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E-grāmata: State-Space Models: Applications in Economics and Finance

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State-space models as an important mathematical tool has been widely used in many different fields. This edited collection explores recent theoretical developments of the models and their applications in economics and finance. The book includes nonlinear and non-Gaussian time series models, regime-switching and hidden Markov models, continuous- or discrete-time state processes, and models of equally-spaced or irregularly-spaced (discrete or continuous) observations. The contributed chapters are divided into four parts. The first part is on Particle Filtering and Parameter Learning in Nonlinear State-Space Models. The second part focuses on the application of Linear State-Space Models in Macroeconomics and Finance. The third part deals with Hidden Markov Models, Regime Switching and Mathematical Finance and the fourth part is on Nonlinear State-Space Models for High Frequency Financial Data. The book will appeal to graduate students and researchers studying state-space modeling in economics, statistics, and mathematics, as well as to finance professionals.



This book explores developments in state-space models and their applications in economics and finance. Coverage includes nonlinear and non-Gaussian time series models, regime-switching and hidden Markov models, and continuous- or discrete-time state processes.

Recenzijas

From the book reviews:

The intention of this edited volume is to provide methodological development in statespace models, as well as study their applications, particularly in economics and finance. this book has an impressive collection of material on useful and interesting topics regarding statespace models. The book will be useful equally to graduate students and researchers interested in space-modeling in statistical science, mathematics, and more importantly, in economics. (Technometrics, Vol. 56 (2), May, 2014)

