Numerical methods in time series modelling

In this paper a certain number of algorithms in the time-domain approach of time series are reviewed. The following subjects are treated: determination of the autocorrelation function of a stationary autoregressive-moving average (ARMA) process; tests of hypotheses and confidence intervals for autocorrelations; tests of randomness based on rank autocorrelations; the corner method for the identification of ARMA models; determination of the sample innovations by a fast Kalman filter algorithm; use of that algorithm in forecasting and generation of artificial time series; estimation of the parameters of an ARMA model by a pseudo-maximum likelihood procedure; recursive estimation methods for the parameters of an ARMA model; evaluation of the asymptotic covariance matrix of the maximum likelihood estimators of the parameters of an ARMA model.