Estimating the turning point location in shifted exponential model of time series

TL;DR

This paper develops a formula to estimate the distribution and confidence interval of the turning point in time series modeled with shifted exponential distributions, validated through simulations and applied to ECG data.

Contribution

It introduces a novel method for estimating the turning point distribution in shifted exponential models of time series, including confidence interval calculation.

Findings

The formula accurately estimates the turning point distribution in simulated data.

The method provides reliable confidence intervals for the minimum location in real ECG data.

Coverage rates depend on the bandwidth parameter in the estimation process.

Abstract

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.