Estimation and forecasting in large datasets with conditionally heteroskedastic dynamic common factors

We propose a new method for multivariate forecasting which combines Dynamic Factor and multivariate GARCH models. The information contained in large datasets is captured by few dynamic common factors, which we assume being conditionally heteroskedastic. After presenting the model, we propose a multi-step estimation technique which combines asymptotic principal components and multivariate GARCH. We also prove consistency of the estimated conditional covariances. We present simulation results in order to assess the finite sample properties of the estimation technique. Finally, we carry out two empirical applications respectively on macroeconomic series, with a particular focus on different measures of inflation, and on financial asset returns. Our model outperforms the benchmarks in fore-casting the inflation level, its conditional variance and the volatility of returns. Moreover, we are able to predict all the conditional covariances among the observable series. JEL Classification: C52, C53Conditional Covariance, Dynamic Factor Models, Inflation forecasting, multivariate GARCH, Volatility Forecasting

Generalized Dynamic Factor Model + GARCH Exploiting Multivariate Information for Univariate Prediction

We propose a new model for multivariate forecasting which combines the Generalized Dynamic Factor Model (GDFM)and the GARCH model. The GDFM, applied to a huge number of series, captures the multivariate information and disentangles the common and the idiosyncratic part of each series of returns. In this financial analysis, both these components are modeled as a GARCH. We compare GDFM+GARCH and standard GARCH performance on samples up to 475 series, predicting both levels and volatility of returns. While results on levels are not significantly different, on volatility the GDFM+GARCH model outperforms the standard GARCH in most cases. These results are robust with respect to different volatility proxies.Dynamic Factors, GARCH, Volatility Forecasting

A Review of Nonfundamentalness and Identification in Structural VAR Models

We review, under a historical perspective, the developement of the problem of non- fundamentalness of Moving Average (MA) representations of economic models, starting from the work by Hansen and Sargent [1980]. Nonfundamentalness typically arises when agents' information space is larger than the econometrican's one. Therefore it is impos- sible for the latter to use standard econometric techniques, as Vector AutoRegression (VAR), to estimate economic models. We re-state the conditions under which it is pos- sible to invert an MA representation in order to get an ordinary VAR, and we consider how the latter is used in the literature to assess the validity of Dynamic Stochastic Gen- eral Equilibrium models, providing some interesting examples. We believe that possible nonfundamental representations of considered models are too often neglected in the liter- ature. We consider how factor models can be seen as an alternative to VAR for assessing the validity of an economic model without having to deal with the problem of nonfun- damentalness. We then review the works by Lippi and Reichlin [1993] and Lippi and Reichlin [1994] which are the first attempts to give to nonfundamental representations the economic relevance that they deserve, and to outline a method to obtain such repre- sentations starting from an estimated VAR.Nonfundamentalness, Structural VAR, Dynamic Stochastic General Equilibrium Models, Factor Models

A robust criterion for determining the number of static factors in approximate factor models.

We propose a refinement of the criterion by Bai and Ng [2002] for determining the number of static factors in factor models with large datasets. It consists in multi-plying the penalty function by a constant which tunes the penalizing power of the function itself as in the Hallin and Liška [2007] criterion for the number of dynamic factors. By iteratively evaluating the criterion for different values of this constant, we achieve more robust results than in the case of fixed penalty function. This is shown by means of Monte Carlo simulations on seven data generating processes, including heteroskedastic processes, on samples of different size. Two empirical applications are carried out on a macroeconomic and a financial dataset. JEL Classification: C52Approximate factor models, Information criterion, Number of factors

A review of nonfundamentalness and identification in structural VAR models

We review, under a historical perspective, the development of the problem of nonfundamentalness of Moving Average (MA) representations of economic models. Nonfundamentalness typically arises when agents’ information space is larger than the econometrician’s one. Therefore it is impossible for the latter to use standard econometric techniques, as Vector AutoRegression (VAR), to estimate economic models. We restate the conditions under which it is possible to invert an MA representation in order to get an ordinary VAR and identify the shocks, which in a VAR are fundamental by construction. By reviewing the work by Lippi and Reichlin [1993] we show that nonfundamental shocks may be very different from fundamental shocks. Therefore, nonfundamental representations should not be ruled out by assumption and indeed methods to detect nonfundamentalness have been recently proposed in the literature. Moreover, Structural VAR (SVAR) can be legitimately used for assessing the validity of Dynamic Stochastic General Equilibrium models only if the representation associated with the economic model is fundamental. Factor models can be an alternative to SVAR for validation purposes as they do not have to deal with the problem of nonfundamentalness. JEL Classification: C32, C51, C52dynamic stochastic general equilibrium models, Factor models, Nonfundamentalness, Structural VAR

On the distributional properties of household consumption expenditures. The case of Italy.

