PredictionTheory 17 08 19 - predictsys.com

1 PREDICTION THEORY FOR CONTROL SYSTEMS August 19, 2017 BY: WILLIAM C. CAVE COPYRIGHT 1989 THROUGH, 2017 309 Morris Avenue Spring Lake, NJ 07762 (732)449-6800 (732)449-0897 www. PREDICTION THEORY FOR CONTROL SYSTEMS August 19, 2017 BY: WILLIAM C. CAVE COPYRIGHT 1989 THROUGH, 2017 309 Morris Avenue Spring Lake, NJ 07762 (732)449-6800 (732)449-0897 www. TABLE OF CONTENTS CHAPTER CONTENTS PAGE PREFACE i 1 INTRODUCTION 1 The Embedded Prediction Component Of A Control

2 system 1 Prediction Versus Forecasting 3 The Prediction Problem 4 Human Judgment Versus Automation 5 Drawing The Line Between Human Judgment And Automation 5 Defining The Prediction Problem 7 Stochastic Nature Of The Problem 10 Dealing With Variations

3 10 Dealing With Large Decision Trees In Time 11 Accounting For Constraints 12 2 MEASURING PREDICTION ERROR 14 3 CHARACTERIZING PREDICTION ACCURACY 16 Specification of a Prediction Envelope 16 Measuring Confidence In The Prediction Envelope 19 A Measure of Prediction Quality 21 4 OPTIMIZING AND VALIDATING MODELS OF SYSTEMS TO PREDICT FUTURE RESPONSES 22 Statistical Models For Prediction 22

4 Deterministic Models For Prediction 23 General Approach To Building And Validating Prediction Models 24 5 A GENERALIZED MODELING FRAMEWORK 25 The State Space Framework 25 A Generalized State Space Framework 26 General Model Formulation 27 Nonlinear Considerations 28 Nonhomogeneous Considerations

5 29 Modeling Inertial Subsystems 31 Modeling Distributed Responses To Events 32 Modeling Housing Completions Based On Building Permits 32 Linear Versus Nonlinear Systems 35 TABLE OF CONTENTS (CONT.)

6 CHAPTER CONTENTS PAGE 6 CLASSIFYING SYSTEMS AND THEIR MODELS TO PREDICT THEIR RESPONSE 36 The Concept of Boundedness 37 The Concept of Randomness 37 Measures of Prediction Error 40 The Concept of Stationarity 41 The Concept of

7 Orthogonality 42 Statistical Stationarity 43 7 TIME CORRELATION 45 Calendar Correlation Models 45 Sample Size Differences Within A Sample Period 47 Requirement For More Data 47 Defining The Periods 48

8 Algorithm For Selecting Weights 50 Algorithm For Computing Weights 50 Weighting Data By Year 50 Using Weights To Improve Prediction Accuracy 51 8 ENVELOPE PREDICTION MODEL 52 Envelopes 52 Updating Envelope Estimates 53 Initial Envelope 53