Wavelet Analysis and Denoising: New Tools for Economists

This paper surveys the techniques of wavelets analysis and the associated methods of denoising. The Discrete Wavelet Transform and its undecimated version, the Maximum Overlapping Discrete Wavelet Transform, are described. The methods of wavelets analysis can be used to show how the frequency content of the data varies with time. This allows us to pinpoint in time such events as major structural breaks. The sparse nature of the wavelets representation also facilitates the process of noise reduction by nonlinear wavelet shrinkage , which can be used to reveal the underlying trends in economic data. An application of these techniques to the UK real GDP (1873-2001) is described. The purpose of the analysis is to reveal the true structure of the data - including its local irregularities and abrupt changes - and the results are surprising.Wavelets, Denoising, Structural breaks, Trend estimation

Orthogonality Conditions for Non-Dyadic Wavelet Analysis

The conventional dyadic multiresolution analysis constructs a succession of frequency intervals in the form of ( π  / 2  j , π  / 2  j  - 1 ); j  = 1, 2, . . . ,  n of which the bandwidths are halved repeatedly in the descent from high frequencies to low frequencies. Whereas this scheme provides an excellent framework for encoding and transmitting signals with a high degree of data compression, it is less appropriate to the purposes of statistical data analysis.       A non-dyadic mixed-radix wavelet analysis is described that allows the wave bands to be defined more flexibly than in the case of a conventional dyadic analysis. The wavelets that form the basis vectors for the wave bands are derived from the Fourier transforms of a variety of functions that specify the frequency responses of the filters corresponding to the sequences of wavelet coefficients.Wavelets, Non-dyadic analysis, Fourier analysis

Comparative Economic Cycles

The income cycles that have been experienced by six OECD countries over the past 24 years are analysed. The amplitude of the cycles relative to the level of aggregate income varies amongst the countries, as does the degree of the damping that affects the cycles. The study aims to reveal both of these characteristics. It also seeks to determine whether there exists a clear relationship between the degree of damping and the length of the cycles. In order to estimate the parameters of the cycles, the data have been subjected to the processes of detrending, anti-alias filtering and subsampling.Business cycles, Autoregressive models

Testing for Contagion: a Time-Scale Decomposition

The aim of the paper is to test for ¯nancial contagion by estimating a simultaneous equation model subject to structural breaks. For this purpose, we use the Maximum Overlapping Discrete Wavelet Transform, MODWT, to decompose the covariance matrix of four asset returns on a scale by scale basis. This decomposition will enable us to identify the structural form model and to test for spillover e®ects between country speci¯c shocks during a crisis period. We distinguish between the case of the structural form model with a single dummy and the one with multiple dummies capturing shifts in the co-movement of asset returns occurring during periods of ¯nancial turmoil. The empirical results for four East Asian emerging stock markets show that, once we account for interdependence through an (unobservable) common factor, there is hardly any evidence of contagion during the 1997-1998 financial turbulence.wavelets; simultaneous equations model; financial contagion

Testing for public debt sustainability using a time-scale decomposition analysis

In this paper we estimate the response of primary surplus to lagged debt to test for debt sustainability within the 17 EMU countries by using a factor model. The analysis is split into two stages. In the first stage we retrieve the cyclical and long-run components of primary surplus and debt ratios of each EMU country using a wavelet decomposition for each fiscal covariate, based on the Maximal Overlapping Discrete Wavelet Transform. In the second stage, we use Full Information Maximum Likelihood for a factor decomposition of thecross covariance matrix of the wavelet coefficients of primary deficit and debt to GDP ratios in order to measure the short run and the long run reaction of the primary surplus to (lagged) debt. The empirical evidence shows a positive response of primary surplus to debt within EMU as a whole. Country specific factor decomposition confirms Germany as the one of the most virtuous countries, and, Italy, as the only PIIGS member on a long-run sustainable path for deb

Territorial Capital and the Great Recession: a Nuts-3 Analysis for Central and Southern Italy

