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on Econometric Time Series |
| By: | Christian Francq (CREST-ENSAE and University of Lille); Baye Matar Kandji (CREST-ENSAE); Jean-Michel Zakoian (University of Lille and CREST-ENSAE) |
| Abstract: | In multiplicative component GARCH models, the volatility is decomposed into the product of two factors which often received interpretations in terms of "short run" (high frequency) and "long run" (low frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order nite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the Quasi-Maximum Likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real nancial data. |
| Keywords: | GARCH-MIDAS, Moments existence, QMLE, Residual Bootstrap, Tests on boundary parameters. |
| JEL: | C12 C13 C22 C58 |
| Date: | 2022–03–18 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2022-09&r= |
| By: | Johannes Huber (University of Augsburg, Department of Economics) |
| Abstract: | We propose a modified version of the augmented Kalman filter (AKF) to evaluate the likelihood of linear and time-invariant state-space models (SSMs). Unlike the regular AKF, this augmented steady-state Kalman filter (ASKF), as we call it, is based on a steady-state Kalman filter (SKF). We show that to apply the ASKF, it is sufficient that the SSM at hand is stationary. We find that the ASKF can significantly reduce the computational burden to evaluate the likelihood of medium- to large-scale SSMs, making it particularly useful to estimate dynamic stochastic general equilibrium (DSGE) models and dynamic factor models. Tests using a medium-scale DSGE model, namely the 2007 version of the Smets and Wouters model, show that the ASKF is up to five times faster than the regular Kalman filter (KF). Other competing algorithms, such as the Chandrasekhar recursion (CR) or a univariate treatment of multivariate observation vectors (UKF), are also outperformed by the ASKF in terms of computational efficiency. |
| Keywords: | kalman filter, dsge, bayesian estimation, maximum-likelihood estimation, computational techniques |
| JEL: | C18 C63 E20 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:aug:augsbe:0343&r= |
| By: | Lin, Yingqian; Tu, Yundong; Yao, Qiwei |
| Abstract: | In recent years statistical inference for nonlinear cointegration has attracted attention from both academics and practitioners. This paper proposes a new type of cointegration in the sense that two univariate time series yt and xt are cointegrated via two (unknown) smooth nonlinear transformations, further generalizing the notion of cointegration initially revealed by Box and Tiao (1977), and more systematically studied by Engle and Granger (1987). More precisely, it holds that G(yt,β0)=g(xt)+ut, where G(⋅,β0) is strictly increasing and known up to an unknown parameter β0, g(⋅) is unknown and smooth, xt is I(1), and ut is the stationary disturbance. This setting nests the nonlinear cointegration model of Wang and Phillips (2009b) as a special case with G(y,β0)=y. It extends the model of Linton et al. (2008) to the cases with a unit-root nonstationary regressor. Sieve approximations to the smooth nonparametric function g are applied, leading to an extremum estimator for β and a plugging-in estimator for g(⋅). Asymptotic properties of the estimators are established, revealing that both the convergence rates and the limiting distributions depend intimately on the properties of the two nonlinear transformation functions. Simulation studies demonstrate that the estimators perform well even with small samples. A real data example on the environmental Kuznets curve portraying the nonlinear impact of per-capita GDP on air-pollution illustrates the practical relevance of the proposed double-nonlinear cointegration. |
| Keywords: | Box–Cox transformation; nonlinear cointegration; semiparametrics; sieve method; transformation models |
| JEL: | J1 C1 |
| Date: | 2020–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:103830&r= |
| By: | Barend Abeln; Jan P.A.M. Jacobs; Machiel Mulder |
| Abstract: | In the last decade large data sets have become available, both in terms of the number of time series and with higher frequencies (weekly, daily and even higher). All series may suffer from seasonality, which hides other important fluctuations. Therefore time series are typically seasonally adjusted. However, standard seasonal adjustment methods cannot handle series with higher than monthly frequencies. Recently, Abeln et al. (2019) presented CAMPLET, a new seasonal adjustment method, which does not produce revisions when new observations become available. The aim of this paper is to show the attractiveness of CAMPLET for seasonal adjustment of daily time series. We apply CAMPLET to daily data on the gas system in the Netherlands. To quote this document: Au cours de la dernière décennie, de vastes ensembles de données sont devenus disponibles, tant en termes de nombre de séries chronologiques que de fréquences plus élevées (hebdomadaires, quotidiennes et même supérieures). Toutes les séries peuvent souffrir d'une saisonnalité, qui masque d'autres fluctuations importantes. C'est pourquoi les séries temporelles sont généralement désaisonnalisées. Cependant, les méthodes standard de désaisonnalisation ne peuvent pas traiter les séries dont la fréquence est supérieure au mois. Récemment, Abeln et al. (2019) ont présenté CAMPLET, une nouvelle méthode de désaisonnalisation, qui ne produit pas de révisions lorsque de nouvelles observations sont disponibles. L'objectif de cet article est de montrer l'attrait de CAMPLET pour l'ajustement saisonnier des séries temporelles quotidiennes. Nous appliquons CAMPLET à des données quotidiennes sur le réseau de gaz aux Pays-Bas. Pour citer ce document: |
| Keywords: | daily data,seasonal adjustment,calendar effect,gas system,the Netherlands, données quotidiennes,ajustement saisonnier,effet de calendrier,système de gaz,les Pays-Bas. |
| JEL: | C22 Q47 |
| Date: | 2022–04–04 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2022s-06&r= |
| By: | Rubens Morita; Zacharias Psaradakis; Martín Sola; Patricio Yunis |
| Abstract: | We consider testing for the presence of rational bubbles during hyperinflations via an analysis of the non-stationarity properties of relevant observable time series. The testing procedure is based on a Markov-regime switching model with independent stochastic changes in its intercept, error variance, and autoregressive coefficients. This model formulation allow us to disentangle fundamentals-driven changes in the drift, bubble-driven explosiveness, and volatility changes that may be fundamentals-driven and/or bubble-driven. The testing strategy is illustrated by applying it to data from hyperinflations in Argentina, Brazil, Germany, and Poland. |
| Keywords: | Bubbles; Explosiveness; Markov-switching autoregressive model; Unit-root test. |
| JEL: | C72 D44 D82 |
| URL: | http://d.repec.org/n?u=RePEc:udt:wpecon:2022_02&r= |
| By: | Alessandro Casini (Università di Roma "Tor Vergata") |
| Abstract: | This comment includes a solution to a problem in Section 8 in Andrews (1991) and points out a method to generalize the mean-squared error (MSE) bounds appearing in Andrews (1988) and Andrews (1991) |
| Date: | 2022–04–02 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:536&r= |
| By: | Pötscher, Benedikt M.; Preinerstorfer, David |
| Abstract: | We show that the theorems in Hansen (2021b) (Econometrica, forthcoming) are not new as they coincide with classical theorems like the good old Gauss-Markov or Aitken Theorem, respectively. |
| Keywords: | Gauss-Markov Theorem, Aitken Theorem, unbiased estimation |
| JEL: | C13 C20 |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:112185&r= |