Part I Particle Filtering and Parameter Learning in Nonlinear State-Space Models
1 Adaptive Filtering, Nonlinear State-Space Models, and Applications in Finance and Econometrics
3(20)
Tze Leung Lai
Vibhav Bukkapatanam
1.1 Introduction
3(1)
1.2 Particle Filters in Nonlinear State-Space Models
4(2)
1.2.1 Bootstrap Filter
4(1)
1.2.2 Auxiliary Particle Filter
5(1)
1.2.3 Residual Bernoulli Resampling
6(1)
1.3 Particle Filters with Sequential Parameter Estimation
6(3)
1.3.1 Liu and West's Filter
7(1)
1.3.2 Storvik's Filter
8(1)
1.3.3 Particle Learning
8(1)
1.3.4 Particle MCMC
9(1)
1.4 A New Approach to Adaptive Particle Filtering
9(5)
1.4.1 A New MCMC Approach to Sequential Parameter Estimation
10(2)
1.4.2 Adaptive Particle Filters and Asymptotic Theory
12(2)
1.5 Applications in Finance and Economics
14(6)
1.5.1 Frailty Models for Corporate Defaults
14(3)
1.5.2 Stochastic Volatility with Contemporaneous Jumps
17(2)
1.5.3 State-Space Models for High-Frequency Transaction Data
19(1)
1.5.4 Other Applications in Finance and Economics
20(1)
1.6 Conclusion
20(3)
References
20(3)
2 The Extended Liu and West Filter: Parameter Learning in Markov Switching Stochastic Volatility Models
23(40)
Maria Paula Rios
Hedibert Freitas Lopes
2.1 Introduction
23(5)
2.1.1 Volatility Models
24(2)
2.1.2 Particle Filters: A Brief Review
26(2)
2.2 Particle Filters with Parameter Learning
28(4)
2.2.1 Kernel Smoothing
28(2)
2.2.2 Sufficient Statistics
30(2)
2.3 Analysis and Results: Simulation Study
32(20)
2.3.1 Simulated Data
33(1)
2.3.2 Exact Estimation Path
33(3)
2.3.3 Estimate Evaluation
36(12)
2.3.4 Economic Insight
48(2)
2.3.5 Robustness
50(2)
2.4 Analysis and Results: Real Data Applications
52(7)
2.4.1 IBOVESPA
53(2)
2.4.2 S&P 500
55(4)
2.5 Conclusions
59(4)
References
60(3)
3 A Survey of Implicit Particle Filters for Data Assimilation
63(28)
Alexandre J. Chorin
Matthias Morzfeld
Xuemin Tu
3.1 Introduction
63(2)
3.2 Implicit Particle Filters
65(6)
3.2.1 Linear Observation Function and Gaussian Noise
67(1)
3.2.2 Sparse Observations
68(1)
3.2.3 Models with Partial Noise
69(1)
3.2.4 Combined State and Parameter Estimation
70(1)
3.3 Implementations of the Implicit Particle Filter
71(2)
3.3.1 Solution of the Implicit Equation via Quadratic Approximation
71(1)
3.3.2 Solution of the Implicit Equation via Random Maps
72(1)
3.4 Comparison with Other Sequential Monte Carlo Schemes
73(4)
3.4.1 Comparison with the SIR Filter
74(1)
3.4.2 Comparison with Optimal Importance Function Filters
75(1)
3.4.3 Comparison with the Kalman Filter and with Variational Data Assimilation Methods
76(1)
3.5 Applications
77(8)
3.5.1 A Simple Example
77(1)
3.5.2 Stochastic Volatility Model
78(1)
3.5.3 The Stochastic Lorenz Attractor
78(3)
3.5.4 The Stochastic Kuramoto-Sivashinsky Equation
81(2)
3.5.5 Application to Geomagnetic Data Assimilation
83(1)
3.5.6 Assimilation of Ocean Color Data from NASA's SeaWiFS Satellite
84(1)
3.6 Conclusion
85(6)
References
86(5)
Part II Linear State-Space Models in Macroeconomics and Finance
4 Model Uncertainty, State Uncertainty, and State-Space Models
91(22)
Yulei Luo
Jun Nie
Eric R. Young
4.1 Introduction
91(1)
4.2 Linear-Quadratic-Gaussian State-Space Models
92(2)
4.3 Incorporating Model Uncertainty and State Uncertainty
94(4)
4.3.1 Introducing Model Uncertainty
94(1)
4.3.2 Introducing State Uncertainty
95(3)
4.4 Applications
98(11)
4.4.1 Explaining Current Account Dynamics
98(3)
4.4.2 Resolving the International Consumption Puzzle
101(3)
4.4.3 Other Possible Applications
104(1)
4.4.4 Quantifying Model Uncertainty
105(2)
4.4.5 Discussions: Risk-Sensitivity and Robustness Under Rational Inattention
107(2)
4.5 Conclusions
109(4)
Appendix
109(1)
A.1 Solving the Current Account Model Explicitly Under Model Uncertainty
109(2)
References
111(2)
5 Hong Kong Inflation Dynamics: Trend and Cycle Relationships with the USA and China
113(20)
Pym Manopimoke
5.1 Introduction
113(2)
5.2 Literature Review
115(2)
5.3 Model Specification
117(6)
5.4 Empirical Results
123(7)
5.5 Conclusion
130(3)
References
131(2)
6 The State Space Representation and Estimation of a Time-Varying Parameter VAR with Stochastic Volatility
133(14)
Taeyoung Doh
Michael Connolly
6.1 Introduction
133(1)
6.2 State Space Representation and Estimation of VARs
134(5)
6.2.1 State Space Representation
134(1)
6.2.2 Estimation of VARs
135(4)
6.3 Application: A Time-Varying Parameter VAR with Stochastic Volatility for Three US Macroeconomic Variables
139(5)
6.3.1 Priors
139(1)
6.3.2 Posterior Simulation
140(1)
6.3.3 Posterior Estimates of Time-Varying Trends and Volatility
140(4)
6.4 Conclusion
144(3)
References
145(2)
7 A Statistical Investigation of Stock Return Decomposition Based on the State-Space Framework
147(22)
Jun Ma
Mark E. Wohar
7.1 Introduction
147(4)
7.2 VAR Variance Decomposition of the Stock Prices
151(3)
7.3 The State-Space Model for Decomposing Stock Prices
154(6)
7.4 The Weak Identification and the Corrected Inference
160(3)
7.5 Conclusion
163(6)
References
164(5)
Part III Hidden Markov Models, Regime-Switching, and Mathematical Finance
8 A HMM Intensity-Based Credit Risk Model and Filtering
169(16)
Robert J. Elliott
Tak Kuen Siu
8.1 Introduction
169(2)
8.2 A HMM Frailty-Based Default Model
171(2)
8.3 Filtering Equations for the Hidden Dynamic Frailty Factor
173(4)
8.4 A Robust Filter-Based EM Algorithm
177(3)
8.5 Variance Dynamics
180(1)
8.6 Default Probabilities
181(1)
8.7 Conclusion
182(3)
References
183(2)
9 Yield Curve Modelling Using a Multivariate Higher-Order HMM
185(20)
Xiaojing Xi
Rogemar Mamon
9.1 Introduction
185(3)
