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Hidden Markov Models in Finance and Other Applications.pdf
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内容超级新，2026的最新上线！
内容非常全面，190多页的详尽讲解！科研项目研究课题必备！
1 Introduction 1
1.1 A Brief History of HMM . 1
1.2 Markov Process 3
1.2.1 Markov Process 3
1.2.2 Example of a Discrete Markov Process . 4
1.3 Hidden Markov Model 7
1.3.1 Discrete HMM 8
1.3.2 Continuous HMM 9
1.3.3 Likelihood of an HMM 10
1.3.4 Examples of Discrete HMMs 12
1.3.5 Examples of a Continuous HMM 16
1.4 Types of an HMM Based on Its Transition Matrix 20
1.4.1 The Ergodic HMM 20
1.4.2 The Left-Right HMM 21
1.4.3 Other Left-Right Model . 21
1.5 Higher-Order HMM . 22
2 Three Main Problems of an HMM and Their Algorithms 25
2.1 Three Main Problems of an HMM . 25
2.2 Forward Algorithm 26
2.2.1 Forward Algorithm for a Single Observation Sequence 26
2.2.2 Forward Algorithm for Multiple Observation Sequences . 27
2.2.3 Example of Using the Forward Algorithm . 27
2.2.4 R Code for the Forward Algorithm . 29
2.3 Backward Algorithm . 31
2.3.1 Backward Algorithm for a Single Observation Sequence . 32
2.3.2 Backward Algorithm for Multiple Observation Sequences 33
2.3.3 Example of Using the Backward Algorithm 33
2.3.4 R Code for the Backward Algorithm 35
2.4 Viterbi Algorithm 36
2.4.1 Viterbi Algorithm for a Single Observation Sequence . 37
2.4.2 Example of Using the Viterbi Algorithm 37
2.4.3 R Code for the Viterbi Algorithm . 38
2.5 Baum-Welch Algorithm . 41
2.5.1 Baum-Welch Algorithm for a Single Observation Sequence 41
2.5.2 Baum-Welch Algorithm for Multiple Observation Sequences . 44
2.5.3 Example of Using the Baum-Welch Algorithm . 46
2.5.4 R Code for the Baum-Welch Algorithm 48
2.5.5 Example of Using the Baum-Welch R Code 55
2.6 Scaling HMM Algorithms with R
vi Contents
2.6.1 Scaled Forward Algorithm 62
2.6.2 Scaled Backward Algorithm . 63
2.6.3 Log Viterbi Algorithm and Its Example 66
2.6.4 Scaled Baum-Welch Algorithm and Its Example . 69
3 Model Selection 79
3.1 Model Selection Indicators 79
3.2 Choosing the Number of States for an HMM . 80
3.3 Comparison of HMMs 81
3.4 Model Evaluation Indicators . 82
4 Applications of HMM in Finance 85
4.1 Overview of Published Work on HMM Applications in Finance . 85
4.1.1 Published Articles on HMM Applications in Finance . 85
4.1.2 Books on HMM and Its Applications in Finance . 85
4.1.2.1 Regime Switching Model vs. HMMs . 86
4.1.2.2 Applications of Regime-Switching Models 86
4.2 R Functions for HMM Implementation . 86
4.3 HMM for Mortgage-Backed Security ETFs . 91
4.3.1 Overview of Mortgage-Backed Securities 91
4.3.2 Data Selection 91
4.3.3 Using an HMM to Identify Hidden States . 92
4.3.4 Using an HMM to Estimate Recession Probabilities . 98
4.3.5 Using an HMM for Price Prediction and MBS ETF Trading . 101
4.3.5.1 Model Selection 101
4.3.5.2 Price Prediction 104
4.3.5.3 Model Validations . 108
4.3.5.4 Trading Mortgage-Backed Securities . 109
4.3.6 Conclusions 110
4.4 HMM for Stock Selection 111
4.4.1 Introduction . 111
4.4.2 Data Selections 112
4.4.3 Model Description 113
4.4.4 Identifying Regimes in Macroeconomic Variables . 114
4.4.5 Stock Selection 116
4.4.6 Conclusions 121
4.5 HMM for Stock Trading . 121
4.5.1 Introduction . 122
4.5.2 Data Selection 126
4.5.3 Model Selection 126
4.5.4 Out-of-Sample Stock Price Prediction . 128
4.5.5 Model Validation . 129
4.5.6 Stock Trading Using an HMM . 134
4.5.7 Conclusions 135
4.6 Enhancing the Hull-White Short Rate Model with an HMM . 135
4.6.1 Introduction . 136
4.6.2 Overview of the HMM 136
4.6.3 Overview of Hull-White Model . 137
4.6.4 Combining the HMM with the Hull-White One-Factor Model 139
4.6.4.1 Methodology 139
4.6.4.2 Implementation and Results . 140
vi Contents
2.6.1 Scaled Forward Algorithm 62
2.6.2 Scaled Backward Algorithm . 63
2.6.3 Log Viterbi Algorithm and Its Example 66
2.6.4 Scaled Baum-Welch Algorithm and Its Example . 69
3 Model Selection 79
3.1 Model Selection Indicators 79
3.2 Choosing the Number of States for an HMM . 80
3.3 Comparison of HMMs 81
3.4 Model Evaluation Indicators . 82
4 Applications of HMM in Finance 85
4.1 Overview of Published Work on HMM Applications in Finance . 85
4.1.1 Published Articles on HMM Applications in Finance . 85
4.1.2 Books on HMM and Its Applications in Finance . 85
4.1.2.1 Regime Switching Model vs. HMMs . 86
4.1.2.2 Applications of Regime-Switching Models 86
4.2 R Functions for HMM Implementation . 86
4.3 HMM for Mortgage-Backed Security ETFs . 91
4.3.1 Overview of Mortgage-Backed Securities 91
4.3.2 Data Selection 91
4.3.3 Using an HMM to Identify Hidden States . 92
4.3.4 Using an HMM to Estimate Recession Probabilities . 98
4.3.5 Using an HMM for Price Prediction and MBS ETF Trading . 101
4.3.5.1 Model Selection 101
4.3.5.2 Price Prediction 104
4.3.5.3 Model Validations . 108
4.3.5.4 Trading Mortgage-Backed Securities . 109
4.3.6 Conclusions 110
4.4 HMM for Stock Selection 111
4.4.1 Introduction . 111
4.4.2 Data Selections 112
4.4.3 Model Description 113
4.4.4 Identifying Regimes in Macroeconomic Variables . 114
4.4.5 Stock Selection 116
4.4.6 Conclusions 121
4.5 HMM for Stock Trading . 121
4.5.1 Introduction . 122
4.5.2 Data Selection 126
4.5.3 Model Selection 126
4.5.4 Out-of-Sample Stock Price Prediction . 128
4.5.5 Model Validation . 129
4.5.6 Stock Trading Using an HMM . 134
4.5.7 Conclusions 135
4.6 Enhancing the Hull-White Short Rate Model with an HMM . 135
4.6.1 Introduction . 136
4.6.2 Overview of the HMM 136
4.6.3 Overview of Hull-White Model . 137
4.6.4 Combining the HMM with the Hull-White One-Factor Model 139
4.6.4.1 Methodology 139
4.6.4.2 Implementation and Results . 140
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