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# AR model

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### AR model

1. 1. SELECTION OFAR MODEL ORDER Presented by: Naveen Kumar M.E. ECE Roll No. : 112610
2. 2. Introduction In the model-based approach, the spectrum estimation procedure consists of two steps.(i) We estimate the parameters{ak}and{bk} of the model.(ii) From these estimates, we compute the power spectrum estimate. There are three types of models :- AR Model MA Model ARMA Model
3. 3. What is AR Model? A model which depends only on the previous outputs of the system is called an autoregressive model (AR). Note that:-  AR model is based on frequency-domain analysis.  AR model has only poles while the MA model has only zeros.
4. 4. AR Model Equation The AR-model of a random process in discrete time is defined by the following expression: where a1,a2…..,ap coefficients of the recursive filter; p is the order of the model; Є(t) are output uncorrelated errors or simply White noise.
5. 5. Need for selection of model order An order selection criterion is used to determine the appropriate order for the AR model. The model parameters are found by solving a set of linear equation obtained by minimizing the mean squared error. The characteristic of this error is that it decreases as the order of the AR model is increased.
6. 6. Need… One of the most important consideration is the choice of the number of terms in the AR model, this is known as its order p. If a model with too low an order, We obtain a highly smoothed spectrum. If a model with too high an order, There is risk of introducing spurious low-level peaks in the spectrum.
7. 7. AR Model Order Selection Two of the better known criteria for selection the model order have been proposed by Akaike –(1969,1974.)2) Known as Finite Prediction Error (FPE) criterion. = estimated variance of the linear prediction error. N = number of samples. p = is the order of model.
8. 8. 1) The second criterion proposed by Akaike (1974),called the Akaike Information Criterion (AIC) decreases & therefore also decreases as the order of the AR model is increased. increases with increases in p.
9. 9. Difference between FPE & AIC(i) FPE (p) Is recommended for longer data records. It never exceeds model order selected by AIC(ii) AIC (p) Is recommended for short data records.
10. 10. 1) An alternative information criterion, proposed by Rissanen (1983),is based on selecting the order that minimizes the description length :-
11. 11. 1) A fourth criterion has been proposed by Parzen(1974). This is called the Criterion Autoregressive Transfer (CAT) function & defined as The order p is selected to minimize CAT(p)
12. 12. Applications Texture modelling of visual content. Speech processing. Models for future sample predictions
13. 13. Drawback AR models linearly relate the signal samples which is not valid for many real-life applications, where there may be many non- linearity.
14. 14. Conclusion The experimental results, just indicate that the model-order selection criteria do not yields definitive results. The FPE(p) criterion tends to underestimate the model order. The AIC criterion is statistically inconsistent as N→∞. The MDL information criterion is statistically consistent.
15. 15. References Proakis John G. , “ Digital Signal Processing “ 4rd edition Comparison of Criteria for Estimating the Order ofAutoregressive Process: www.eurojournals.com/ejsr.htm http://www.hindawi.com/journals/asp/2009/475147/