ABSTRACT Score-driven models for the t distribution are robust to outliers because outliers are discounted in the updating terms of the filters. We suggest outlier-robust unit root tests using two important score-driven models for the t distribution, the quasi-autoregressive (QAR) model and the Beta- t -EGARCH (exponential generalized autoregressive conditional heteroskedasticity) model. QAR and Beta- t -EGARCH have covariance stationary and unit root versions. The updating terms of these models are information-theoretically optimal extensions of the updating terms of the AR and GARCH models, respectively. For the asymptotic theory of the maximum likelihood (ML) estimation of the QAR and Beta- t -EGARCH models, the correct choice of the order of integration is important. QAR and Beta- t -EGARCH discount outliers in the filters, partly due to this, the covariance stationarity statistics are almost 1 in many applications. Motivated by these points, our contribution is to report unit root test critical value tables for QAR and Beta- t -EGARCH using extensive Monte Carlo simulation experiments. We present an application of the QAR unit root tests for the United States (US) inflation rate from January 1961 to June 2023. We present applications of the Beta- t -EGARCH unit root test for the NASDAQ Composite, S&P 500, and Bitcoin volatility from August 2018 to August 2023.
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