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A Measure of Comovement for Economic Variables: Theory and Empirics

TL;DR: In this article, a measure of dynamic comovement between (possibly many) time series and names it cohesion is defined in the frequency domain and is appropriate for processes that are costationary, possibly after suitable transformations.
Abstract: This paper proposes a measure of dynamic comovement between (possibly many) time series and names it cohesion. The measure is defined in the frequency domain and is appropriate for processes that are costationary, possibly after suitable transformations. In the bivariate case, the measure reduces to dynamic correlation and is related, but not equal, to the well known quantities of coherence and coherency. Dynamic correlation on a frequency band equals (static) correlation of bandpass-filtered series. Moreover, long-run correlation and cohesion relate in a simple way to co-integration. Cohesion is useful to study problems of business-cycle synchronization, to investigate short-run and long-run dynamic properties of multiple time series, and to identify dynamic clusters. We use state income data for the United States and GDP data for European nations to provide an empirical illustration that is focused on the geographical aspects of business-cycle fluctuations.

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Citations
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Journal ArticleDOI
TL;DR: In this article, the authors presented a robust appraisal of the parametric model in the presence of notoriously short economic time series and provided a proof of the theoretically desirable ME-property of the ML-estimated autoregressive model.
Abstract: The paradox that a parametric approach makes less assumptions than a nonparametric one can be seen as an obstacle for a wider use of frequency domain techniques in econometrics. This paper offers a throrough appraisal of the parametric model in the presence of notoriously short economic time series. Confronted with its nonparametric alternatives, pragmatic and theoretical aspects are addressed. Based on a duality framework, a proof of the theoretically desirable ME-property of the ML-estimated autoregressive model is provided. In the case of the true series following a fairly general stochastic process, it is numerically demonstrated that the parametric model in combination with a Bayesian order identification criterion offers the better representation of the true spectral density.

3 citations


Cites background from "A Measure of Comovement for Economi..."

  • ...As pointed out by Croux et al. (2001), a measure like the (isolated) squared coherency presented above is not suited for analyzing the comovement of time series, inasmuch it does not contain information about possible phase shifts between cycles in the series Xt and Yt....

    [...]

  • ...As pointed out by Croux et al. (2001), a measure like the (isolated) squared coherency presented above is not suited for analyzing the comovement of time series, inasmuch it does not contain information about possible phase shifts between cycles in the series Xt and Yt. In this sense, the correlation coefficient in time domain is more informative, since it is calculated lag by lag, providing both information on the lead-lag structure and the degree of linear relationship between the two series. It is possible to overcome this problem by also presenting the phase spectrum. However, the phase spectrum is difficult to interpret, since it is only defined mod2π, and cannot easily be summarized over a frequency band like in the case of the explained variance. Croux et al. (2001) propose an alternative measure, the so-called dynamic correlation ρ(ω), which measures the correlation between the “in-phase” components of the two series at frequency ω:...

    [...]

  • ...Croux et al. (2001) propose an alternative measure, the so-called dynamic correlation ρ(ω), which measures the correlation between the “in-phase” components of the two series at frequency ω: ρ (ω) = cxy (ω)√ fx (ω) fy (ω) ; − 1 ≤ ρ (ω) ≤ 1....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors re-visited the inflation-growth nexus in India using the tools of wavelet, i.e., wavelet correlation, wavelet cross-correlation and scale by scale Granger causality test.
Abstract: This article re-visits the inflation–growth nexus in India using the tools of wavelet, i.e. wavelet correlation, wavelet cross-correlation and scale by scale Granger causality test. Wavelet cross-c...

3 citations


Cites background or methods from "A Measure of Comovement for Economi..."

  • ...The relevance of frequency domain concepts as developed by Croux et al. (2001) and Ftiti (2010) shows that the extent and direction of comovement can differ between frequency bands. Thus, we introduce time concept with frequency domain, and analyse the time–frequency relationship because in the frequency-domain framework time information is lost. Hence, in our contribution, we use the evolutionary co-spectral analysis (ESA), as presented Priestley and Tong (1973) and based on the methodology of Ftiti (2010)....

    [...]

  • ...The relevance of frequency domain concepts as developed by Croux et al. (2001) and Ftiti (2010) shows that the extent and direction of comovement can differ between frequency bands. Thus, we introduce time concept with frequency domain, and analyse the time–frequency relationship because in the frequency-domain framework time information is lost. Hence, in our contribution, we use the evolutionary co-spectral analysis (ESA), as presented Priestley and Tong (1973) and based on the methodology of Ftiti (2010). The ESA illustrates the evolution of the co-variance of a time-series at the different frequencies and demonstrates the correlation coefficient in the time–frequency space....

    [...]

  • ...The relevance of frequency domain concepts as developed by Croux et al. (2001) and Ftiti (2010) shows that the extent and direction of comovement can differ between frequency bands....

    [...]

Dissertation
01 Jan 2015
TL;DR: Another Look at Stock Return Comovement: Some New Evidence and Test as mentioned in this paper, some new evidence and test for stock return co-commitment, and some new empirical studies.
Abstract: Another Look at Stock Return Comovement: Some New Evidence and Test

3 citations


Cites background or methods from "A Measure of Comovement for Economi..."

  • ...…average correlation (Preis et al. 2012), dynamic correlation and GARCH-type models (Syllignakis and Kouretas, 2011), factor pricing models (Bekaert et al., 2008), stochastic matrix theory (Reigneron et al. 2011), spectral analysis (Croux et al. 2001), and wavelet analysis (Rua 2010)....

    [...]

  • ...2011), spectral analysis (Croux et al. 2001), and wavelet analysis (Rua 2010)....

