Matteo Barigozzi

Identifying the community structure of the international-trade multi-network

We study the community structure of the multi-network of commodity-specific trade relations among world countries over the 1992–2003 period. We compare structures across commodities and time by means of the normalized mutual information index (NMI). We also compare them with exogenous community structures induced by geography and regional trade agreements. We find that commodity-specific community structures are very heterogeneous and much more fragmented than that characterizing the aggregate ITN. This shows that the aggregate properties of the ITN may result (and be very different) from the aggregation of very diverse commodity-specific layers of the multi-network. We also show that commodity-specific community structures, especially those related to the chemical sector, are becoming more and more similar to the aggregate one. Finally, our findings suggest that geography-induced partitions of our set of countries are much more correlated with observed community structures than partitions induced by regional-trade agreements. This result strengthens previous findings from the empirical literature on trade.

NETS: Network Estimation for Time Series

This work proposes novel network analysis techniques for multivariate time series. We define the network of a multivariate time series as a graph where vertices denote the components of the process and edges denote non zero long run partial correlations. We then introduce a two step LASSO procedure, called NETS, to estimate high dimensional sparse Long Run Partial Correlation networks. This approach is based on a VAR approximation of the process and allows to decompose the long run linkages into the contribution of the dynamic and contemporaneous dependence relations of the system. The large sample properties of the estimator are analysed and we establish conditions for consistent selection and estimation of the non zero long run partial correlations. The methodology is illustrated with an application to a panel of U.S. bluechips.

ON APPROXIMATING THE DISTRIBUTIONS OF GOODNESS-OF-FIT TEST STATISTICS BASED ON THE EMPIRICAL DISTRIBUTION FUNCTION: THE CASE OF UNKNOWN PARAMETERS

This paper discusses some problems possibly arising when approximating via Monte-Carlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to re-estimate unknown parameters on each simulated Monte-Carlo sample — and thus avoiding to employ this information to build the test statistic — may lead to wrong, overly-conservative. Furthermore, we present some simple examples suggesting that the impact of this possible mistake may turn out to be dramatic and does not vanish as the sample size increases.

Community Structure in the Multi-network of International Trade

We study the community structure of the multi-network of commodity-specific and aggregate trade relations among world countries over the 1992-2003 period. We compare structures across products and time by means of the normalized mutual information index (NMI). We also compare them with exogenous community structures induced by geographical distances and regional trade agreements. We find that: (i) plastics and mineral fuels —and in general commodities belonging to the chemical sector— have the highest similarity with aggregate trade communities; (ii) both at aggregated and disaggregated levels, physical variables such as geographical distance are more correlated with the observed trade fluxes than regional-trade agreements.

Dynamic Factor Models, Cointegration, and Error Correction Mechanisms

The paper studies Non-Stationary Dynamic Factor Models such that: (1) the factors Ft are I(1) and singular, i.e. Ft has dimension r and is driven by a q-dimensional white noise, the common shocks, with q < r, and (2) the idiosyncratic components are I(1). We show that Ft is driven by r-c permanent shocks, where c is the cointegration rank of Ft, and q - (r - c) < c transitory shocks, thus the same result as in the non-singular case for the permanent shocks but not for the transitory shocks. Our main result is obtained by combining the classic Granger Representation Theorem with recent results by Anderson and Deistler on singular stochastic vectors: if (1 - L)Ft is singular and has rational spectral density then, for generic values of the parameters, Ft has an autoregressive representation with a finite-degree matrix polynomial fulfilling the restrictions of a Vector Error Correction Mechanism with c error terms. This result is the basis for consistent estimation of Non-Stationary Dynamic Factor Models. The relationship between cointegration of the factors and cointegration of the observable variables is also discussed.

Generalized dynamic factor models and volatilities: recovering the market volatility shocks

Decomposing volatilities into a common market‐driven component and an idiosyncratic item‐specific component is an important issue in financial econometrics. However, this requires the statistical analysis of large panels of time series, and hence faces the usual challenges associated with high‐dimensional data. Factor model methods in such a context are an ideal tool, but they do not readily apply to the analysis of volatilities. Focusing on the reconstruction of the unobserved market shocks and the way they are loaded by the various items (stocks) in the panel, we propose an entirely non‐parametric and model‐free two‐step general dynamic factor approach to the problem, which avoids the usual curse of dimensionality. Applied to the Standard & Poors 100 asset return data set, the method provides evidence that a non‐negligible proportion of the market‐driven volatility of returns originates in the volatilities of the idiosyncratic components of returns.

