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

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.NNI - Nortel Networks Inc(To CHAIR - POCI-01-0145-FEDER-028247)This research was funded by FEDER/COMPETE/NORTE 2020/POCI/FCT funds through grants UID/EEA/-00147/20 13/UID/IEEA/00147/006933-SYSTEC project and To CHAIR - POCI-01- 0145-FEDER-028247. A. Manuela Gonçalves was partially financed by Portuguese Funds through FCT (Fundação para a Ciência e a Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM. Marco Costa was partially supported by The Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. F. Catarina Pereira was financed by national funds through FCT (Fundação para a Ciência e a Tecnologia) through the individual PhD research grant UI/BD/150967/2021 of CMAT-U