On February 20th from 11.00 to 12.00 Alessandro Casini from Boston University will give a seminar on "Theory of Evolutionary Spectra for Heteroskesdasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models".

The event will take place in room B, first floor, building B.

Abstract:  We develop a theory of evolutionary spectra for heteroskedasticity- and autocorrelation-robust (HAR)
inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic
time series which may arise either from model misspecification or parameter variation. In such a context, the main
theory that supports classical heteroskedasticity and autocorrelation consistent (HAC) estimators is not applicable.
F- and t-tests standardized by classical HAC estimators then may display size distortions and other undesirable
properties such as little or no power. We introduce a class of nonstationary stochastic processes that have a timevarying spectral representation which evolves continuously except at a finite number of time points and presents
a new positive semidefinite HAC estimator that is consistent for the covariance matrix of any time series within
this class. The HAC estimator applies two smoothing procedures. One is over the autocovariance lag order—akin
to classical HAC estimators—and the other is over time. The latter element is not shared by the classical HAC
estimators but it is crucial because the covariance structure of economic time series can evolve over time. We
show the consistency of the estimator and obtain an optimal HAC estimator under the mean-squared error (MSE)
criterion. The optimal HAC estimator uses the Quadratic Spectral (QS) kernel for smoothing over autocovariance
lag order and a quadratic-type kernel for smoothing over time. We propose a data-dependent procedure based on
a “plug-in” approach that determines the bandwidth parameters for given kernels and a given sample size. Overall,
F- and t-tests standardized by the proposed HAC estimator control the size well and have good power. In those
empirically relevant situations in which test statistics standardized by classical HAC estimators have little or no
statistical power, the proposed HAC estimator leads to test statistics that have good power so that HAR inference
is then meaningful.