How do you make a time series sing like a choir? Using the Hilbert-Huang transform to extract embedded frequencies from economic or financial time series

The Hilbert-Huang transform (HHT) was developed late last century but has still to be introduced to the vast majority of economists. The HHT transform is a way of extracting the frequency mode features of cycles embedded in any time series using an adaptive data method that can be applied without making any assumptions about stationarity or linear data-generating properties. This paper introduces economists to the two constituent parts of the HHT transform, namely empirical mode decomposition (EMD) and Hilbert spectral analysis. Illustrative applications using HHT are also made to two financial and three economic time series.business cycles; growth cycles; Hilbert-Huang transform (HHT); empirical mode decomposition (EMD); economic time series; non-stationarity; spectral analysis

A single currency for Asia? Evaluation and comparison using hierarchical and model-based cluster analysis

Today, there is increased speculation on the possibility of an Asian currency, as the region begins to show increased promise as a region of nascent economic activity. Any monetary integration scheme in East Asia would likely have to include both China and India though, so this paper attempts to assess the evolution of convergence among the East Asian countries, including China and India, according to the optimum currency area theory criteria, which is operationalized through the use of cluster analysis. In this paper we use both traditional "hierarchical" clustering as well as the more recently developed "model-based" clustering techniques and compare the outcome in each case. As the East Asian crisis of 1997-98 is likely to a¤ect the results, the exercise is done for pre-crisis, crisis, and post-crisis periods. The results reveal some structure among the countries, an increase in the degree of subregional homogeneity, and a robust relationship between Malaysia and Singapore

Evaluating the stresses from ECB monetary policy in the euro area

This paper investigates the extent to which euro area monetary policy has responded to evolving economic conditions in individual member states as opposed to the euro area as a whole. Based on a forward-looking Taylor rule-type policy reaction function, we conduct counterfactual exercises that compare the monetary policy behaviour of the ECB under alternative hypothetical scenarios: (1) the euro member states make individual policy decisions, and (2) the ECB responds to the economic conditions of individual members. Stress measures are then constructed to evaluate the degree of divergence of member state economies under these two hypothetical scenarios. The results we obtain reflect the extent of heterogeneity among the national economies in the monetary union, indicating that euro area policy rates have been particularly close to the ‘counterfactual’ interest rates of the largest euro members and countries with similar economic conditions, namely Germany, Austria, Belgium and France.European Central Bank; monetary policy reaction; Taylor rule; counterfactual analysis

The great moderation under the microscope: decomposition of macroeconomic cycles in US and UK aggregate demand

In this paper the relationship between the growth of real GDP components is explored in the frequency domain using both static and dynamic wavelet analysis. This analysis is carried out separately for the US and UK using quarterly data, and the results are found to be substantially different for the two countries. One of the key findings of this research is that the ‘great moderation’ shows up only at certain frequencies, and not in all components of real GDP. We use these results to explain why the incidence of the great moderation has been so patchy across GDP components, countries and time periods. This also explains why it has been so hard to detect periods of moderation (or other periods) reliably in the aggregate data. We argue this cannot be done without separating the GDP components into their frequency components over time. Our results show why: the predictions of traditional real business cycle theory often appear not to be upheld in the data.business cycles; growth cycles; discrete wavelet analysis; US real GDP; UK real GDP

One money with several cycles? Evaluation of European business cycles using cluster analysis. ACES Cases No. 2009.3

Optimal currency area theory suggests that business cycle comovement is a sufficient condition for monetary union, particularly if there are low levels of labour mobility between potential members of the monetary union. Previous studies of co-movement of business cycle variables (mainly authored by Artis and Zhang in the late 1990s) found that there was a core of member states in the EU that could be grouped together as having similar business cycle comovements, but these studies always used Germany as the country against which to compare. In this study, the analysis of Artis and Zhang is extended and updated but correlating against both German and euro area macroeconomic aggregates and using more recent techniques in cluster analysis, namely model-based clustering techniques

An intuitive guide to wavelets for economists

Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not yet fully entered the economics discipline. In this discussion paper, wavelet analysis is introduced in an intuitive manner, and the existing economics and finance literature that utilises wavelets is explored. Extensive examples of exploratory wavelet analysis are given, many using Canadian, US and Finnish industrial production data. Finally, potential future applications for wavelet analysis in economics are also discussed and explored.statistical methodology, multiresolution analysis, wavelets, business cycles, economic growth

Is Economic Growth Synchronicity Higher in Europe than Elsewhere?

