Spectral Analysis by Stationary Time Series Modeling - Spectral Analysis: Parametric and Non-Parametric Digital Methods - page 153

,

,

,

Calculation using
the eigenvalues of

,

Calculation using
the prediction error

Figure 6.4. Comparison of the MDL criteria [6.35] and [6.37] for SNR = 0 dB

In the case of a Prony model, the model order corresponds to the number of
searched exponential components, which evidently reduces to an order
determination problem of AR model. All the preceding criteria are applicable.

In the case of an ARMA model, selecting the models p and q of the respective
AR and MA parts is not a simple problem. Few published works tackle this problem,
excepting the very simple cases. The AIC criterion is one of the most used in the
form:

( ) (

( ) )

ˆ

AIC p,q = N ln ρ + 2 p + q

pq

where ˆ p ρ represents the estimated power of the entrance noise of the ARMA
model. As in the case of the AR model, the minimum of this function with two
variables provides the couple ( p , q ) of the AR and MA orders to be taken into
account.

6.3. Properties of spectral estimators produced

In the case of a signal made up of a sinusoid and an additive white noise, we take
interest in the AR model spectrum evolution, according to the signal to noise ratio
(SNR), for a fixed AR order. Various results can be found in the literature,
depending on the hypotheses taken for the modeled signal. For an example, we can