Inference for Monotone Functions Under Short- and Long-Range Dependence
Pramita Bagchi, University of Michigan
Existence of a monotone trend is quite common in time series data. We introduce new point-wise confidence interval estimates for monotone functions observed with additive and dependent noise. We study both short- and long-range dependence regimes for the errors. The interval estimates are obtained via the method of inversion of certain discrepancy statistics. This approach avoids the estimation of nuisance parameters such as the derivative of the unknown function, which other methods are forced to deal with. The resulting estimates are therefore more accurate, stable and widely applicable in practice under mild assumptions on the trend and error structure. While motivated by earlier work in the independent context, the dependence of the errors, especially long-range dependence leads to new phenomena and new universal limits based on convex minorant functionals of drifted fractional Brownian motion.