|
on Econometric Time Series |
| By: | Anders Bredahl Kock; Rasmus S{\o}ndergaard Pedersen; Jesper Riis-Vestergaard S{\o}rensen |
| Abstract: | Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for Lasso typically require the penalty level to be chosen in a suitable fashion often depending on unknown population quantities. Furthermore, the resulting estimates and the number of variables retained in the model depend crucially on the chosen penalty level. However, there is currently no theoretically founded guidance for this choice in the context of high-dimensional time series. Instead one resorts to selecting the penalty level in an ad hoc manner using, e.g., information criteria or cross-validation. We resolve this problem by considering estimation of the perhaps most commonly employed multivariate time series model, the linear vector autoregressive (VAR) model, and propose a weighted Lasso estimator with penalization chosen in a fully data-driven way. The theoretical guarantees that we establish for the resulting estimation and prediction error match those currently available for methods based on infeasible choices of penalization. We thus provide a first solution for choosing the penalization in high-dimensional time series models. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.06657&r=ets |
| By: | Emanuele Bacchiocchi; Andrea Bastianin; Toru Kitagawa; Elisabetta Mirto |
| Abstract: | This paper studies the identification of Structural Vector Autoregressions (SVARs) exploiting a break in the variances of the structural shocks. Point-identification for this class of models relies on an eigen-decomposition involving the covariance matrices of reduced-form errors and requires that all the eigenvalues are distinct. This point-identification, however, fails in the presence of multiplicity of eigenvalues. This occurs in an empirically relevant scenario where, for instance, only a subset of structural shocks had the break in their variances, or where a group of variables shows a variance shift of the same amount. Together with zero or sign restrictions on the structural parameters and impulse responses, we derive the identified sets for impulse responses and show how to compute them. We perform inference on the impulse response functions, building on the robust Bayesian approach developed for set identified SVARs. To illustrate our proposal, we present an empirical example based on the literature on the global crude oil market where the identification is expected to fail due to multiplicity of eigenvalues. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.06879&r=ets |
| By: | Giovanni Angelini; Luca Fanelli; Luca Neri |
| Abstract: | When in proxy-SVARs the covariance matrix of VAR disturbances is subject to exogenous, permanent, nonrecurring breaks that generate target impulse response functions (IRFs) that change across volatility regimes, even strong, exogenous external instruments can result in inconsistent estimates of the dynamic causal effects of interest if the breaks are not properly accounted for. In such cases, it is essential to explicitly incorporate the shifts in unconditional volatility in order to point-identify the target structural shocks and possibly restore consistency. We demonstrate that, under a necessary and sufficient rank condition that leverages moments implied by changes in volatility, the target IRFs can be point-identified and consistently estimated. Importantly, standard asymptotic inference remains valid in this context despite (i) the covariance between the proxies and the instrumented structural shocks being local-to-zero, as in Staiger and Stock (1997), and (ii) the potential failure of instrument exogeneity. We introduce a novel identification strategy that appropriately combines external instruments with "informative" changes in volatility, thus obviating the need to assume proxy relevance and exogeneity in estimation. We illustrate the effectiveness of the suggested method by revisiting a fiscal proxy-SVAR previously estimated in the literature, complementing the fiscal instruments with information derived from the massive reduction in volatility observed in the transition from the Great Inflation to the Great Moderation regimes. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.08753&r=ets |
| By: | Degui Li; Oliver Linton; Haoxuan Zhang |
| Abstract: | We propose a new estimator of high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure from noisy and asynchronous high-frequency data collected for an ultra-large number of assets. The noise processes are allowed to be temporally correlated, heteroskedastic, asymptotically vanishing and dependent on the efficient prices. We define a kernel-weighted pre-averaging method to jointly tackle the microstructure noise and asynchronicity issues, and we obtain uniformly consistent estimates for latent prices. We impose a continuous-time factor model with time-varying factor loadings on the price processes, and estimate the common factors and loadings via a local principal component analysis. Assuming a uniform sparsity condition on the idiosyncratic volatility structure, we combine the POET and kernel-smoothing techniques to estimate the spot volatility matrices for both the latent prices and idiosyncratic errors. Under some mild restrictions, the estimated spot volatility matrices are shown to be uniformly consistent under various matrix norms. We provide Monte-Carlo simulation and empirical studies to examine the numerical performance of the developed estimation methodology. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.06246&r=ets |
| By: | Bailly, Gabriel (Université catholique de Louvain, LIDAM/ISBA, Belgium); von Sachs, Rainer (Université catholique de Louvain, LIDAM/ISBA, Belgium) |
| Abstract: | We tackle the problem of estimating time-varying covariance matrices (TVCM; i.e. covariance matrices with entries being time-dependent curves) whose elements show inhomogeneous smoothness over time (e.g. pronounced local peaks). To address this challenge, wavelet denoising estimators are particularly appropriate. Specifically, we model TVCM using a signal-noise model within the Riemannian manifold of symmetric positive definite matrices (endowed with the log-Euclidean metric) and use the intrinsic wavelet transform, designed for curves in Riemannian manifolds. Within this non-Euclidean framework, the proposed estimators preserve positive definiteness. Although linear wavelet estimators for smooth TVCM achieve good results in various scenarios, they are less suitable if the underlying curve features singularities. Consequently, our estimator is designed around a nonlinear thresholding scheme, tailored to the characteristics of the noise in covariance matrix regression models. The effectiveness of this novel nonlinear scheme is assessed by deriving mean-squared error consistency and by numerical simulations, and its practical application is demonstrated on TVCM of electroencephalography (EEG) data showing abrupt transients over time. |
| Keywords: | Nonlinear wavelet thresholding ; non-Euclidean geometry ; sample covariance matrices ; time-varying second-order structure ; log-Wishart distribution |
| Date: | 2024–02–12 |
| URL: | http://d.repec.org/n?u=RePEc:aiz:louvad:2024004&r=ets |