159 research outputs found
Sequential testing for structural stability in approximate factor models
We develop a monitoring procedure to detect changes in a large approximate
factor model. Letting be the number of common factors, we base our
statistics on the fact that the -th eigenvalue of the
sample covariance matrix is bounded under the null of no change, whereas it
becomes spiked under changes. Given that sample eigenvalues cannot be estimated
consistently under the null, we randomise the test statistic, obtaining a
sequence of \textit{i.i.d} statistics, which are used for the monitoring
scheme. Numerical evidence shows a very small probability of false detections,
and tight detection times of change-points
Consistent estimation of high-dimensional factor models when the factor number is over-estimated
A high-dimensional -factor model for an -dimensional vector time series
is characterised by the presence of a large eigengap (increasing with )
between the -th and the -th largest eigenvalues of the covariance
matrix. Consequently, Principal Component (PC) analysis is the most popular
estimation method for factor models and its consistency, when is correctly
estimated, is well-established in the literature. However, popular factor
number estimators often suffer from the lack of an obvious eigengap in
empirical eigenvalues and tend to over-estimate due, for example, to the
existence of non-pervasive factors affecting only a subset of the series. We
show that the errors in the PC estimators resulting from the over-estimation of
are non-negligible, which in turn lead to the violation of the conditions
required for factor-based large covariance estimation. To remedy this, we
propose new estimators of the factor model based on scaling the entries of the
sample eigenvectors. We show both theoretically and numerically that the
proposed estimators successfully control for the over-estimation error, and
investigate their performance when applied to risk minimisation of a portfolio
of financial time series
A Multivariate Perspective for Modeling and Forecasting Inflation's Conditional Mean and Variance
We test the importance of multivariate information for modelling and forecasting in- flation's conditional mean and variance. In the literature, the existence of inflation's conditional heteroskedasticity has been debated for years, as it seemed to appear only in some datasets and for some lag lengths. This phenomenon might be due to the fact that inflation depends on a linear combination of economy-wide dynamic common fac- tors, some of which are conditionally heteroskedastic and some are not. Modelling the conditional heteroskedasticity of the common factors can thus improve the forecasts of inflation's conditional mean and variance. Moreover, it allows to detect and predict con- ditional correlations between inflation and other macroeconomic variables, correlations that might be exploited when planning monetary policies. The Dynamic Factor GARCH (DF-GARCH) by Alessi et al. [2006] is used here to exploit the relations between inflation and the other macroeconomic variables for inflation fore- casting purposes. The DF-GARCH is a dynamic factor model as the one by Forni et al. [2005], with the addition of an equation for the evolution of static factors as in Giannone et al. [2004] and the assumption of heteroskedastic dynamic factors. When comparing the Dynamic Factor GARCH with univariate models and with the classical dynamic factor models, the DF-GARCH is able to provide better forecasts both of inflation and of its conditional variance.Inflation, Factor Models, GARCH
Measuring Euro Area Monetary Policy Transmission in a Structural Dynamic Factor Model
We study the effects of euro area common monetary policy by means of a structural dynamic factor model estimated on a large panel of euro area quarterly series. While we estimate a flat response of prices to a monetary policy shock, which we explain as aggregation of heterogeneous country-specific responses, we find no relevant asymmetries between countries in terms of output reaction. However, for both Spain and Italy, we find asymmetries in consumption, investment and unemployment. The introduction of the single currency in 1999 has helped reducing asymmetries in price responses but not in consumption and investment.
Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models
This paper investigates the properties of Quasi Maximum Likelihood estimation
of an approximate factor model for an -dimensional vector of stationary time
series. We prove that the factor loadings estimated by Quasi Maximum Likelihood
are asymptotically equivalent, as , to those estimated via
Principal Components. Both estimators are, in turn, also asymptotically
equivalent, as , to the unfeasible Ordinary Least Squares estimator
we would have if the factors were observed. We also show that the usual
sandwich form of the asymptotic covariance matrix of the Quasi Maximum
Likelihood estimator is asymptotically equivalent to the simpler asymptotic
covariance matrix of the unfeasible Ordinary Least Squares. These results hold
in the general case in which the idiosyncratic components are cross-sectionally
heteroskedastic, as well as serially and cross-sectionally weakly correlated.
This paper provides a simple solution to computing the Quasi Maximum Likelihood
estimator and its asymptotic confidence intervals without the need of running
any iterated algorithm, whose convergence properties are unclear, and
estimating the Hessian and Fisher information matrices, whose expressions are
very complex.Comment: arXiv admin note: text overlap with arXiv:2211.01921 which is written
by the same autho
On the stability of euro area money demand and its implications for monetary policy
On the Stability of Euro Area Money Demandand its Implications for Monetary PolicyFebruary 27, 2018AbstractWe employ a recent time-varying cointegration test to revisit the usefulness of long-runmoney demand equations for the ECB, addressing the issue of their instability by meansof a model evaluation exercise. Building on the results, we make a twofold contribution.First, we propose a novel stable money demand equation relying on two crucial factors:a speculative motive, represented by domestic and foreign price-earnings ratios, and aprecautionary motive, measured by changes in unemployment. Second, we use the modelto derive relevant policy implications for the ECB, since excess liquidity looks more usefulfor forecasting stock market busts than future inflation. Overall, this evidence pointsto (i) a possible evolution of the monetary pillar in the direction of pursuing financialstability and (ii) the exclusion of a sudden liquidity–driven inflationary burst after theexit from the prolonged period of unconventional monetary measures
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