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In view of detecting the stochastic non-stationarity in time series, successive Yule-Walker estimates are considered for general seasonal ARIMA models and their asymptotic laws are obtained. This extends results known on least squares estimates for stable-unstable ARMA. Furthermore, these asymptotic laws are then compared with analogous results obtained under some additive seasonal model that corresponds to the case of deterministic seasonal behaviour. These results, combined with a simulation study, reveal that successive autoregressions provide a very useful tool both for identifying seasonal ARIMA processes and for distinguishing between stochastic and deterministic seasonal behaviours. [ABSTRACT FROM AUTHOR]