Discriminant analysis by quantile regression with application on the climate change problem

- This study proposes discriminant analysis for quantile regression models.
- The proposed discriminant method exhibits a good fundamental property.
- The statistic allows one to classify time series data into one of k categories, k≥2.
- We evaluate the performance of the statistics when the categories are contiguous.
- Our results confirm climate change for the recent 36-year period in Melbourne.

With the widespread use of discriminant analysis in various fields, e.g. multivariate data, regression models, and times series observations, this paper introduces a quantile regression statistic to classify time series data into a certain category. Results show that the misclassification probability of the discriminant statistic converges to zero as the sample size tends to infinity. We also evaluate the performance of the statistics when the categories are contiguous. We apply the proposed method in quantile autoregression to a dataset of the monthly mean maximum temperature at Melbourne, Australia from January 1944 to December 2015. The findings illuminate interesting features of climate change and allow us to check the change at each quantile of the innovation distribution. Because the proposed method is general, there are many potential applications of this approach.