Tuning-free inference on fixed-dimensional parameters of
dependent time series using affine-equivariant adjusted-range
self-normalization. The centered partial-sum path of estimated
influence contributions is normalized by its increment hull, the
convex hull of all path increments. The gauge of the hull provides
an asymptotically pivotal test statistic and an affine-equivariant
confidence region without estimating the long-run covariance matrix,
and its support function gives simultaneous confidence intervals for
linear contrasts. For a single parameter the construction reduces
exactly to adjusted-range self-normalization, whose limiting
distribution is available in closed form. The Brownian reference law
is simulated on a grid matched to the sample size or a supplied
common variance-accumulation profile; inference for dependent
observations remains asymptotic. Five further methods are provided
for comparison on the same estimate and influence contributions:
componentwise adjusted ranges after lag-zero partial prewhitening,
quadratic self-normalization following Shao (2010)