An Application of a Linear Gaussian State Space Model and the Kalman Filter In Estimating Expectations of the Natural Logarithmic Monthly Market Returns of the US 1838 Bond Debenture Closed-End Fund

2018 ◽  
Author(s):  
Michel Guirguis
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
State Space Model ◽  
Gaussian State ◽  
Market Returns ◽  
Space Model ◽  
The Us

scholarly journals Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 117
Author(s):  
Xuyou Li ◽  
Yanda Guo ◽  
Qingwen Meng
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Space Model ◽  
Performance Evaluations ◽  
Gaussian State ◽  
Variational Bayesian ◽  
Space Model ◽  
Bandwidth Parameter ◽  
Non Gaussian ◽  
Filtering Problem

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.

scholarly journals A Hybrid Nonlinear Forecasting Strategy for Short-Term Wind Speed

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1596 ◽  
Author(s):  
Xin Zhao ◽  
Haikun Wei ◽  
Chenxi Li ◽  
Kanjian Zhang
Keyword(s):  
Kalman Filter ◽  
Wind Speed ◽  
State Space ◽  
State Space Model ◽  
Hybrid Approach ◽  
Wind Farms ◽  
Short Term ◽  
Forecasting Accuracy ◽  
Space Model ◽  
Wind Speeds

The ability to predict wind speeds is very important for the security and stability of wind farms and power system operations. Wind speeds typically vary slowly over time, which makes them difficult to forecast. In this study, a hybrid nonlinear estimation approach combining Gaussian process (GP) and unscented Kalman filter (UKF) is proposed to predict dynamic changes of wind speed and improve forecasting accuracy. The proposed approach can provide both point and interval predictions for wind speed. Firstly, the GP method is established as the nonlinear transition function of a state space model, and the covariance obtained from the GP predictive model is used as the process noise. Secondly, UKF is used to solve the state space model and update the initial prediction of short-term wind speed. The proposed hybrid approach can adjust dynamically in conjunction with the distribution changes. In order to evaluate the performance of the proposed hybrid approach, the persistence model, GP model, autoregressive (AR) model, and AR integrated with Kalman filter (KF) model are used to predict the results for comparison. Taking two wind farms in China and the National Renewable Energy Laboratory (NREL) database as the experimental data, the results show that the proposed hybrid approach is suitable for wind speed predictions, and that it can increase forecasting accuracy.

ASSESSING PRE-CRISIS FUNDAMENTALS IN SELECTED ASIAN STOCK MARKETS

2005 ◽  
Vol 50 (02) ◽  
pp. 175-196 ◽  
Author(s):  
EE LENG LAU ◽  
G. K. RANDOLPH TAN ◽  
SHAHIDUR RAHMAN
Keyword(s):  
Kalman Filter ◽  
Emerging Markets ◽  
State Space ◽  
Stock Prices ◽  
Stock Markets ◽  
Bubble Formation ◽  
State Space Model ◽  
Space Model ◽  
Rational Bubbles ◽  
Space Formulation

In the folklore of emerging markets, there is a popular belief that bubbles are inevitable. In this paper, our objective is to estimate a state-space model for rational bubbles in selected Asian economies with the aid of the Kalman Filter. For each economy, we derive a possible picture of the bubble formation process that is implied by the state-space formulation. The estimation is based on the rational valuation formula for stock prices. Our results provide a possible way of defining the presence of rational bubbles in the stock markets of Taiwan, Singapore, Korea, and Malaysia.

Identification of Stochastic System and Controller via Projection Filters

1996 ◽  
Vol 118 (2) ◽  
pp. 169-176 ◽  
Author(s):  
Hyun Chang Lee ◽  
Min-Hung Hsiao ◽  
Jen-Kuang Huang ◽  
Chung-Wen Chen
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Stochastic System ◽  
State Space Model ◽  
Open Loop ◽  
The State ◽  
Loop System ◽  
Test Facility ◽  
System Response ◽  
Space Model

A method based on projection filters is presented for identifying an open-loop stochastic system with an existing feedback controller. The projection filters are derived from the relationship between the state-space model and the AutoRegressive with eXogeneous input (ARX) model including the system, Kalman filter and controller. Two ARX models are identified from the control input, closed-loop system response and feedback signal using least-squares method. Markov parameters of the open-loop system, Kalman filter and controller are then calculated from the coefficients of the identified ARX models. Finally, the state-space model of the open-loop stochastic system and the gain matrices for the Kalman filter and controller are realized. The method is validated by simulations and test data from an unstable large-angle magnetic suspension test facility.

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