Minimax MSE Bounds and Nonlinear VAR Prewhitening for Long-Run Variance Estimation Under Nonstationarity

03/03/2021
by   Alessandro Casini, et al.
0

We establish new mean-squared error (MSE) bounds for long-run variance (LRV) estimation, valid for both stationary and nonstationary sequences that are sharper than previously established. The key element to construct such bounds is to use restrictions onthe degree of nonstationarity. Unlike previous bounds, they show how nonstationarity influences the bias-variance trade-off. Unlike previously established bounds, either under stationarity or nonstationarity, the new bounds depends on the form of nonstationarity. The bounds are established for double kernel long-run variance estimators. The corresponding bounds for classical long-run variance estimators follow as a special case. We use them to construct new data-dependent methods for the selection of bandwidths for (double) kernel heteroskedasticity autocorrelation consistent (DK-HAC) estimators. These account more flexibly for nonstationarity and lead to tests with The new MSE bounds and associated bandwidths help to to improve good finite-sample performance, especially good power when existing LRV estimators lead to tests having little or no or no power. The second contribution is to introduce a nonparametric nonlinear VAR prewhitened LRV estimator. This accounts explicitly for nonstationarity unlike previous prewhitened procedures which are known to be unstable. Its consistency, rate of convergence and MSE bounds are established. The prewhitened DK-HAC estimators lead to tests with good finite-sample size while maintaining good monotonic power.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

02/26/2021

Simultaneous Bandwidths Determination for DK-HAC Estimators and Long-Run Variance Estimation in Nonparametric Settings

We consider the derivation of data-dependent simultaneous bandwidths for...
12/07/2021

Bless and curse of smoothness and phase transitions in nonparametric regressions: a nonasymptotic perspective

When the regression function belongs to the standard smooth classes cons...
10/01/2021

Expected Validation Performance and Estimation of a Random Variable's Maximum

Research in NLP is often supported by experimental results, and improved...
11/29/2021

The Fixed-b Limiting Distribution and the ERP of HAR Tests Under Nonstationarity

We show that the nonstandard limiting distribution of HAR test statistic...
11/14/2019

On Data Enriched Logistic Regression

Biomedical researchers usually study the effects of certain exposures on...
07/07/2020

Estimation and Inference with Trees and Forests in High Dimensions

We analyze the finite sample mean squared error (MSE) performance of reg...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.