In this article,relative curvature measures are derived for nonseasonal and multiplicative seasonal autoregressive moving average(ARMA)models to be used as diagnostic tools to asses the degree model nonlinearity.The maximum and root mean square curvature are computed for 16 time series data sets modeled in the literature by ARMA models;it is seen that more than half the sets exhibit significally large intrinsic or parameter- effectscurvature.The effect of curvature on the confidence regions for parameters is discussed and illustrated by examples.