the political winds in the USA as reflected in the 3 polls are pretty much in lock step with presaging instabilities in the price of oil. There are gaps and exceptions here and there, but from 2004 onwards, a column of blue bars more or less lines up under spikes in oil price variance.
Notice also that prior to 2004 the relationship between oil and polling data is not all that close. There is a transitional period from 2004-2006 in which phase appears to become locked. But after this transition spike tops in Presidential approval, Congressional approval and Direction of the Country dance as if on a "tractor beam" determined by oil price.
Fourier Transform Analysis of the Volatility Frequency Domain
The first two goals of objectively defining a volatility spike and optimizing the alignment of spike patterns over time have been broached. What of the third and final goal of determining whether the relationships between oil and polling data are real and meaningful ?
I asked my fried Mike (the McCanic), a Professor with an engineering background, to take look at the data sets to help me with this problem. Mike told me that a "Fourier Transformation" would be a useful thing to do. This analysis, he said, would pull out the frequency domain spectra, enabling a comparison of the degree to which volatility patterns over time were mathematically related.
The phrase frequency domain spectrum looks scary because it has the words frequency, domain and spectra in it. The easiest way to grasp how the Fourier works is by using music as an example.
The frequency domain spectra of the middle C note from a tuned piano can be rendered in a simple plot of the frequency of oscillation of sound waves coming from the piano versus the amplitude or intensity of those sound waves. As middle C oscillates at 523 cycles per second (Hz), its spectra would be a single sharp peak at this frequency. There would be a small amount spread around the predominant peak at 523 Hz due to vagaries associated with the specific instrument, instabilities in the air and other extraneous variables affecting the recording and computation of the Fourier transformation.
By contrast, the frequency domain spectra for the chord C major from the same piano would be three sharp peaks representing the oscillations of its three component notes C, E and G. Thus for C major, though your ear perceived a single sound, 3 notes would be being played simultaneously. With the magic of the Fourier transformation, the complex sound of C major is able to be broken-down mathematically, enabling identification of its constituent notes.
Based on this ability to mathematically break-down complex patterns and isolate recurring notes or features, Fourier transformation has a broad set of practical uses. In another example from music , Fourier is at the heart of the "autotune" technology that is heard on top 40 radio. With the aid of computers, sound engineers use Fourier transformation to "correct" off-key notes.
Fourier transformation is also used by doctors to look for disease clues in the heart beat of their patients. This diagnostic tool can predict the likelihood of whether the patient will suffer a heart attack in the future.
Take your pick of an analogy to explain the Fourier transformation - searching for the tune in a Lady Gaga song or the signs of an unstable heart beat. Whatever way its understood, the final, and most important dissection of the data concludes with Mike's Fourier transform hunt for embedded rhythms in the volatility data sets.
Any Relationship Between Oil and Political Polling Data Between 2000 and 2005 is Limited
The story so far indicates that the pattern of volatility in oil price and political polls from 2000 to 2005 is distinct from that observed between 2005 to 2010. The watershed year of 2005 between these two time periods is marked by what I have termed the "Bush Crossover" (figure 2). In 2005, the global rate of oil production also plateaued and has remained stuck at this level for the last 6 years.
From 2000 up until the auspicious year of 2005, repeating volatility spikes were not observed for any of the variables under scrutiny (figure 11). However, between 2005 and 2010, a distinct pattern of recurring spikes was established. Consequently, separate fast Fourier transformation (FFT) analyses were carried out on the 5 year period leading up to 2005 and the subsequent 5 year period.
The FFT frequency domain spectra for monthly volatility in oil price, Presidential approval, Congressional approval and "Direction of the Country" between December 1999 and March 2005 are shown in Figure 12.
Figure 12 provides little evidence that any of the variables display a predominant frequency, indicative of an underlying sequence of repeating spikes. The largest peaks in the FFT-derived spectra for oil, Presidential approval, Direction of the Country and Congressional approval occur at frequencies of 0.078, 0.031, 0.063 and 0.078 cycles per month. These numbers correspond to a primary tendency for volatility spikes in oil price, Presidential approval, Congressional approval and Direction of the Country to repeat at intervals of 12.8, 32.3, 15.9 and 12.8 months respectively.
However, these are modest tendencies only. Each spectra contains multiple peaks, which represent further secondary or tertiary levels of repeating structure within the frequency domain of each volatility time series. If there is any organized pattern in the spectra shown in figure 12 over this earlier period it would be more like a Rachmaninoff piano chord than a single note tolling in a Pink Floyd song.
