Times series data are often subject to measurement error, usually the result of needing to estimate the variable of interest (population size, unemployment rate, etc.) In this talk, we will survey the literature on this problem and then present some new work when the measurement error is additive but has unequal variance due to changes in the ``population'' over time and/or changes in sampling effort. We will first discuss this heteroscedastic measurement error model, (which has application in many other settings) in order to carefully
distinguish conditional and unconditional heteroscedasticity. We will then overview results with measurement error arising in two settings; linear autoregressive models and a random walk model. For the first problem the focus is on estimation of the autoregressive parameters. The asymptotic biases of naive estimators, which ignore measurement error are presented and various estimators which correct for measurement error are presented and evaluated. The random walk model, which has been used in ecology for a number of threatened species, generally has a different focus with the primary goal being estimation of functions of the parameters. These include the intrinsic rate of increase, the probability of eventual extinction and probabilities about abundance at future points in time. We examine biases in naive estimators of these quantities and overview correction techniques.
This is joint work with John Staudenmayer.
Refreshments will be served at 3:45 p.m. in Room 008 of the Statistics Building