Comparison of estimation methods for the density of autoregressive parameter in aggregated AR(1) processes

The article investigates the properties of two alternative disaggregation methods. First one, proposed in Chong (2006), is based on the assumption of polynomial autoregressive parameter density. Second one, proposed in Leipus et al. (2006), uses the approximation of the density by the means of Gegenbauer polynomials. Examining results of Monte-Carlo simulations it is shown that none of the methods was found to outperform another. Chong’s method is narrowed by the class of polynomial densities, and the secondmethod is not effective in the presence of common innovations.Bothmethodswork correctly under assumptions proposed in the corresponding articles.

IDENTIFICATION ROBUST INFERENCE FOR MOMENTS-BASED ANALYSIS OF LINEAR DYNAMIC PANEL DATA MODELS

We use identification robust tests to show that difference (Dif), level (Lev), and nonlinear (NL) moment conditions, as proposed by Arellano and Bond (1991, Review of Economic Studies 58, 277–297), Ahn and Schmidt (1995, Journal of Econometrics 68, 5–27), Arellano and Bover (1995, Journal of Econometrics 68, 29–51), and Blundell and Bond (1998, Journal of Econometrics 87, 115–143) for the linear dynamic panel data model, do not separately identify the autoregressive parameter when its true value is close to one and the variance of the initial observations is large. We prove that combinations of these moment conditions, however, do so when there are more than three time series observations. This identification then solely results from a set of, so-called, robust moment conditions. These robust moments are spanned by the combined Dif, Lev, and NL moment conditions and only depend on differenced data. We show that, when only the robust moments contain identifying information on the autoregressive parameter, the discriminatory power of the Kleibergen (2005, Econometrica 73, 1103–1124) Lagrange multiplier (KLM) test using the combined moments is identical to the largest rejection frequencies that can be obtained from solely using the robust moments. This shows that the KLM test implicitly uses the robust moments when only they contain information on the autoregressive parameter.

Adversarial Inference Is Efficient

We study properties of the adversarial framework, introduced in Kaji, Manresa and Pouliot (2020). We show that the adversarial inference with an oracle classifier is statistically efficient. In addition, we study the finite sample properties of the adversarial estimation framework for the autoregressive parameter of a linear dynamic fixed effects panel data model with Gaussian errors. Unlike maximum likelihood, but similarly as other minimum distance estimators, the adversarial estimators do not suffer from the incidental parameter bias. In our simulations, using a one-hidden-layer neural network as discriminator delivers the estimates with smallest root mean squared error.

Testing for asymmetric adjustment in weekly Brazilian inflation

This study analyses the nature of weekly inflation response to shocks in the Brazilian economy by adopting a generalized quantile autoregression model in which the autoregressive parameter is allowed to be quantile-dependent. We test for unit root at different conditional quantiles of the response variable, by characterizing its asymmetric dynamics along the business cycle. The method allows us to estimate the magnitude, sign, and the significance of actual shocks that affect Brazilian inflation. We evaluate the robustness of results by adopting a bootstrap procedure. Concerning previous studies, we find evidence of stronger asymmetric persistence in inflationary dynamics in which an inflationary shock below the average dissipates very fast when compared to an inflationary impulse occurring above the average. Location, size, and the sign of a random shock might be essential for inflation adjustment towards long-run equilibrium. The results do not support the full inertia hypothesis.

Statistical Learning of the Worst Regional Smog Extremes with Dynamic Conditional Modeling

This paper is concerned with the statistical learning of the extreme smog (PM 2.5 ) dynamics of a vast region in China. Differently from classical extreme value modeling approaches, this paper develops a dynamic model of conditional, exponentiated Weibull distribution modeling and analysis of regional smog extremes, particularly for the worst scenarios observed in each day. To gain higher modeling efficiency, weather factors will be introduced in an enhanced model. The proposed model and the enhanced model are illustrated with temporal/spatial maxima of hourly PM 2.5 observations each day from smog monitoring stations located in the Beijing–Tianjin–Hebei geographical region between 2014 and 2019. The proposed model performs more precisely on fittings compared with other previous models dealing with maxima with autoregressive parameter dynamics, and provides relatively accurate prediction as well. The findings enhance the understanding of how severe extreme smog scenarios can be and provide useful information for the central/local government to conduct coordinated PM 2.5 control and treatment. For completeness, probabilistic properties of the proposed model were investigated. Statistical estimation based on the conditional maximum likelihood principle is established. To demonstrate the estimation and inference efficiency of studies, extensive simulations were also implemented.

Non-asymptotic Confidence Estimation of the Autoregressive Parameter in AR(1) Process with an Unknown Noise Variance

The paper considers the estimation problem of the autoregressive parameter in the first-order autoregressive process with Gaussian noises when the noise variance is unknown. We propose a non-asymptotic technique to compensate the unknown variance, and then, to construct a point estimator with any prescribed mean square accuracy. Also a fixed-width confidence interval with any prescribed coverage accuracy is proposed. The results of Monte-Carlo simulations are given.