Using Weighted Nonlinear Least Squares to Estimate Fish Population Dynamics Models

Estimation and inference for weighted nonlinear least squares regressions are examined for the case in which the regressors are stochastic, rather than fixed, and where erros may be both heteroscedastic and serially correlated. The usual least squares parameter covarience matrix estimator may be invalid in such cases, and a new covariance matrix estimator is given. General statistics for testing hypotheses about the parameters are provided, as well as new tests for model misspecification. The methodology is applied to the estimation of population dynamics models for the anchovy ("Engraulis mordax").