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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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Posted Content
01 Jan 2012-Series
TL;DR: In this paper, the authors employ a two-step approach in investigating the dynamic transmission chan- nels under which globalization factors foster technical efficiency by combining a dynamic efficiency analysis in the stochastic frontier framework, and a time series approach based on VAR and spectral analysis.
Abstract: We employ a two-step approach in investigating the dynamic transmission chan- nels under which globalization factors foster technical efficiency by combining a dynamic efficiency analysis in the stochastic frontier framework, and a time series approach based on VAR and spectral analysis. Using the dataset of the 18 EU countries over 1970-2004, we find that both import and FDI are significant factors in spreading efficiency externalities and thus accelerating technology catch-up in the EU. In particular, the impacts of the import are more prominent in the short-run while those of FDI play a more important role over the longer-run. Furthermore, the impacts of the import are pro-cyclical only in the short-run whereas those of FDI are pro-cyclical mostly over the medium- to the long-run. This evidence is broadly consistent with the sample observation that the recent slowdown of the EU productivity has been closely related to the corresponding FDI decline espe- cially after 2000. Hence, any protection-oriented policy will be likely to be more detrimental for the EU.

24 citations

Journal ArticleDOI
TL;DR: The proposed method for estimating a codispersion coefficient is useful for quantifying spatial associations between two variables measured at the same location and performs better than the classic Matheron's estimator.
Abstract: We propose a new method for estimating a codispersion coefficient to quantify the association between two spatial variables. Our proposal is based on a Nadaraya–Watson version of the codispersion coefficient through a suitable kernel. Under regularity conditions, we derive expressions for the bias and mean square error for a kernel version of the cross-variogram and establish the consistency of a Nadaraya–Watson estimator of the codispersion coefficient. In addition, we propose a bandwidth selection method for both the variogram and the cross-variogram. Monte Carlo simulations support the theoretical findings, and as a result, the new proposal performs better than the classic Matheron's estimator. The proposed method is useful for quantifying spatial associations between two variables measured at the same location. Finally, we study forest data concerning the relationship among the tree height, basal area, elevation and slope of Pinus radiata plantations. A two-dimensional codispersion map is constructed ...

24 citations


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

  • ...The codispersion coefficient has also been studied in time series to address how two time sequences change concurrently; it is a geometrically natural comovement coefficient since it compares proportional slopes at matched pairs of points across sequences (Croux, Forni, and Reichlin 2001)....

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors exploit dynamic correlations to estimate determinants of output comovement between OECD countries, showing that trade intensity, financial integration, and specialization patterns have significantly different effects on comovements at different frequencies.

24 citations

Journal ArticleDOI
TL;DR: This commentary provides the background of how coverage decisions for new medical technologies are currently made in the United States and focuses on the statistical issues regarding how to use the ensemble of information for inferring comparative effectiveness.
Abstract: The assumption that comparative effectiveness research will provide timely, relevant evidence rests on changing the current framework for assembling evidence. In this commentary, we provide the background of how coverage decisions for new medical technologies are currently made in the United States. We focus on the statistical issues regarding how to use the ensemble of information for inferring comparative effectiveness. It is clear a paradigm shift in how clinical information is integrated in real-world settings to establish effectiveness is required.

23 citations

Journal ArticleDOI
TL;DR: The authors showed that the detrending of financial variables with the Hodrick and Prescott (1981, 1997) (HP) and band-pass filters leads to spurious cycles, i.e., cycles that exceed the duration of regular business cycles.
Abstract: I show that the detrending of financial variables with the Hodrick and Prescott (1981, 1997) (HP) and band-pass filters leads to spurious cycles. I find that distortions become especially severe when considering medium-term cycles, i.e., cycles that exceed the duration of regular business cycles. In particular, these medium-term filters amplify the variances of cycles of duration around 20 to 30 years up to a factor of 204, completely cancelling out shorter-term fluctuations. This is important because it is common practice, and recommended under Basel III, to extract medium-term cycles using such filters; e.g., the HP filter with a smoothing parameter of 400,000. In addition, I find that financial cycle facts, i.e., differing amplitude, duration, and synchronisation of cycles in financial variables relative to cycles in GDP, are robust. For HP and band-pass filters, differences to GDP become marginal due to spurious cycles.

23 citations


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

  • ...Thus, while dynamic correlation cohesion – as proposed by Croux et al. (2001) – can be used to study linear similarities of two processes at each frequency ω, the suggested measure provides information on the relative importance of frequencies with respect to the indicators’ overall fluctuations....

    [...]

  • ...For instance, Croux et al. (2001) show that while a white noise process and its one-period lagged value have zero correlation, the co-spectrum indicates perfect positive correlation in the long run (at frequency 0) and perfect negative in the short run (at frequency π), overall, however, integrating to zero. Thus, dynamic correlation makes it possible to gain more insights on the linear relation of two stationary processes than the standard correlation measure. Finally, note that dynamic power cohesion differs from cohesion based on dynamic correlation (see Croux et al. (2001)) by relating the co-spectrum to the overall standard deviations and not the respective auto-spectra at frequency ω. Thus, while dynamic correlation cohesion – as proposed by Croux et al. (2001) – can be used to study linear similarities of two processes at each frequency ω, the suggested measure provides information on the relative importance of frequencies with respect to the indicators’ overall fluctuations....

    [...]

  • ...For instance, Croux et al. (2001) show that while a white noise process and its one-period lagged value have zero correlation, the co-spectrum indicates perfect positive correlation in the long run (at frequency 0) and perfect negative in the short run (at frequency π), overall, however, integrating to zero....

    [...]

  • ...For instance, Croux et al. (2001) show that while a white noise process and its one-period lagged value have zero correlation, the co-spectrum indicates perfect positive correlation in the long run (at frequency 0) and perfect negative in the short run (at frequency π), overall, however, integrating to zero. Thus, dynamic correlation makes it possible to gain more insights on the linear relation of two stationary processes than the standard correlation measure. Finally, note that dynamic power cohesion differs from cohesion based on dynamic correlation (see Croux et al. (2001)) by relating the co-spectrum to the overall standard deviations and not the respective auto-spectra at frequency ω....

    [...]

  • ...Finally, note that dynamic power cohesion differs from cohesion based on dynamic correlation (see Croux et al. (2001)) by relating the co-spectrum to the overall standard deviations and not the respective auto-spectra at frequency ω....

    [...]

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