1. Identification of models for linear and nonlinear non-causal data structures 1 Uwe Kruger and 2 Jochen Einbeck 1 Department of Mechanical & Industrial Engineering, Sultan Qaboos University, P.O. Box 33, Muscat, Oman 2 Department of Mathematical Sciences, Durham University, DH1 3LE, U.K.

2. Uwe Kruger and Jochen Einbeck Identification of models for linear and nonlinear non-causal data structures Durham, 7. May, 2013 Slide 2 Presentation Outline 1.Linear non-causal data structures with simple diagonal error covariance matrix containing unknown and equal diagonal elements 2.Linear non-causal data structures with known symmetric and positive definite error covariance matrix 3.Linear non-causal data structures with unknown diagonal error covariance matrix containing unequal and unknown diagonal elements 4.Estimating of fractal dimension for nonlinear non-causal data structures.

3. Uwe Kruger and Jochen Einbeck Identification of models for linear and nonlinear non-causal data structures Durham, 7. May, 2013 Linear non-causal data structures diagonal error covariance matrix with unknown but identical diagonal elements (i) Slide 3

4. Uwe Kruger and Jochen Einbeck Identification of models for linear and nonlinear non-causal data structures Durham, 7. May, 2013 Slide 4 Linear non-causal data structures diagonal error covariance matrix with unknown but identical diagonal elements (ii)

5. Uwe Kruger and Jochen Einbeck Identification of models for linear and nonlinear non-causal data structures Durham, 7. May, 2013 Slide 5 Linear non-causal data structures symmetric and positive definite error covariance matrix that is known (i)

6. Uwe Kruger and Jochen Einbeck Identification of models for linear and nonlinear non-causal data structures Durham, 7. May, 2013 Slide 6 Linear non-causal data structures symmetric and positive definite error covariance matrix that is known (ii)

7. Uwe Kruger and Jochen Einbeck Identification of models for linear and nonlinear non-causal data structures Durham, 7. May, 2013 Slide 7 Linear non-causal data structures unknown diagonal error covariance matrix with unequal diagonal elements (i)

8. Uwe Kruger and Jochen Einbeck Identification of models for linear and nonlinear non-causal data structures Durham, 7. May, 2013 Slide 8 Linear non-causal data structures unknown diagonal error covariance matrix with unequal diagonal elements (ii)

9. Uwe Kruger and Jochen Einbeck Identification of models for linear and nonlinear non-causal data structures Durham, 7. May, 2013 Slide 9 Linear non-causal data structures unknown diagonal error covariance matrix with unequal diagonal elements (iii)