On a class of nonlinear time series models for biological population abundance data

Abstract

A class of nonlinear time series models are developed based on the Ricker biological population abundance model. These models are useful in providing some description to aid understanding of the complex underlying population dynamics. They are proved to have some desirable probabilistic and statistical properties like geometric ergodicity and asymptotic stationarity. 'Conditional least squares' (CLS) is used to estimate the parameters of these models. Consistency and asymptotic normality of the CLS estimators are established. Tests of hypotheses for subsets of the parameters are examined. Simulation studies suggest that the asymptotic results are applicable to small samples. Finally, we apply the methodology to analyse two real data sets. One of these is the classic Canadian lynx data. One of the models developed fits the lynx data quite well and is parsimonious in that it involves estimation of only three parameters; as many as 24 parameters have been used.