    [...]

  • ...Hence from a spectral density integral point of view, the frequency domain construction of comovement (e.g., Croux et al., 2001) can be approximated by the state-dependent correlation matrix....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a comparative study of broad economic developments during the 20 years of the European Monetary Union (EMU) and 20 years (EMS) is presented, showing that the EMU does not display a macroeconomic development inferior to the EMS period.
Abstract: Abstract This comparative study looks at broad economic developments during the 20 years of the European Monetary Union (EMU) and 20 years of the European Monetary System (EMS). We analyze the economic performance by looking at a set of macroeconomic variables. The analysis of macroeconomic performance includes two perspectives: one is internal, i. e. how did the countries perform relative to each other; the other is external, i. e. how did the group of member countries perform vis-à-vis other countries. Overall, the analysis of the two periods suggest that the EMU does not display a macroeconomic development inferior to the EMS period. On the contrary, some crucial macroeconomic indicators point to a greater stability during the EMU period compared to the EMS period.

3 citations


Cites background from "A Measure of Comovement for Economi..."

  • ...Croux et al. (2001) present a good survey on how to measure co-movements of economic variables. cycles have been more synchronized during the EMU period than they were during the EMS period....

    [...]

Journal ArticleDOI
09 Apr 2018
TL;DR: This study proposes a model-free approach for electricity price forcasting (EPF), based on Partial Wavelet Coherency (PWC) and Multiple Wavelet coherency(MWC) method, which are capable of uncovering the coherent time intervals simultaneously for time and frequency domains between the examined time series.
Abstract: The aim of this paper is to bring out a new perspective for Electricity price forecasting. Numerous studies have focused on forecasting the day-ahead or long-term price forecasting of electricity, ...

3 citations

References
More filters
Journal ArticleDOI
TL;DR: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples.
Abstract: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x first achieves stationarity after differencing, but a linear combination a'x is already stationary, the time series x are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a becomes a matrix. Interpreting a'x,= 0 as a long run equilibrium, co-integration implies that deviations from equilibrium are stationary, with finite variance, even though the series themselves are nonstationary and have infinite variance. The paper presents a representation theorem based on Granger (1983), which connects the moving average, autoregressive, and error correction representations for co-integrated systems. A vector autoregression in differenced variables is incompatible with these representations. Estimation of these models is discussed and a simple but asymptotically efficient two-step estimator is proposed. Testing for co-integration combines the problems of unit root tests and tests with parameters unidentified under the null. Seven statistics are formulated and analyzed. The critical values of these statistics are calculated based on a Monte Carlo simulation. Using these critical values, the power properties of the tests are examined and one test procedure is recommended for application. In a series of examples it is found that consumption and income are co-integrated, wages and prices are not, short and long interest rates are, and nominal GNP is co-integrated with M2, but not M1, M3, or aggregate liquid assets.

27,170 citations

01 Jan 1987

3,983 citations


"A Measure of Comovement for Economi..." refers background in this paper

  • ...In this category belong the following three concepts: (i) the idea of co-integration (Engle & Granger, 1987): two processes are co-integrated if the spectral density at frequency zero has rank one; (ii) codependence (Gourieroux & Peaucelle, 1992), which refers to linear combinations of correlated…...

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors present evidence that most of the unemployment fluctuations of the seventies (unlike those in the sixties) were induced by unusual structural shifts within the U.S. economy.
Abstract: A substantial fraction of cyclical unemployment is better characterized as fluctuations of the "frictional" or "natural" rate than as deviations from some relatively stable natural rate. Shifts of employment demand between sectors of the economy necessitate continuous labor reallocation. Since it takes time for workers to find new jobs, some unemployment is unavoidable. This paper presents evidence that most of the unemployment fluctuations of the seventies (unlike those in the sixties) were induced by unusual structural shifts within the U.S. economy. Simple time-series models of layoffs and unemployment are constructed that include a measure of structural shifts within the labor market. These models are estimated and a derived natural rate series is constructed.

1,128 citations

ReportDOI
TL;DR: In this paper, the authors introduce a class of statistical tests for the hypothesis that some feature that is present in each of several variables is common to them, which are data properties such as serial correlation, trends, seasonality, heteroscedasticity, auto-regression, and excess kurtosis.
Abstract: This article introduces a class of statistical tests for the hypothesis that some feature that is present in each of several variables is common to them. Features are data properties such as serial correlation, trends, seasonality, heteroscedasticity, autoregressive conditional hetero-scedasticity, and excess kurtosis. A feature is detected by a hypothesis test taking no feature as the null, and a common feature is detected by a test that finds linear combinations of variables with no feature. Often, an exact asymptotic critical value can be obtained that is simply a test of overidentifying restrictions in an instrumental variable regression. This article tests for a common international business cycle.

550 citations

Posted Content
TL;DR: The existence of a serial correlation common feature among the first differences of a set of I(1) variables implies the existence of common cycle in the Beveridge-Nelson-Stock-Watson decomposition of those variables as mentioned in this paper.
Abstract: The existence of a serial correlation common feature among the first differences of a set of I(1) variables implies the existence of a common cycle in the Beveridge-Nelson-Stock-Watson decomposition of those variables. A test for the existence of common cycles among cointegrated variables is developed. The test is used to examine the validity of the common trend-common cycle structure implied by Flavin's excess sensitivity hypothesis and Campbell and Mankiw's mixture of rational expectations and rule-of-thumb hypothesis for consumption and income. Linear independence between the cointegration and the cofeature vectors is exploited to decompose consumption and income into their trend and cycle components. Copyright 1993 by John Wiley & Sons, Ltd.

511 citations