Synchronization of growth rates are an important feature of international business cycles, particularly in relation to regional integration projects such as the single currency in Europe. Synchronization of growth rates clearly enhances the effectiveness of European Central Bank monetary policy, ensuring that policy changes are more attuned to the dynamics of growth and business cycles in the majority of euro area member states. In this paper a dissimilarity metric is constructed by measuring the topological differences between the GDP growth patterns in recurrence plots for individual countries. The results show that synchronization of growth rates were higher among the euro area member states during the second half of the 1980s and from 1997 to roughly 2002. Apart from these two time periods, euro area member states do not appear to be more synchronized than a group of major international countries, suggesting that apart from specific times when European integration initiatives were being implemented, globalization was the dominant factor behind international business cycle synchronization

Does All Fit One Size? An evaluation of the ECB policy response to changing economic conditions in the Euro area member states. ACES Cases No. 2008.1

This paper empirically investigates the extent to which the European Central Bank has responded to evolving economic conditions in its member states as opposed to the euro area as a whole. Based on a forward-looking Taylor rule-type policy reaction function, we conduct counterfactual exercises that compare the monetary policy behavior of the ECB with two alternative hypothetical scenarios: (1) were the euro member states to make individual policy decisions, and (2) were the ECB to respond to the economic conditions of individual members. The results reflect the extent of heterogeneity among the national economies in the monetary union and indicate that the ECB's monetary policy rates have been particularly close to the "counterfactual" interest rates of its largest euro members, as well as of countries with similar economic conditions, which includes Germany, Austria, Belgium and France

Measuring the intermittent synchronicity of macroeconomic growth in Europe. ACES Cases No. 2010.1

Synchronization of growth rates are an important feature of international business cycles, particularly in relation to regional integration projects such as the single currency in Europe. Synchronization of growth rates clearly enhances the effectiveness of European Central Bank monetary policy, ensuring that policy changes are attuned to the dynamics of growth and business cycles in the majority of member states. In this paper a dissimilarity metric is constructed by measuring the topological differences between the GDP growth patterns in recurrence plots for individual countries. The results show that synchronization of growth rates were higher among the Euro area member states during the second half of the 1980s and from 1997 to roughly 2002. Apart from these two time periods, Euro area member states do not appear to be more synchronized than a group of major international countries, signifying that globalization was the major cause of international business cycle synchronization

Late Triassic to Jurassic Magmatic and Tectonic Evolution of the Intermontane Terranes in Yukon, Northern Canadian Cordillera: Transition From Arc to Syn-Collisional Magmatism and Post-Collisional Lithospheric Delamination

End-on arc collision and onset of the northern Cordilleran orogen is recorded in Late Triassic to Jurassic plutons in the Intermontane terranes of Yukon, and in development of the synorogenic Whitehorse trough (WT). A synthesis of the extensive data set for these plutons supports interpretation of the magmatic and tectonic evolution of the northern Intermontane terranes. Late Triassic juvenile plutons that locally intrude the Yukon-Tanana terrane represent the northern extension of arc magmatism within Stikinia. Early Jurassic plutons that intrude Stikinia and Yukon-Tanana terranes were emplaced during crustal thickening (200–195 Ma) and subsequent exhumation (190–178 Ma). The syn-collisional magmatism migrated to the south and shows increasing crustal contributions with time. This style of magmatism in Yukon contrasts with coeval, juvenile arc magmatism in British Columbia (Hazelton Group), that records southward arc migration in the Early Jurassic. Exhumation and subsidence of the WT in the north were probably linked to the retreating Hazelton arc by a sinistral transform. East of WT, Early Jurassic plutons intruded into Yukon-Tanana record continued arc magmatism in Quesnellia. Middle Jurassic plutons were intruded after final enclosure of the Cache Creek terrane and imbrication of the Intermontane terranes. The post-collisional plutons have juvenile isotopic compositions that, together with stratigraphic evidence of surface uplift, are interpreted to record asthenospheric upwelling and lithospheric delamination. A revised tectonic model proposes that entrapment of the Cache Creek terrane was the result of Hazelton slab rollback and development of a sinistral transform fault system linked to the collision zone to the north