Estimation of time series models using residuals dependence measures Articles uri icon

publication date

  • October 2022

start page

  • 3039

end page

  • 3063


  • 5


  • 50

International Standard Serial Number (ISSN)

  • 0090-5364

Electronic International Standard Serial Number (EISSN)

  • 0003-4851


  • We propose new estimation methods for time series models, possibly noncausal and/or noninvertible, using serial dependence information from the characteristic function of model residuals. This allows to impose the i.i.d. or martingale difference assumptions on the model errors to identify the unknown location of the roots of the lag polynomials for ARMA models without resorting to higher order moments or distributional assumptions. We consider generalized spectral density and cumulative distribution functions to measure residuals dependence at an increasing number of lags under both assumptions and discuss robust inference to higher order dependence when only mean independence is imposed on model errors. We study the consistency and asymptotic distribution of parameter estimates and discuss efficiency when different restrictions on error dependence are used simultaneously, including serial uncorrelation. Optimal weighting of continuous moment conditions yields maximum likelihood efficiency under independence for unknown error distribution. We investigate numerical implementation and finite sample properties of the new classes of estimates.


  • Economics


  • characteristic function; martingale difference; generalized method of moments; generalized spectral density; non-causal processes; non-invertible processes