Financial products (e.g. stocks, bonds and precious metals or derivatives such as futures and options) and energy products (e.g. electricity or petroleum distillates) tend to experience comovements in the form of correlated or similar evolution of their prices over time. Obviously, the analysis of such common behaviour and interactions is important in order to better understand the causes and consequences of economic crises and financial crashes as well as to predict their likelihood.

In the long run, comovements usually have a positive connotation as they indicate market integration which occurs when prices among different assets or products fluctuate in a similar manner over time. For example, since the creation of the European Monetary Union, correlation among European stock markets, as a measure of their integration, has attracted quite some interest in the economic and financial literature.

On the other hand, in financial and energy markets short-run comovements may also have a negative undertone as they can be linked to spillovers and contagion during periods of market distress related to real economic and financial events such as, e.g., those experienced recently during the European debt crisis.

Furthermore, energy markets are typically characterised by spreads, that is, margins or differences in prices between the corresponding raw materials and the finished products, whose determination is crucial for the economy. For example, the so called "crack spread” is a term used in the oil industry for the margin between the output prices of distillates and the crude oil costs. Similarly, ”spark spreads” are intermarket spreads for electricity and its sources such as natural gas or renewable energies, or ”frac spreads” are the margins from NGLs in the fracking industry. However, spread analysis is anything but straightforward since the underlying markets involved are independently subject to a large number of dynamic interactions between variables of supply and demand from diverse economic, technological and environmental sectors and activities. This means that the strength of the relationships among different energy products determining spread behaviour, and, besides, the further relationship of the latter to financial and macroeconomic variables, may vary significantly across different long-run/short-run time-scales.

These long-term and short-term phenomena can and usually do happen concurrently since financial and energy markets involve heterogeneous agents that make decisions over different time horizons and operate on different time-scales and a recent challenge is how they can be analysed separately. To further complicate the matter, the term structure of comovements in these markets has been far from homogeneous both over time and across time-scales, in other words they are highly non-stationary over time, and new statistical tools are needed to advance in the study of these events as characterised by a deeper understanding of their comovement dynamics.

Time-scale multiresolution

As mentioned above, one important aspect in the analysis of financial and energy markets data is the study of the degree and evolution of comovements at different time-scales or frequencies, a process that is sometimes referred to as multiresolution. In this respect, whilst traditional data analysis over time is mostly based on statistical cross-correlation functions in the time domain, that is, on an observation-by-observation basis but neglecting all frequency information and ignoring non-stationary behaviour, the more recent wavelet analysis offers a compromise between time and frequency domains [1]. A ’wavelet’ is simply a sort of wave-like mathematical function that oscillates briefly around zero, i.e. with a shape resembling a small wave or ripple in the water. Wavelets are typically designed to transform the original data for signal processing and signal extraction purposes and have been routinely used in many different scientific fields such as climatology, ecology, engineering, geophysics, medicine and, more recently, economics and finance. In short, wavelet transforms allow for a combined visualization of data features and their comovements as a function of both time and scale, separating their different periodic components as they evolve over time.

Among the most recent wavelet-based statistical tools, the so-called wavelet local multiple correlation (WLMC) has been specifically tailored to the analysis of multiscale comovements within a set of variables evolving over time [2].

Integration and contagion in financial stocks

As already pointed out, correlation among stock markets is a common measure of market integration in the economic and financial literature. However, these studies do not usually take into account the fact that stock markets are characterised by a diversity of agents each operating with a different time horizon in mind or that such comovement structure across different time-scales may be evolving over time. These are important salient features in these markets. For example, in a recent study using the WLMC, the time-localized multiscale wavelet analysis of daily returns obtained from a set of Eurozone stock markets during a period in which several financial and debt crises have occurred reveals the existence of a stable and practically exact linear relationship among these stock markets for periods of time of one year and longer, which can be interpreted as perfect integration. On the other hand, the WLMC shows that for intraweek and intramonth periods the correlation structure is clearly evolving over time, experiencing a sharp increase during financial crises which can be interpreted as evidence of financial ’contagion’.

In general, these results may help to better understand how the multivariate relationship connecting financial markets evolves over time in a totally different way depending on the time-scale and it has been suggested that this can be used for prediction purposes.

Integration vs. short-run dynamics in energy markets

Dynamic analysis of the multivariate relationship over a recent period among petroleum products, namely WTI crude oil and distillates, suggests that wavelet multiple correlations are very strong for the two longest time-scales, implying a not very surprising integration of these markets [3]. However, WLMC analysis shows that the strength of the relationship varies significantly over time and across time-scales in the short run. In particular, WLMC reveals a sharp fall in the correlation values of the shorter time-scales (up to two weeks) taking place between 2013 and 2015 and it can be suggested that a plausible explanation for this fall might be related to the overproduction of tight oil in the U.S. and the subsequent slowdown in the global demand for crude oil. Furthermore, it appears that heating oil, diesel and kerosene are the most dependent petroleum products so that their prices, at increasing specific time horizons, can, to a large extent, be determined by linear combinations of the other prices.

These results are important to better understand the relationship among prices of crude oil and its products, and it is particularly relevant for the petroleum industry, as well as for policymakers and traders.

Further reading:

[1] Paul S. Addison. The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance. CRC Press, Taylor & Francis, Boca Raton, FL, 2017.
[2] Javier Fernández-Macho. Time-localized wavelet multiple regression and correlation. Physica A, 492: 1226–1238, 2018. doi:10.1016/j.physa.2017.11.050.
[3] JM Polanco, LM Abadie, and J Fernández-Macho. A multi-resolution and multivariate analysis of the dynamic relationships between crude oil and petroleum-product prices. Applied energy, 228:1550–1560, 2018. doi:10.1016/j.apenergy.2018.07.021.