The COVID-19 Shock and Challenges for Time Series Models

Abstract

We document the impact of COVID-19 on frequently employed time series models, with a focus on euro area inflation. We show that for both single equation models (Phillips curves) and Vector Autoregressions (VARs) estimated parameters change notably with the pandemic. In a VAR, allowing the errors to have a distribution with fatter tails than the Gaussian one equips the model to better deal with the COVID-19 shock. A standard Gaussian VAR can still be used for producing conditional forecasts when relevant off-model information is used. We illustrate this by conditioning on official projections for a set of variables, but also by tilting to expectations from the Survey of Professional Forecasters. For Phillips curves, averaging across many conditional forecasts in a thick modelling framework offers some hedge against parameter instability.

Modelling Okun’s law: Does non-Gaussianity matter?

“…2, the swings in the variables associated with this period were very large-so large that they perhaps should be considered outliers; see, for example, the discussion in Carriero et al (2021). Issues associated with modelling the corona pandemic have recently been discussed in the literature; see, for example, Bobeica and Hartwig (2021), Carriero et al (2021) and Hartwig (2021). Seeing that these data are something that empirical macroeconomists will have to handle in the future, we next assess the effects that they have in the context of the analysis in this paper.…”

Macroeconomic Effects of COVID-19 in a Commodity-Exporting Economy: Evidence from Mongolia

“…Values typically found in the literature were chosen for the overall tightness, 𝜆 1 = 0.1, 6 and the lag decay, 𝜆 3 = 2. As suggested by Bobeica and Hartwig (2021), the choice of 5 The PRC's real GDP is calculated as a ratio of seasonally adjusted current price GDP in the PRC (CHNGDPNQDSMEI) to CPI, all items for the PRC, index 2015=100 (CHNCPIALLQINMEI), data are collected from FRED economic data of the Federal Reserve Bank of St. Louis. 6 Dieppe, Legrand, and Roye (2018) suggested setting 𝜆 1 for the normal-Wishart prior at a smaller value than for the Minnesota prior to compensate for the lack of extra shrinkage from 𝜆 2 , which controls tightness on cross-variable parameters in the case of Minnesota prior.…”

“…Gharehgozli et al (2020) used a two-step VAR model to forecast and estimate the effect of the COVID-19 outbreak on New York's GDP for the first and second quarters of 2020. Bobeica and Hartwig (2021) showed that for both single equation models (Phillips curves) and Vector Autoregressions (VARs), estimated parameters changed notably with the pandemic. They found that a large Gaussian VAR with a higher degree of prior shrinkage mitigated the problem of changing parameters after adding the COVID-19 observations.…”

Data outliers and Bayesian VARs in the euro area

“…Another paper contributing to the topic of outlier specifications includes Bobeica and Hartwig (2021), who use euro area data to show that the Covid-19 outliers cause a substantial change in the estimated coefficients of a BVAR without stochastic volatility unless the regression coefficient prior is set very tight. As a remedy, the authors propose to estimate a BVAR with an error term that is drawn from a Student's t distribution to allow for larger shocks.…”