  We consider the distribution of the turning point location of time series
modeled as the sum of deterministic trend plus random noise. If the variables
are modeled by shifted exponentials, whose location parameters define the
trend, we provide a formula for computing the distribution of the turning point
location and consequently to estimate a confidence interval for the location.
We test this formula in simulated data series having a trend with asymmetric
minimum, investigating the coverage rate as a function of a bandwidth
parameter. The method is applied to estimate the confidence interval of the
minimum location of the time series of RT intervals extracted from the
electrocardiogram recorded during the exercise test. We discuss the connection
with stochastic ordering.