9.2 Filtering and Parameter Estimation
188(5)
9.3 Implementation
193(4)
9.4 Forecasting and Error Analysis
197(5)
9.5 Conclusion
202(3)
References
202(3)
10 Numerical Methods for Optimal Annuity Purchasing and Dividend Optimization Strategies under Regime-Switching Models: Review of Recent Results
205(22)
Zhuo Jin
George Yin
10.1 Introduction
205(2)
10.2 Optimal Annuity-Purchasing Strategies
207(7)
10.2.1 Motivation
207(1)
10.2.2 Formulation
208(2)
10.2.3 Constant Hazard Rate
210(1)
10.2.4 General Hazard Rate
211(1)
10.2.5 Examples
212(2)
10.3 Optimal Dividend Payment Policies
214(9)
10.3.1 Motivation
214(1)
10.3.2 Formulation
215(2)
10.3.3 Algorithm
217(2)
10.3.4 Convergence
219(1)
10.3.5 Examples
220(3)
10.4 Concluding Remarks
223(4)
References
224(3)
11 Trading a Mean-Reverting Asset with Regime Switching: An Asymptotic Approach
227(20)
Eunju Sohn
Qing Zhang
11.1 Introduction
227(2)
11.2 Problem Formulation
229(4)
11.3 Properties of the Value Functions
233(2)
11.4 Asymptotic Properties
235(3)
11.5 Further Approximations
238(1)
11.6 A Numerical Example
239(1)
11.7 Concluding Remarks
240(7)
Appendix
242(2)
References
244(3)
12 CPPI in the Jump-Diffusion Model
247(32)
Mingming Wang
Allanus Tsoi
12.1 Introduction
247(1)
12.2 The Jump-Diffusion Model
248(5)
12.2.1 Density
249(2)
12.2.2 Martingale Measure
251(2)
12.3 The CPPI Strategies
253(6)
12.3.1 The constant multiple case
253(6)
12.3.2 The Time-Varying Multiple Case
259(1)
12.4 The CPPI Portfolio as a Hedging Tool
259(12)
12.4.1 PIDE Approach
260(4)
12.4.2 Martingale Approach
264(7)
12.5 Mean-Variance Hedging
271(4)
12.5.1 The Idea
271(2)
12.5.2 The Problem
273(2)
12.6 Conclusion
275(4)
References
275(4)
Part IV Nonlinear State-Space Models for High Frequency Financial Data
13 An Asymmetric Information Modeling Framework for Ultra-High Frequency Transaction Data: A Nonlinear Filtering Approach
279(32)
Yoonjung Lee
13.1 Introduction
279(4)
13.2 The Model
283(4)
13.2.1 The Information Structure Dynamics
283(2)
13.2.2 Informed Traders' Signal Extraction
285(1)
13.2.3 Order Arrivals
286(1)
13.3 Bayesian Updating of the Market Maker's Beliefs via Filtering
287(6)
13.3.1 Construction of a Reference Measure
289(2)
13.3.2 Filtering Equation
291(1)
13.3.3 Uniqueness of the System
292(1)
13.4 Key Implications of the Model
293(2)
13.4.1 The Quality of the Signal
293(1)
13.4.2 Informed Traders' Trading Rate
294(1)
13.4.3 The Price Impact of a Trade
294(1)
13.5 Parameter Estimation
295(3)
13.5.1 Maximum Likelihood Estimation
296(1)
13.5.2 Parameter Estimation for Simulated Data
297(1)
13.6 Conclusion
298(13)
Appendix
300(8)
References
308(3)
14 Heterogenous Autoregressive Realized Volatility Model
311(10)
Yazhen Wang
Xin Zhang
14.1 Introduction
311(1)
14.2 High-Frequency Financial Data and Price Model
312(1)
14.3 GARCH and Stochastic Volatility Approximations to the Price Model
313(1)
14.4 The HAR Model for Volatility Processes
314(1)
14.5 The HAR Model for Realized Volatilities
315(2)
14.6 The Temporal Aggregation of AR Processes
317(4)
References
320(1)
15 Parameter Estimation via Particle MCMC for Ultra-High Frequency Models
321(24)
Cai Zhu
Jian Hui Huang
15.1 Introduction
321(2)
15.2 The Model
323(4)
15.2.1 Trading Times
324(1)
15.2.2 Micro-Structure Noise
324(2)
15.2.3 Intrinsic Value Processes
326(1)
15.3 Estimation Method
327(5)
15.3.1 Likelihood Calculation via Simulation
327(2)
15.3.2 Importance Sampling
329(1)
15.3.3 Sequential Importance Sampling: Particle Filtering
330(1)
15.3.4 Particle MCMC
331(1)
15.4 Simulation and Empirical Studies
332(10)
15.4.1 Variance Reduction Effect of Particle Filtering Method
332(1)
15.4.2 Simulation Study: GBM Case
333(3)
15.4.3 Comparison Algorithm Under Trading Rules with 1/8 and 1/100 Tick Size
336(2)
15.4.4 Simulation Study: Jump-Diffusion Case
338(3)
15.4.5 Real Data Application
341(1)
15.5 Conclusion
342(3)
References
343(2)
Index 345
Yong Zeng is a professor in Department of Mathematics and Statistics at University of Missouri at Kansas City. His main research interest includes mathematical finance, financial econometrics, stochastic nonlinear filtering, and Bayesian statistical analysis. Notably, he developed the statistical analysis via filtering for financial ultra-high frequency data, where the model can be viewed as a random-arrival-time state space model. He has published in Mathematical Finance, International Journal of Theoretical and Applied Finance, Applied Mathematical Finance, IEEE Transactions on Automatic Control, Statistical Inference for Stochastic Processes, among others. He held visiting associate professor positions at Princeton University and the University of Tennessee.  He received his B.S. from Fudan University in 1990, M.S. from University of Georgia in 1994, and Ph.D. from University of Wisconsin at Madison in 1999. All degrees were in statistics.





Shu Wu is an associate professor in Department of Economics at University of Kansas. His main research areas are empirical macroeconomics and finance. He has held visiting positions at Federal Reserve Bank at Kansas City, City University of Hong Kong. His publications have appeared in Journal of Monetary Economics, Journal of Money, Credit and Banking, Macroeconomic Dynamics, International Journal of Theoretical and Applied Finance, Journal of International Financial Markets, Institutions and Money, Handbook of Quantitative Finance and Risk Management, Hidden Markov Models in Finance among others. He received his Ph.D. in economics from Stanford University in 2000.
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