Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series


Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models

Shaojun Guo
Dong Li
Muyi Li

In this article we develop a tractable procedure for testing strict stationarity in a
double autoregressive model and formulate the problem as testing if the top Lyapunov
exponent is negative. Without strict stationarity assumption, we construct a consistent
estimator of the associated top Lyapunov exponent and employ a random weighting
approach for its variance estimation, which in turn are used in a t-type test. We also
propose a GLAD estimation for parameters of interest, relaxing key assumptions on
the commonly used QMLE. All estimators, except for the intercept, are shown to be
consistent and asymptotically normal in both stationary and explosive situations. The
nite-sample performance of the proposed procedures is evaluated via Monte Carlo
simulation studies and a real dataset of interest rates is analyzed.

DAR model, GLAD estimation, Nonstationarity, Random weighting, Strict
stationarity testing.

JEL Classification:
C15, C22