Factor State-Space Models for High-Dimensional Realized Covariance Matrices of Asset Returns

2018 ◽  
Author(s):  
Bastian Gribisch ◽  
Jan Patrick Hartkopf ◽  
Roman Liesenfeld
Keyword(s):  
State Space ◽  
Asset Returns ◽  
Covariance Matrices ◽  
State Space Models ◽  
High Dimensional ◽  
Realized Covariance ◽  
Factor State

scholarly journals Extended Ensemble Filter for High-dimensional Nonlinear State Space Models

2021 ◽  
pp. 84-97
Author(s):  
Oryiema Robert ◽  
David Angwenyi ◽  
Kevin Midenyo
Keyword(s):  
State Space ◽  
Negative Impact ◽  
High Dimensional Data ◽  
Innovation Process ◽  
State Space Models ◽  
High Dimensional ◽  
First Order ◽  
Filter Performance ◽  
Noisy Observation ◽  
Nonlinear State Space Models

There are several functional forms for non-linear dynamical filters. Extended Kalman filters are algorithms that are used to estimate more accurate values of unknown quantities of internal dynamical systems from a sequence of noisy observation measured over a period of time. This filtering process becomes computationally expensive when subjected to high dimensional data which consequently has a negative impact on the filter performance in real time. This is because integration of the equation of evolution of covariances is extremely costly, especially when the dimension of the problem is huge which is the case in numerical weather prediction.This study has developed a new filter, the First order Extended Ensemble Filter (FoEEF), with a new extended innovation process to improve on the measurement and be able to estimate the state value of high dimensional data. We propose to estimate the covariances empirically, which lends the filter amenable to large dimensional models. The new filter is derived from stochastic state-space models and its performance is tested using Lorenz 63 system of ordinary differential equations and Matlab software.The performance of the newly developed filter is then compared with the performances of three other filters, that is, Bootstrap particle Filter (BPF), First order Extended Kalman Bucy Filter (FoEKBF) and Second order Extended Kalman Bucy Filter (SoEKBF).The performance of the FoEEF improves with the increase in ensemble size. Even with as low number of ensembles as 40, the FoEEF performs as good as the FoEKBF and SoEKBF. This shows, that the proposed filter can register a good performance when used in high-dimensional state-space models.

scholarly journals Efficient Forced Response Computations of Acoustical Systems with a State-Space Approach

Acoustics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 581-594
Author(s):  
Art J. R. Pelling ◽  
Ennes Sarradj
Keyword(s):  
State Space ◽  
Large Scale ◽  
State Space Model ◽  
Measurement Data ◽  
Numerical Linear Algebra ◽  
Forced Response ◽  
State Space Models ◽  
High Dimensional ◽  
Diagonal Form ◽  
The Past

State-space models have been successfully employed for model order reduction and control purposes in acoustics in the past. However, due to the cubic complexity of the singular value decomposition, which makes up the core of many subspace system identification (SSID) methods, the construction of large scale state-space models from high-dimensional measurement data has been problematic in the past. Recent advances of numerical linear algebra have brought forth computationally efficient randomized rank-revealing matrix factorizations and it has been shown that these factorizations can be used to enhance SSID methods such as the Eigensystem Realization Algorithm (ERA). In this paper, we demonstrate the applicability of the so-called generalized ERA to acoustical systems and high-dimensional input data by means of an example. Furthermore, we introduce a new efficient method of forced response computation that relies on a state-space model in quasi-diagonal form. Numerical experiments reveal that our proposed method is more efficient than previous state-space methods and can even outperform frequency domain convolutions in certain scenarios.

scholarly journals Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Jacob Vorstrup Goldman ◽  
Sumeetpal S. Singh
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Simulated Data ◽  
State Space Models ◽  
High Dimensional ◽  
Effective Sample Size ◽  
Stat Assoc ◽  
Dimensional State Space ◽  
State Inference ◽  
New Algorithms

AbstractWe propose a novel blocked version of the continuous-time bouncy particle sampler of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855–867, 2018) which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state-space models (Singh et al. in Biometrika 104(4):953–969, 2017) and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state-space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. (J R Stat Soc Ser B Stat Methodol 72(3):269–342, 2010), is illustrated numerically for both simulated data and a challenging real-world financial dataset.

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