A network analysis of the volatility of high dimensional financial series

We consider weighted directed networks for analysing, over the period 2000-2013, the interdependencies between volatilities of a large panel of stocks belonging to the S&P100 index. In particular, we focus on the so-called Long-Run Variance Decomposition Network (LVDN), where the nodes are stocks, and the weight associated with edge (i, j) represents the proportion of h-step-ahead forecast error variance of variable i accounted for by variable j’s innovations. To overcome the curse of dimensionality, we decompose the panel into a component driven by few global, market-wide, factors, and an idiosyncratic one modelled by means of a sparse vector autoregression (VAR) model. Inversion of the VAR together with suitable identification restrictions, produces the estimated network, by means of which we can assess how systemic each firm is. Our analysis demonstrates the prominent role of financial firms as sources of contagion, especially during the 2007-2008 crisis.In this paper, we define weighted directed networks for large panels of financial time series wherethe edges and the associated weights are reflecting the dynamic conditional correlation structureof the panel. Those networks produce a most informative picture of the interconnections amongthe various series in the panel. In particular, we are combining this network-based analysis and ageneral dynamic factor decomposition in a study of the volatilities of the stocks of the Standard&Poor’s 100 index over the period 2000-2013. This approach allows us to decompose the panelinto two components which represent the two main sources of variation of financial time series:common or market shocks, and the stock-specific or idiosyncratic ones. While the common components,driven by market shocks, are related to the non-diversifiable or systematic components ofrisk, the idiosyncratic components show important interdependencies which are nicely describedthrough network structures. Those networks shed some light on the contagion phenomenons associatedwith financial crises, and help assessing how systemic a given firm is likely to be. We showhow to estimate them by combining dynamic principal components and sparse VAR techniques.The results provide evidence of high positive intra-sectoral and lower, but nevertheless quite important,negative inter-sectoral, dependencies, the Energy and Financials sectors being the mostinterconnected ones. In particular, the Financials stocks appear to be the most central vertices inthe network, making them the main source of contagion.

Non-Stationary Dynamic Factor Models for Large Datasets

We study a Large-Dimensional Non-Stationary Dynamic Factor Model where (1) the factors Ft are I (1) and singular, that is Ft has dimension r and is driven by q dynamic shocks with q less than r, (2) the idiosyncratic components are either I (0) or I (1). Under these assumption the factors Ft are cointegrated and modeled by a singular Error Correction Model. We provide conditions for consistent estimation, as both the cross-sectional size n, and the time dimension T, go to infinity, of the factors, the loadings, the shocks, the ECM coefficients and therefore the Impulse Response Functions. Finally, the numerical properties of our estimator are explored by means of a MonteCarlo exercise and of a real-data application, in which we study the effects of monetary policy and supply shocks on the US economy.

On the Stability of Euro Area Money Demand and its Implications for Monetary Policy

Following the renewed interest for the role of money and credit in monetary policy, we assess the usefulness of long-run money demand equations for the European Central Bank. We perform a model evaluation exercise by means of the time varying cointegration test by Bierens and Martins (2010), comparing different models claiming to find a stable behaviour of Euro Area monetary aggregate M3. A time-invariant long-run relation is not rejected by data, when correctly specifying the set of explanatory variables. In particular, we find that the most relevant drivers of real money balances are a speculative motive represented by international financial markets, and a precautionary motive proxied by changes in the unemployment rate. We then estimate a stable cointegrated VAR including both motives, which allows us (i) to explain the anomalous behavior of M3 in the last decade and during the recent Great Financial Crisis, and (ii) to build a leading indicator of stock market busts. Our results have not negligible implications for policy decisions aimed at achieving financial stability.We revisit the usefulness of long-run money demand equations for the European Central Bank. We first conduct a model evaluation exercise by means of a recent timeovarying cointegration test. A stable relation for euro area M3 is not rejected by data only when accounting for both a speculative motive, represented by international financial markets, and a precautionary motive, proxied by changes in the unemployment rate. Second, relying on this finding, we propose and estimate a novel time-invariant specification for money demand which allows us (i) to build a leading indicator of stock market busts and (ii) to describe the anomalous behavior of M3 in the last decade. Excess liquidity matters for both financial and price stability.

Simultaneous multiple change-point and factor analysis for high-dimensional time series

We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate the number and locations of change-points consistently as well as identifying whether they originate in the common or idiosyncratic components. Through the use of wavelets, we transform the problem of change-point detection in the second-order structure of a high-dimensional time series, into the (relatively easier) problem of change-point detection in the means of high-dimensional panel data. Also, our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change-points by adopting a screening procedure. We further show that consistent factor analysis is achieved over each segment defined by the change-points estimated by the proposed methodology. In extensive simulation studies, we observe that factor analysis prior to change-point detection improves the detectability of change-points, and identify and describe an interesting ‘spillover’ effect in which substantial breaks in the idiosyncratic components get, naturally enough, identified as change-points in the common components, which prompts us to regard the corresponding change-points as also acting as a form of ‘factors’. Our methodology is implemented in the R package factorcpt, available from CRAN.