From figure 12 it can be concluded that neither oil nor the political polling data display readily identifiable embedded rhythms between 2000 and 2005. The broad variation in shape and peak frequencies within each spectra tell us that any relationship between oil price and political life during the first part of President Bush's tenure would have been rather complex. As such, the conclusion reached earlier in the essay that there is no obvious correlation between instability in oil markets and the changeableness of politics before 2005 is reinforced by the Fourier transformation analysis.
In the next section Fourier Transformation will provide strong quantitative support for the other main conclusion of this essay. Namely, that from the mid-2000s onwards swings in US political polls demonstrate an unusual level of entrainment with spikes in volatility in the price of oil.
Fourier Transformation Throws Relationships between Oil Price and Political Polling Data from 2005 and 2010 into Sharp Relief
Figure 13 provides frequency domain spectra for volatility in oil price, Presidential approval, Congressional approval and Direction of the Country between April 2005 and July 2010.
As expected, the patterns from 2005 to 2010 are quite different from those of the earlier time frame. Most notably, the spectra from oil price, Presidential approval and "Direction of the Country" measurements now display a single predominant frequency at 0.031 cycles per month- consistent with a period between spikes in volatility of 32.3 months.
Minor secondary peaks are seen for the oil, Presidential approval and "Direction" indices. But these bumps in the frequency domain spectra are at least an order of magnitude smaller than the peak at 0.031 cycles per month.
In effect, volatility in oil price and Presidential approval and Direction of the Country polls are now all tuned to a single note with a dominant oscillation that booms out every 2 years, 8 months, 1 day, 3 hours, and 33 minutes, or thereabouts.
The FFT analysis indicates that the relationship between variance in oil price with swings in Congressional approval is not as strong as with the other two political polls. Monthly volatility in Congressional approval decomposes to a spectrum of 3 to 4 peaks of similar magnitude, with the largest of these sitting at 0.14 cycles per month. The next largest (asterisked) is at 0.031 cycles per month. Thus, although there is not an exact match, the spectra for Congressional approval harmonizes somewhat with the predominant frequency for oil.
By contrast, the frequency domain spectra for oil price and "Direction of the Country" polling data are remarkably similar - sharing a nearly identical shape. The spectrum from Presidential approval also displays strong confluence with the plot for oil.
Together with the "best-fit" alignments (figure 11), figure 13 indicates that swings in "Presidential approval" and "Direction of the Country" occur downstream from, and are strongly entrained to spikes in oil price volatility that repeats every 32.3 months.
Fourier Transformation Analysis Indicates that the Signal for Repeating Spike in Volatility Was Evident From ????
This part of the story is on temporary hold - Mathlab is expensive software and our license ran out. So we're saving up so we can do the Fourier transform windowing that will enable us to figure out when during the 2000s oil and polling data volatility cycles became entrained. This is an important part of the interwoven tale of oil and elections being told here - but also my earlier story linking spiking volatility in oil price to the 2008 financial collapse. I suspect a quantitative rationale for the apparently irrational behavior of the financial industry during this sorry period may lurking therein. Stay tuned.
Tom Therramus is the pen name of Robert G. Gourdie.
- ↑ Volatility in the Price of Oil since Hubbert's Peak and Investment Risk, Tom Therramus, Idea Wiki, January 2009
- ↑ Was Volatility in the Price of Oil a Cause of the 2008 Financial Crisis? Tom Therramus, editor: Gail the Actuary - The Oil Drum, December 2009
- ↑ Oil Caused Recession, Not Wall Street, Tom Therramus, editor: Steve Austin - Oil-Price.Net, January, 2010
- ↑ RealClearPolitics.com President Obama job approval polls 2008-present
- ↑ RealClearPolitics.com President Bush job approval polls 2000-2008
- ↑ World Crude Oil Production, 1960-2009, United States Department of Energy, 2010
- ↑ WikiLeaks cables: Saudi Arabia cannot pump enough oil to keep a lid on prices, UK Guardian Newspaper, 8 February, 2011
- ↑ PRICE TRENDS OVER A COMPLETE HUBBERT CYCLE: THE CASE OF THE AMERICAN WHALING INDUSTRY IN 19th CENTURY. Ugo Bardi, ASPO, 2004)
- ↑ Status of Fishery Resources off the Northeastern US, NEFSC - Resource Evaluation and Assessment Division. NOAA, US National Marine Fisheries Service, December, 2006
- ↑ Mechanics of Future Oil Price Volatility (A Flubber Cobweb) TheOilDrum.com, 6 February, 2009
- ↑ Quantitative greasing, Chris Cook, Asia Times Newspaper 11 July 2011
- ↑ Comments on :Was Volatility in the Price of Oil a Cause of the 2008 Financial Crisis? - The Oil Drum, December 2009