An Application of Data Filtering Extracting Super Cycles in Commodity Prices

Authors and guest post by Daniel L. Jerrett, Ph.D and Abdel M. Zellou, Ph.D.

EViews offers numerous techniques to filter time series including the Hodrick Prescott filter as well as various band-pass filters.

This article will describe an application of one of these filtering techniques, namely the asymmetric Christiano Fitzgerald band pass filter, and its applications to real oil prices in order to extract the various cycle and trend components.

Super Cycles and Christiano Fitzgerald Band Pass Filter

There is a long standing interest in commodity price dynamics, i.e. their trend, cycle and volatility (Cuddington et al. 2007, Cashin and McDermott 2002). Recently, a number of papers have focused on the super cycle hypothesis. A super cycle (SC) is “a prolonged (decades) long trend rise in real commodity prices. Heap (2005) and Cuddington and Jerrett (2008) define a super cycle as a cycle lasting 20 to 70 years (trough to trough) as an economy goes through structural transformation caused by industrialization and urbanization. This structural transformation is accompanied by increased demand for energy and metals commodities as the manufacturing sector expands. Historically, these periods of urbanization and industrialization have occurred in Europe during the Industrial Revolution in the 19th century, in the U.S. at the beginning of the 20th century, in Western Europe again during the reconstruction that followed the Second World War, in South-East Asia in the 1960s and finally in the BRIC¹ countries in the 1990s². The increase in demand for energy and metals commodities during these periods, combined with the delay for the supply to catch up with the demand surge, created sustained periods of high commodity prices according to the super-cycle hypothesis.

Trends and cycles have been widely studied in various subfields in economics. Seasonal fluctuations, business cycles (6 to 32 quarters), Kitchin inventory cycles (3-5 years), Juglar fixed investment cycles (7-11 years), Kuznets cycles applied to real estate and infrastructural investment (15 to 25 years), Bronson asset allocation cycles (around 30 years) and Kondratiev waves or “grand super cycles” (45 to 60 years) are among those that have received attention.

The ‘‘ideal’’ band-pass filter, which isolates only specified frequencies, uses an infinite number of leads and lags when calculating the filter weights from the underlying spectral theory. Of course, a finite number of leads and lags must be used in practice; so a truncation decision must be made. Using a larger number of leads and lags allows for more precise results, but renders unusable more observations at the beginning and the end of the sample. Baxter and King (1995) stress that a filter must be symmetric in terms of the number of leads and lags to avoid causing phase shift in the cycles in filtered series. Baxter and King and Christiano and Fitzgerald (2003) develop alternative finite sample approximations to the ideal symmetric filter. Christiano and Fitzgerald also derive asymmetric filters, which have the advantage that they allow us to compute cyclical components for all observations at the beginning and end of the data span. The cost, as Christiano and Fitzgerald show, is very minor phase shifting, at least in their applications. 

Although Christiano and Fitzgerald are interested in business-cycle analysis, they also provide a couple of interesting macroeconomic applications of their symmetric and asymmetric filters for extracting lower frequency components of economic time series. The first involves an analysis of the Phillips curve relationship between unemployment and inflation in the short run versus the long run (that is, the high versus low frequency components). The second application examines the correlations between the low-frequency components of monetary growth and inflation. 

Cuddington and Jerrett (2008) are the first to apply band-pass filters to natural resource issues, including metal markets. Band-pass filters are well suited for our objective of attempting to measure super cycles in metals prices. One can define the range of cyclical periodicities that constitute super cycles, and then use the band-pass filter to extract those cyclical components. Given current interest in whether a new super cycle is emerging in the final years of the data sample, the asymmetric Christiano and Fitzgerald band-pass filter is especially useful because it allows one to calculate super-cycle components at the end of our data sample.

An Application to Crude Oil

Crude oil is the most traded commodity around the world. The asymmetric Christiano Fitzgerald band-pass filter has been applied to the price of real crude oil using EViews (see graph below).

The band-pass filter is available as a series Proc in EViews. To display the band-pass filter dialog, select Proc/Frequency Filter from the main series menu.

The first thing you will do is to select a filter type. There are three types: Fixed-length symmetric Baxter King, Fixed-length symmetric Christiano Fitzgerald, and Full-length asymmetric Christiano Fitzgerald.

The asymmetric Christiano Fitzgerald filter is applied to the real price of crude oil. Two components of the crude oil price are extracted: the trend component (in green in the figure below) and the super-cycle component (in red in the figure below).

• The trend component remains on its post World War II course with a positive slope averaging roughly 2% per year in real terms.
• The crude oil super cycle component peaked in 2010. 
• The current super cycle is showing similar duration to the previous one (SC2) with a duration of 29 years from trough to trough. If we consider that the current SC (SC3) will have same duration and amplitude, one could expect the trough to be reached around 2025 with a value around $50/bbl in real terms using 2015 dollars. 
• One should see a downward movement in the Super Cycle component continuing over the next decade (through roughly 2025).
• The super cycle in oil prices peaked in 2010. This was barely detected in the 2011 study, but seemed to be confirmed in this 2015 update.
• Super cycle EViews workfile. 
• For more information and updates, visit Clear Future Consulting.

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¹The BRIC countries represent Brazil, Russia, India and China.  The original acronym, BRICS, was invented in 2001 by Jim O’Neill, an economist at Goldman Sachs, and it includes South Africa.

²These clubs of countries are similar because of their economic transformation rather than geographical similarities.