Categorical Time Series:prediction and Control

Abstract

4.6 Geometric Properties of the Proposed Algorithm ν 4.7 Self-tuning of the Control Law 4.8 Simulations 5 Main Results and Further Research 109 5.1 Main Results 5.2 Further Research A The TOGA/COARE Data 112 Bibliography 113 vi 4.1 (a) Norm of the estimators (b) Controlled probabilities around 1/2 (c) Norm of the difference ß t -kß for the model λ ί+ ι = -1.5Î/Î + 2u t -Ut-i with u t = s'm(t) + cos(i) 97 4.2 (a) Iterations for ß\ (b) Iterations for ß 2 (c) Iterations for /5 3 for the model X t+i = -l.5y t + 2u t -u t -i with u t = sin(i) + cos(t). . . 98 4.3 (a) Norm of the estimators (b) Controlled probabilities around 1/2. (c) Norm of the difference ß t -kß for the model \ t+ i --1.5J/Ì + 2u t -«i_i with u t = .3u t + e t 99 4.4 (a) Iterations for ß\ (b) Iterations for ß 2 (c) Iterations for β Ά for the model A i+i = -1.5y< + 2u t -u<_i with u t = .3u t + e t 100 4.5 (a) Norm of the estimators (b) Controlled probabilities around 1/2 (c) Norm of the difference ß t -kß for the model \ t +i = -1.5y< + 2u t -u t -\ with starting values (-2,3.1,2) 101 4.6 (a) Iterations for βι (b) Iterations for ß 2 (c) Iterations for ß 3 for the model X t +i = -1.5?/* + 2u t -u t -\ with starting values (-2,3.1,2).102 4.7 (a) Norm of the estimators (b) Controlled probabilities around 1/2 (c) Norm of the difference ß t -kß for the model A t+ i = yt -.5y t _i -2tt t •+ u t -i 103 4.8 (a) Iterations for βχ (b) Iterations for ß 2 (c) Iterations for ß 3 (d) Iterations for β± for the model A i+i = y t -.5y<_i -2u t + u t -i. . . 104 4.9 (a) Norm of the estimators (b) Controlled probabilities aroun 1/2 (c) Norm of the difference ß t -kß for the model A i+J = -1.2y< -1.32u t + .lut-i + u t -2 105 χ 4.10 (a) Iterations for βχ (b) Iterations for ß (c) Iterations for ß 3 (d) Iterations for β 4 for the model λ ί+ ι = -1.2y t -1.32u t + Au t -i + u t -2 106 4.11 (a) Norm of the estimators (b) Controlled probabilities around .2 (c) Norm of the difference ß t -kß 107 4.12 (a) Iterations for βχ (b) Iterations for β 2 (c) Iterations for βζ for the control of probabilities around .2 108 xi