Global Index (short | long) | Local contents | Local Index (short | long)
THETA is a matrix containing information about model structure, estimated parameters and their estimated accuracy. For STATE-SPACE and MULTI-OUTPUT structures, see also THSS. For the general input-output model, the structure is as follows: A(q) y(t) = [B(q)/F(q)] u(t-nk) + [C(q)/D(q)] e(t) A, B, C, D and F are polynomials in the delay operator of orders na, nb, nc, nd and nf, respectively. If the system has nu inputs, u has nu columns and nb, nf and nk are then row vectors of dimension nu, con- taining information about the orders and delays associated with each of the inputs. In the case of a time series (no u) B and F are not defined. Let n be the sum of all the orders (=the number of estimated parameters). Let r=max(n,7,6+3*nu). Then THETA is a (3+n) x r matrix organized as follows: Row 1 has entries: Estimated variance of e, sampling interval, nu,na, nb,nc,nd,nf,nk. Row 2 has entries, FPE, year, month, date, hour, minute and command by which the model was generated. Row 3 is the vector of estimated parameters A,B,C,D and F (excluding leading 1's and zeros). Rows 4 to 3+n contain the estimated covariance matrix. THETA-matrices are created by the commands, and see also, POLY2TH, PEM, IV, IV4, ARX, ARMAX, OE, BJ, AR and IVAR, and they are transformed to other representations by the commands TRF, ZP, TH2POLY, TH2TF, TH2SS, and TH2PAR.
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% L. Ljung % Copyright (c) 1986-98 by The MathWorks, Inc. % $Revision: 2.3 $ $Date: 1997/12/02 03:43:16 $