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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
More filters
Dissertation
01 Jan 2007
TL;DR: In this article, the forecast performance of factor models using a meta-analysis has been investigated, and it has been shown that factor models are relatively better at predicting US and euro-area than British variables, and they work relatively better on average for inflation than for output.
Abstract: This dissertation both examines the forecast performance of large-scale factor models (chapter II) and employs these models to investigate international economic comovements (chapters III and IV). Chapter II investigates the forecast performance of factor models using a meta-analysis. We summarize the seemingly ambiguous results from existing studies which evaluate the forecast performance of factor models, and we identify the determinants of forecast quality in factor models using a meta-analysis. The main focus of chapter II has been the relative forecast performance of large-scale dynamic factor models for real economic activity and inflation. This meta-analysis has the main advantage of being less prone to subjectivity regarding the choice of papers and results than narrative survey articles. Our analysis reaches several conclusions. First, forecasts can be improved if information from large datasets is exploited. This has been derived from our finding that factor models outperform smaller time series models. Alternative methods which are also able to exploit information from large datasets even outperform or are comparable to factor models. This is also supported by the result that the size of the dataset from which the factors are extracted positively affects the predictions. Second, the target variable itself alters the quality of factor forecasts. According to our analysis, factor models are relatively better at predicting US and euro-area than British variables, and they work relatively better on average for inflation than for output. Third, it can pay off to carefully specify the model. More complex factor estimation techniques by Forni et al. (2000) and Kapetanios and Marcellino (2004) are shown to be better at predicting output than the Stock and Watson (1998, 2002a) approach which is less demanding on the specification. Chapter III estimates the extent and the dynamics of the transmission of macroeconomic shocks from the US to Germany between 1975 and 2002. From a large dataset containing almost 300 German and US macroeconomic variables, we estimate common factors by means of the structural dynamic factor model suggested by Forni and Reichlin (1998). We then identify US supply and demand shocks, and we investigate the impact of these shocks on German macroeconomic variables and variables covering the various transmission channels. We finally decompose the forecast error of German GDP for the second half of the 1990s and the recession phase in the US in 2001. The analysis is one of the first applications of the structural factor model to an international macroeconomic topic. Also, the focus on transmission channels is new. A US demand shock leads to a significant rise of German GDP; the impact dies out after a year. German GDP also goes up after a US supply shock, but the impulse response is insignificant. The trade channel dominates. We are not able to draw clear conclusions on the role of financial markets and the confidence channel. A historical decomposition of German GDP finally shows that negative domestic factors overcompensated positive influences from the US between 1995 and 2000. In contrast, the US recession in 2001 was the main culprit for the German slump. Chapter IV is motivated by the observation that comovements at business-cycle and long-run frequencies among EMU-members are far from perfect, and there is still persistent heterogeneity. We establish stylized facts about comovements and heterogeneity of output and price developments in EMU member states. We combine the non-stationary dynamic factor approach of Bai and Ng (2004) and the structural factor setup based on Forni and Reichlin (1998) and apply them to a newly constructed partly non-stationary dataset containing a total of 173 quarterly macroeconomic times series from 1981 to 2003, which mainly capture economic developments in euro-area countries. Previous studies that examine economic linkages in the euro area fit stationary factor models to stationary datasets. The Bai and Ng (2004) approach allows us to examine comovements and heterogeneity without imposing restrictions on the persistence of the variables and their components (which are allowed to be non-stationary) and hence also on comovements and heterogeneity. Second, most of the previous studies are not concerned about the economic interpretation of the factors. Chapter IV investigates the transmission of a rich set of identified structural shocks. We find that individual euro-area countries� output and prices are hit by permanent common and idiosyncratic shocks. Idiosyncratic shocks and adjustments to them seem to be mainly responsible for cross-country heterogeneity throughout most of the sample period. The asymmetric transmission of common shocks seems to play a minor role. We find no strong evidence that some common shocks lead to greater cross-country heterogeneity than others.

