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 measured using chi-measure. This work is motivated by the structural changes in chi-measure between the daily return rates of the two largest Indian airlines in 2019, IndiGo and SpiceJet, during the COVID-19 pandemic. We model the daily maximum return rate vectors (potentially transformed) using the bivariate Husler-Reiss (BHR) distribution, which is the only possible non-degenerate limiting distribution of a renormalized element-wise block maxima of a sequence of bivariate Gaussian random vectors. To estimate the changepoint in the chi-measure of the BHR distribution, we explore the changepoint detection procedures based on 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, the most prominent changepoint detected by LRT and MIC coincides with the announcement of the first phase of lockdown declared by the Government of India, which is realistic; thus, our study would be beneficial for portfolio optimization in the case of future pandemic situations.