Quantile regression-based seasonal adjustment

Time series of different nature might be characterised by the presence of deterministic and/or stochastic seasonal patterns. By seasonality, we refer to periodic fluctuations affecting not only the mean but also the shape, the dispersion and in general the density of the variable of interest over time. Using traditional approaches for seasonal adjustment might not be efficient because they do not ensure, for instance, that the adjusted data are free from periodic behaviours in, say, higher-order moments. We introduce a seasonal adjustment method based on quantile regression that is capable of capturing different forms of deterministic and/or stochastic seasonal patterns. Given a variable of interest, by describing its seasonal behaviour over an approximation of the entire conditional distribution, we are capable of removing seasonal patterns affecting the mean and/or the variance, or seasonal patterns varying over quantiles of the conditional distribution. In the first part of this work, we provide a proposed approach to deal with the deterministic seasonal pattern cases. We provide empirical examples based on simulated and real data where we compare our proposal to least-squares approaches. The results are in favour of the proposed approach in case if the seasonal patterns change across quantiles. In the second part of this work, we improve the proposed approach flexibly to account for the essential effect of the structural breaks in the time series. Again, we compare the proposed methods to segmented-least squares and provide several empirical examples based on simulated and real data that are affected by both the structural breaks and seasonal patterns. The results, in case of stochastic periodic behaviour, are in favour of the proposed approaches especially when the seasonal patterns change across quantiles.