Outliers impact on parameter estimation of gaussian and non-gaussian state space models: a simulation study

Abstract

State space models are powerful and quite flexible tools that allow systems that vary significantly over time due to their formulation to be dealt with, because the models’ parameters vary over time. Assuming a known distribution of errors, in particular the Gaussian distribution, parameter estimation is usually performed by maximum likelihood. However, in time series data, it is common to have discrepant values that can impact statistical data analysis. This paper presents a simulation study with several scenarios to find out in which situations outliers can affect the maximum likelihood estimators. The results obtained were evaluated in terms of the difference between the maximum likelihood estimate and the true value of the parameter and the rate of valid estimates. It was found that both for Gaussian and exponential errors, outliers had more impact in two situations: when the sample size is small and the autoregressive parameter is close to 1, and when the sample size is large and the autoregressive parameter is close to 0.25.