The analyses on the effects of the actual crisis have been mainly concentrated on a national and international dimension, leaving aside the differential effects of the crisis on regions and sub-regional areas. Notwithstanding the international character of the Great Recession, it has to be stressed that the different structural features of regions and urban areas might influence the economic and social impact of the crisis. They also might have an important effect on the resilience and recover chance. In the present paper, we focus on territorial capital, a concept that takes into account of the different features of goods and services in terms of their degree of appropriability and rivalry and, also, of their material-immaterial content. The aim is to identify the strategic territorial elements which help in the evaluation of the absorption capacity of the recession at regional and sub-regional levels. For that purpose, we use a wide dataset for Central and Southern Italian provinces in order to measure the empirical relations between the territorial capital and the change in the provincial performance. The intent is to measure how the territorial capital endowment might have determined different reactions on a sub-regional scale and, conversely, how the crisis might influence the territorial capital in different areas. If, on one hand, we expect that the “soft” dimensions of the territorial capital (relations among firms, cooperation networks, public-private partnership, territorial governance, innovation linkages, and so on) have some relevance in shaping the growth process of less developed and peripheral areas, the role of these dimensions in the reaction to crisis is still to be debated. The paper examines the relation between territorial capital and performance at NUTS-3 (provincial) level. during the period 1999-2011 and on the basis of exports and employment dynamics

A wavelet analysis of US fiscal sustainability

In this paper, we reassess the relationship between primary deficit and lagged debt to GDP ratio (Bohn, 1998), to test for US debt sustainability over the period 1795–2012. Our analysis is rooted in the wavelet domain enabling the detection of interesting patterns and otherwise hidden information. We find evidence of long term fiscal sustainability but only up until 1995 and also we show that governments tend to respond more vigorously to budget deficits when the level of debt is high rather than low

The Decline in U.S. Output Growth Volatility: A Wavelet Analysis

The aim of the paper is to determine whether or not the volatility of the growth rate of US output has changed in the period since late 1940's, and to attribute a precise date, if possible, to any such change. By applying the Discrete Wavelet Transform (DWT) to the annualized quarter-to quarter output growth series, we can test the homogeneity of the variance on a scale by scale basis without needing to fit a parametric model to the observed time series. A version of the Inclan and Tiao (1994) Normalised and Centered Cumulative Sum of Squares test, adapted to wavelet analysis, leads us to reject the null hypothesis of constant variance in the two levels of decomposition of the highest resolution or frequency and to locate a single break in 1982. The economic implications are explored

Wavelet Analysis and Denoising: New Tools for Economists

This paper surveys the techniques of wavelets analysis and the associated methods of denoising. The Discrete Wavelet Transform and its undecimated version, the Maximum Overlapping Discrete Wavelet Transform, are described. The methods of wavelets analysis can be used show how the frequency content of the data varies with time. This allow us to pinpoint in time such events as major structural breaks. The sparse nature of the wavelets representation also facilitates the process of noise reduction by nonlinear \textit{wavelet shrinkage,} which can be used to reveal the underlying trends in economic data. An application of these techniques to the UK real GDP (1873--2001) is described. The purpose of the analysis is to reveal the true structure of the data---including its local irregularities and abrupt changes---and the results are surprising

Volatility co-movements: a time scale decomposition analysis

In this paper we investigate short-run co-movements before and after the Lehman Brothers’ collapse among the volatility series of US and a number of European countries. The series under investigation (implied and realized volatility) exhibit long-memory and, in order to avoid missspecification errors related to the parameterization of a long memory multivariate model, we rely on wavelet analysis. More specifically, we retrieve the time series of wavelet coefficients for each volatility series for high frequency scales, using the Maximal Overlapping Discrete Wavelet transform and we apply Maximum Likelihood for a factor decomposition of the short-run covariance matrix. The empirical evidence shows an increased interdependence in the post-break period and points at an increasing (decreasing) role of the common shock underlying the dynamics of the implied (realized) volatility series, once we move from the 2-4 days investment time horizon to the 8-16 days. Moreover, there is evidence of contagion from the US to Europe immediately after the Lehman Brothers’ collapse, only for realized volatilities over an investment time horizon between 8 and 16 days