Patrick M. Crowley

A Guide to Wavelets for Economists

Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not fully entered the economics discipline yet. In this survey article, wavelet analysis is introduced in an intuitive manner, and the existing economics and finance literature that utilizes wavelets is surveyed and explored. Extensive examples of exploratory wavelet analysis are given, most using Canadian, US and Finnish industrial production data. Finally, potential and possible future applications for wavelet analysis in economics are discussed. Copyright 2007 The Author Journal compilation

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.

Decomposing the Co-Movement of the Business Cycle: A Time-Frequency Analysis of Growth Cycles in the Euro Area

This article analyses the frequency components of European business cycles using real GDP by employing multiresolution decomposition (MRD) with the use of maximal overlap discrete wavelet transforms (MODWT). Static wavelet variance and correlation analysis is performed, and phasing is studied using co-correlation with the eurozone by scale. Lastly dynamic conditional correlation GARCH models are used to obtain dynamic correlation estimates by scale against the EU to evaluate synchronicity of cycles through time. The general …ndings are that eurozone members fall into one of three categories: i) high static and dynamic correlations at all frequency cycles (e.g. France, Belgium, Germany), ii) low static and dynamic correlations, with little sign of convergence occurring (e.g. Greece), and iii) low static correlation but convergent dynamic correlations (e.g. Finland and Ireland)

One Money, Several Cycles? Evaluation of European Business Cycles using Model-Based Cluster Analysis

Optimal currency area theory suggests that business cycle co-movement 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 found that there was a core of member states in the EU that could be grouped together as having similar business cycle co-movements, but these studies have always used Germany as the country against which to compare. This study updates and extends corresponding previous analyses. More specifically, it correlates the countries against both German and euro area macroeconomic aggregates and uses more recent techniques in cluster analysis, namely model-based clustering techniques. Keywords: business cycles, co-movement, optimal currency areas, model-based cluster analysis JEL classification numbers: F15, F31

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.

Long Cycles in Growth: Explorations Using New Frequency Domain Techniques with US Data

In his celebrated 1966 Econometrica article, Granger first hypothesized that there is a ‘typical’ spectral shape for an economic variable. This ‘typical’ shape implies decreasing levels of energy as frequency increases, which in turn implies an extremely long cycle in economic fluctuations and particulary in growth. Spectral analysis is however based on certain assumptions particulary in that render these basic frequency domain techniques inappropriate for analysing non-stationary economic data. In this paper three recent frequency domain methods for extracting cycles from non-stationary data are used with US real GNP data to analyse fluctuations in economic growth. The findings, among others, are that these more recent frequency domain techniques do not provide evidence to support the ‘typical’ spectral shape and nor an extremely long growth cycle a la Granger.

How Hard is the Euro Area Core? An Evaluation of Growth Cycles Using Wavelet Analysis

Using recent advances in time-varying spectral methods, this research analyses the growth cycles of the core of the euro area in terms of frequency content and phasing of cycles.The methodology uses the continuous wavelet transform (CWT) and also Hilbert wavelet pairs in the setting of a non-decimated discrete wavelet transform in order to analyse bivariate time series in terms of conventional frequency domain measures from spectral analysis.The findings are that coherence and phasing between the three core members of the euro area (France, Germany and Italy) have increased since the launch of the euro. Key words: time-varying spectral analysis, coherence, phase, business cycles, EMU, growth cycles, Hilbert transform, wavelet analysis JEL classification numbers: C19, C63, C65, E32, E39, E58, F40

EXCHANGE RATE VOLATILITY AND FOREIGN INVESTMENT: International Evidence

The assertion that exchange rate volatility has no real effects on trade volumes has been a contentious issue for over a decade. The European Union established the euro on the basis of a contrarian view to this assertion, and also maintained relatively fixed exchange rates following the collapse of the Bretton Woods exchange rate system in the early 1970s. Indeed, anecdotal evidence appears to support the view that there is an inverse relationship between trade volumes and exchange rate volatility. Business associations also consistently support more fixity in exchange rates, despite the existence of derivative markets for the purposes of hedging. While exports and imports appear on the current account of balance of payments, foreign direct investment appears on the capital account. Much of the world’s foreign direct investment (FDI) is undertaken by multinational enterprises (MNEs), about 60 percent on average during the 1990s. The nature of FDI flows is very unlike merchandise trade flows, as FDI largely consists of

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.

Euro Area Monetary and Fiscal Policy Tracking Design in the Time-Frequency Domain

This paper first applies the MODWT (Maximal Overlap Discrete Wavelet Transform) to Euro Area quarterly GDP data from 1995 – 2014 to obtain the underlying cyclical structure of the GDP components. We then design optimal fiscal and monetary policy within a large state-space LQ-tracking wavelet decomposition model. Our study builds a MATLAB program that simulates optimal policy thrusts at each frequency range where: (1) both fiscal and monetary policy are emphasized, (2) only fiscal policy is relatively active, and (3) when only monetary policy is relatively active. The results show that the monetary authorities should utilize a strategy that influences the short-term market interest rate to undulate based on the cyclical wavelet decomposition in order to compute the optimal timing and levels for the aggregate interest rate adjustments. We also find that modest emphasis on active interest rate movements can alleviate much of the volatility in optimal government spending, while rendering similarly favorable levels of aggregate consumption and investment. This research is the first to construct joint fiscal and monetary policies in an applied optimal control model based on the short and long cyclical lag structures obtained from wavelet analysis.