arXiv subjects

Paolo Paruolo

Publications and source records attributed to Paolo Paruolo.

6 recordsLinked to original sources

arXiv2025

Inference on the attractor spaces via functional approximation

This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for $I(1)$ linear processes with moderately large cross-sectional dimension. The approach is based on empirical canonical correlations and functional approximation of Brownian motions, and it can be applied both to the whole system and or to any set of linear combinations of it. The hypotheses of interest are cast in terms of the number of stochastic trends in specified subsystems, and inference is based either on selection criteria or on sequences of tests. This paper derives the limit distribution of these tests in the special one-dimensional case, and discusses asymptotic properties of the derived inference criteria for hypotheses on the attractor space for sequentially diverging sample size and number of basis elements in the functional approximation. Finite sample properties are analyzed via a Monte Carlo study and an empirical illustration on exchange rates is provided.

stat.ME↗

arXiv2025

Canonical correlation analysis of stochastic trends via functional approximation

This paper proposes a novel approach for semiparametric inference on the number $s$ of common trends and their loading matrix $ψ$ in $I(1)/I(0)$ systems. It combines functional approximation of limits of random walks and canonical correlations analysis, performed between the $p$ observed time series of length $T$ and the first $K$ discretized elements of an $L^2$ basis. Tests and selection criteria on $s$, and estimators and tests on $ψ$ are proposed; their properties are discussed as $T$ and $K$ diverge sequentially for fixed $p$ and $s$. It is found that tests on $s$ are asymptotically pivotal, selection criteria of $s$ are consistent, estimators of $ψ$ are $T$-consistent, mixed-Gaussian and efficient, so that Wald tests on $ψ$ are asymptotically Normal or $χ^2$. The paper also discusses asymptotically pivotal misspecification tests for checking model assumptions. The approach can be coherently applied to subsets or aggregations of variables in a given panel. Monte Carlo simulations show that these tools have reasonable performance for $T\geq 10 p$ and $p\leq 300$. An empirical analysis of 20 exchange rates illustrates the methods.

econ.EM↗

arXiv2021

GARCH density and functional forecasts

This paper derives the analytic form of the $h$-step ahead prediction density of a GARCH(1,1) process under Gaussian innovations, with a possibly asymmetric news impact curve. The contributions of the paper consists both in the derivation of the analytic form of the density, and in its application to a number of econometric problems. A first application of the explicit formulae is to characterize the degree of non-Gaussianity of the prediction distribution; for some values encountered in applications, deviations of the prediction distribution from the Gaussian are found to be small, and sometimes not. the Gaussian density as an approximation of the true prediction density. A second application of the formulae is to compute exact tail probabilities and functionals, such as the Value at Risk and the Expected Shortfall, that measure risk when the underlying asset return is generated by a Gaussian GARCH(1,1). This improves on existing methods based on Monte Carlo simulations and (non-parametric) estimation techniques, because the present exact formulae are free of Monte Carlo estimation uncertainty. A third application is the definition of uncertainty regions for functionals of the prediction distribution that reflect in-sample estimation uncertainty. These applications are illustrated on selected empirical examples.

math.ST↗

arXiv2018

Cointegration in functional autoregressive processes

This paper defines the class of $\mathcal{H}$-valued autoregressive (AR) processes with a unit root of finite type, where $\mathcal{H}$ is an infinite dimensional separable Hilbert space, and derives a generalization of the Granger-Johansen Representation Theorem valid for any integration order $d=1,2,\dots$. An existence theorem shows that the solution of an AR with a unit root of finite type is necessarily integrated of some finite integer $d$ and displays a common trends representation with a finite number of common stochastic trends of the type of (cumulated) bilateral random walks and an infinite dimensional cointegrating space. A characterization theorem clarifies the connections between the structure of the AR operators and $(i)$ the order of integration, $(ii)$ the structure of the attractor space and the cointegrating space, $(iii)$ the expression of the cointegrating relations, and $(iv)$ the Triangular representation of the process. Except for the fact that the number of cointegrating relations that are integrated of order 0 is infinite, the representation of $\mathcal{H}$-valued ARs with a unit root of finite type coincides with that of usual finite dimensional VARs, which corresponds to the special case $\mathcal{H}=\mathbb{R}^p$.

econ.EM↗

arXiv2014

Exploring Hoover and Perez's experimental designs using global sensitivity analysis

This paper investigates variable-selection procedures in regression that make use of global sensitivity analysis. The approach is combined with existing algorithms and it is applied to the time series regression designs proposed by Hoover and Perez. A comparison of an algorithm employing global sensitivity analysis and the (optimized) algorithm of Hoover and Perez shows that the former significantly improves the recovery rates of original specifications.

stat.CO↗

arXiv2012

Ratings and rankings: Voodoo or Science?

Composite indicators aggregate a set of variables using weights which are understood to reflect the variables' importance in the index. In this paper we propose to measure the importance of a given variable within existing composite indicators via Karl Pearson's `correlation ratio'; we call this measure `main effect'. Because socio-economic variables are heteroskedastic and correlated, (relative) nominal weights are hardly ever found to match (relative) main effects; we propose to summarize their discrepancy with a divergence measure. We further discuss to what extent the mapping from nominal weights to main effects can be inverted. This analysis is applied to five composite indicators, including the Human Development Index and two popular league tables of university performance. It is found that in many cases the declared importance of single indicators and their main effect are very different, and that the data correlation structure often prevents developers from obtaining the stated importance, even when modifying the nominal weights in the set of nonnegative numbers with unit sum.

stat.AP↗