ARMA model order/Data length tradeoff for specified frequency resolution

A relation between model order and length of data set for resolution capabilities of autoregressive moving average (ARMA) time series models is presented. One representative block ARMA technique and an unnormalized ARMA lattice technique are considered. The results are based on an example of two sinusoids in white noise, closely spaced with different SNR levels. Resolution is defined as a 1 to 3 dB dip in the ARMA PSD between the location of the two sinusoids. A significant inverse relationship between model order and data set length, up to about 300 data points, for both the techniques is demonstrated. Above 300 data points, there is a very gradual decrease in model order required. Also, for a given number of data points, the block technique requires a significantly lower model order than the recursive technique.