Estimating Changepoints in Extremal Dependence, Applied to Aviation Stock Prices During COVID-19 Pandemic

The dependence in the tails of the joint distribution of two random variables is generally assessed using $\chi$-measure, the limiting conditional probability of one variable being extremely high given the other variable is also extremely high. This work is motivated by the structural changes in $\chi$-measure between the daily rate of return (RoR) of the two Indian airlines, IndiGo and SpiceJet, during the COVID-19 pandemic. We model the daily maximum and minimum RoR vectors (potentially transformed) using the bivariate H\"usler-Reiss (BHR) distribution. To estimate the changepoint in the $\chi$-measure of the BHR distribution, we explore two changepoint detection procedures based on the Likelihood Ratio Test (LRT) and Modified Information Criterion (MIC). We obtain critical values and power curves of the LRT and MIC test statistics for low through high values of $\chi$-measure. We also explore the consistency of the estimators of the changepoint based on LRT and MIC numerically. In our data application, for RoR maxima and minima, the most prominent changepoints detected by LRT and MIC are close to the announcement of the first phases of lockdown and unlock, respectively, which are realistic; thus, our study would be beneficial for portfolio optimization in the case of future pandemic situations.