In this paper we explore the statistical properties of the distributions of consumption expenditures for a large sample of Italian households in the period 1989-2004. Goodness-of-fit tests show that household aggregate (and age-conditioned) consumption distributions are not log-normal. Rather, their logs can be invariably characterized by asymmetric exponential-power densities. Departures from log-normality are mainly due to the presence of thick lower tails coexisting with upper tails thinner than Gaussian ones. The emergence of this irreducible heterogeneity in statistical patterns casts some doubts on the attempts to explain log-normality of household consumption patterns by means of simple models based on Gibrat's Law applied to permanent income and marginal utility.Consumption, Asymmetric Exponential-Power Distribution, Income Distribution, Log-Normal Distribution, Gibrat's Law

The distribution of households consumption-expenditure budget shares

This paper explores the statistical properties of house-hold consumption-expenditure budget share distributions —defined as the share of household total expenditure spent for purchasing a specific category of commodities— for a large sample of Italian households in the period 1989-2004. We find that household budget share distributions are fairly stable over time for each specific category, but profoundly heterogeneous across commodity categories. We then derive a para-metric density that is able to satisfactorily characterize household budget share distributions and: (i) is consistent with the observed statistical properties of the underlying levels of household consumption-expenditure distributions; (ii) can accommodate the observed across-category heterogeneity in household budget share distributions. Finally, we taxonomize commodity categories according to the estimated parameters of the proposed density. We show that the resulting classification is consistent with the traditional economic scheme that labels commodities as necessary, luxury or inferior. JEL Classification: D3, D12, C12.Budget Shares, Household Consumption Expenditure, Sum of Log-Normal Distributions

A review of nonfundamentalness and identification in structural VAR models

We review, under a historical perspective, the developement of the problem of non-fundamentalness of Moving Average (MA) representations of economic models, starting from the work by Hansen and Sargent [1980]. Nonfundamentalness typically arises when agents' information space is larger than the econometrican's one. Therefore it is impossible for the latter to use standard econometric techniques, as Vector AutoRegression (VAR), to estimate economic models. We re-state the conditions under which it is possible to invert an MA representation in order to get an ordinary VAR, and we consider how the latter is used in the literature to assess the validity of Dynamic Stochastic General Equilibrium models, providing some interesting examples. We believe that possible nonfundamental representations of considered models are too often neglected in the literature. We consider how factor models can be seen as an alternative to VAR for assessing the validity of an economic model without having to deal with the problem of nonfundamentalness. We then review the works by Lippi and Reichlin [1993] and Lippi and Reichlin [1994] which are the first attempts to give to nonfundamental representations the economic relevance that they deserve, and to outline a method to obtain such representations starting from an estimated VAR

A robust criterion for determining the number of static factors in approximate factor models.

We propose a refinement of the criterion by Bai and Ng [2002] for determining the number of static factors in factor models with large datasets. It consists in multi-plying the penalty function by a constant which tunes the penalizing power of the function itself as in the Hallin and Liška [2007] criterion for the number of dynamic factors. By iteratively evaluating the criterion for different values of this constant, we achieve more robust results than in the case of fixed penalty function. This is shown by means of Monte Carlo simulations on seven data generating processes, including heteroskedastic processes, on samples of different size. Two empirical applications are carried out on a macroeconomic and a financial dataset

Dynamic factor GARCH: Multivariate volatility forecast for a large number of series

We propose a new method for multivariate forecasting which combines the Generalized Dynamic Factor Model (GDFM) and the multivariate Generalized Autoregressive Conditionally Heteroskedastic (GARCH) model. We assume that the dynamic common factors are conditionally heteroskedastic. The GDFM, applied to a large number of series, captures the multivariate information and disentangles the common and the idiosyncratic part of each series; it also provides a first identification and estimation of the dynamic factors governing the data set. A time-varying correlation GARCH model applied on the estimated dynamic factors finds the parameters governing their covariances ’ evolution. A method is suggested for estimating and predicting conditional variances and covariances of the original data series. We suggest also a modified version of the Kalman filter as a way to get a more precise estimation of the static and dynamic factors ’ in-sample levels and covariances in order to achieve better forecasts. Simulation results on different panels with large time and cross sections are presented. Finally, we carry out an empirical application aiming at comparing estimates and predictions of the volatility of financial asset returns. The Dynamic Factor GARCH model outperforms the univariate GARCH