3 citations

Posted Content
TL;DR: In this paper, the authors analyzed the business cycle movements of the EU, ASEAN+3, NAFTA, MERCOSUR and SAARC regions to investigate why the subprime mortgage crisis of 2007 did not spread globally compared to the crisis that began with the fall of Lehman Brothers in September 2008.
Abstract: The recent global recession requires policy makers to identify the relative importance of shock transmission mechanisms in each region and devise counter policy measures against future idiosyncratic shocks. In the last decade, world dynamics have changed considerably due to increased openness and integration requiring considering business cycles at regional levels. This paper analyzes the business cycle movements of the EU, ASEAN+3, NAFTA, MERCOSUR and SAARC regions to investigate why the subprime mortgage crisis of 2007 did not spread globally compared to the crisis that began with the fall of Lehman Brothers in September 2008. Employing a Panel Vector Autoregressive framework (PVEC), this study finds that the subprime mortgage crisis shock originated in the real sector (falling US housing prices) and was transmitted through trade variables. Due to absence of short term trade variables transmission mechanism in all regions except the MERCOSUR and SAARC, the shock did not spread widely to other regions. Even in the MERCOSUR and SAARC, due to limited goods exports exposure to the US, the shock was not significant. Resultantly, these regions exhibited a decoupling phenomenon during the subprime mortgage crisis. In contrast, the second shock originated with the fall of Lehman Brothers in 2008 and was transmitted through financial variables. Due to the presence of the short term causal relationship of the financial variable with GDP in all regions except SAARC, the slowdown contagion spread to most regions. As a result, the slowdown triggered the trade variables shock transmission mechanism and the SAARC region was also affected. Consequently, a business cycle convergence phenomenon was observed in the regions. Therefore, business cycles decoupling and convergence phenomena in the regions depend not only on the origin of the shock but also on the relative importance of the transmission mechanisms in each region.

3 citations


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

  • ...These include dynamic correlations (Croux et al. 2001; Fidrmuc et al. 2008), dynamic factor models (Kose et al. 2008; Gregory et al. 1997) which focus on the outcome....

    [...]

Journal ArticleDOI
01 Jan 2015
TL;DR: In this article, the authors compared the performance of the Baxter-King, the FEC, and the Hamming window filter for the identification of a business cycle in selected EU countries.
Abstract: We compare three filters commonly used for business cycle analysis: the Baxter-King, the Christiano-Fitzgerald and the Hamming window filter. Empirical contribution of the paper is numerical evaluation of the approximation of the ideal band-pass filters in the discussion of the filters' theoretical properties (gain and attenuation within the business cycle frequencies, as well as the leakage in the remaining frequencies). We consider the truncation factor for the BaxterKing filter and the sample size for the latter two. We show that the leakage and attenuation of the Christiano-Fitzgerald and the Hamming window filter perform similarly across the range of chosen sample sizes and better than the Baxter-King filter. Moreover, we apply the filters to data of selected EU countries and point out differences in their estimation of growth business cycles. Our findings indicate that Christiano-Fitzgerald filter and the Hamming window both are appropriate for the identification of a business cycle. The Hamming window filter introduces smaller attenuation near the edges but in case of small samples its approximation of ideal filter is very rough.

3 citations


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

  • ...Identifi cation of cyclical fl uctuation in the context of convergence analysis is used in Drake and Mills (2011). They focused on examination of properties of GDP in the euro area with the stress to the adoption euro in 1999....

    [...]

  • ...Croux et al. (2001) focused on theory and empirics of comovement of economic variables asking whether it can be explained by large aggregate shocks or if the answer should be found in non-linear propagation mechanism....

    [...]

  • ...Identifi cation of cyclical fl uctuation in the context of convergence analysis is used in Drake and Mills (2011). They focused on examination of properties of GDP in the euro area with the stress to the adoption euro in 1999. Drake and Mills (2011) have particular interest in the time series decomposition into trend and cyclical components using Christiano-Fitzgerald fi lter, and the Baxter-King fi lter....

    [...]

  • ...From a methodical point of view in the last decade the time domain and the frequency domain (Iacobucci, 2003; Iacobucci and Noullez, 2005) analysis has been extended to an integrated view of the time-frequency domain (Croux et al., 2001; Hallett and Richter, 2007; Rua, 2010; Maršálek et al., 2013)....

    [...]

  • ...Croux et al. (2001) focused on theory and empirics of comovement of economic variables asking whether it can be explained by large aggregate shocks or if the answer should be found in non-linear propagation mechanism. They propose dynamic correlation and cohesion as the relevant measurement for comovement analysis. Macroeconomic literature often presents standard approach of correlation pre-fi ltered (high-pass or band-pass fi lter application) data. Croux et al. (2001) discuss the difference between correlation of pre-fi ltered data and application of dynamic measure....

    [...]

Posted Content
TL;DR: In this paper, a multi-output Gaussian process (MOGP) with expressive covariance functions is proposed to learn the relationships among financial time series by modeling them through a multioutput Gaussian process.
Abstract: In Financial Signal Processing, multiple time series such as financial indicators, stock prices and exchange rates are strongly coupled due to their dependence on the latent state of the market and therefore they are required to be jointly analysed. We focus on learning the relationships among financial time series by modelling them through a multi-output Gaussian process (MOGP) with expressive covariance functions. Learning these market dependencies among financial series is crucial for the imputation and prediction of financial observations. The proposed model is validated experimentally on two real-world financial datasets for which their correlations across channels are analysed. We compare our model against other MOGPs and the independent Gaussian process on real financial data.

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