scholarly journals Block circulant matrices and the spectra of multivariate stationary sequences

2021 ◽  
Vol 9 (1) ◽  
pp. 36-51
Author(s):  
Marianna Bolla ◽  
Tamás Szabados ◽  
Máté Baranyi ◽  
Fatma Abdelkhalek
Keyword(s):  
Time Series ◽  
Toeplitz Matrix ◽  
Financial Time Series ◽  
Multivariate Time Series ◽  
Asymptotic Relation ◽  
Low Rank ◽  
Circulant Matrices ◽  
Low Rank Approximation ◽  
Proved Theorem ◽  
Block Toeplitz Matrix

Abstract Given a weakly stationary, multivariate time series with absolutely summable autocovariances, asymptotic relation is proved between the eigenvalues of the block Toeplitz matrix of the first n autocovariances and the union of spectra of the spectral density matrices at the n Fourier frequencies, as n → ∞. For the proof, eigenvalues and eigenvectors of block circulant matrices are used. The proved theorem has important consequences as for the analogies between the time and frequency domain calculations. In particular, the complex principal components are used for low-rank approximation of the process; whereas, the block Cholesky decomposition of the block Toeplitz matrix gives rise to dimension reduction within the innovation subspaces. The results are illustrated on a financial time series.

PATTERN RECOGNITION OF THE TERM STRUCTURE USING INDEPENDENT COMPONENT ANALYSIS

2006 ◽  
Vol 20 (02) ◽  
pp. 173-188 ◽  
Author(s):  
EDMOND HAOCUN WU ◽  
PHILIP L. H. YU
Keyword(s):  
Time Series ◽  
Pattern Recognition ◽  
Independent Component Analysis ◽  
Term Structure ◽  
Financial Time Series ◽  
Empirical Studies ◽  
Multivariate Time Series ◽  
Principal Component ◽  
Component Analysis ◽  
Independent Component

Term structure is a useful curve describing some financial asset as a function of time to maturity or expiration. In this paper, we propose to use Independent Component Analysis (ICA) to model the term structure of multiple yield curves. The idea is that we first employ ICA to decompose the multivariate time series, then we suggest two ICA methods for dimension reduction and pattern recognition of the term structure. We also compare the results by using an alternative method, Principal Component Analysis (PCA). The empirical studies suggest that the proposed ICA approaches outperform PCA methods in modeling the term structure. This model can be used in financial time series analysis as well as related financial applications.

scholarly journals On Independent Component Analysis with Stochastic Volatility Models

2017 ◽  
Vol 46 (3-4) ◽  
pp. 57-66 ◽  
Author(s):  
Markus Matilainen ◽  
Jari Miettinen ◽  
Klaus Nordhausen ◽  
Hannu Oja ◽  
Sara Taskinen
Keyword(s):  
Time Series ◽  
Independent Component Analysis ◽  
Stochastic Volatility ◽  
Financial Time Series ◽  
Multivariate Time Series ◽  
Component Analysis ◽  
Independent Component ◽  
Stationary Time Series ◽  
Volatility Models ◽  
High Volatility

Consider a multivariate time series where each component series is assumed to be a linear mixture of latent mutually independent stationary time series. Classical independent component analysis (ICA) tools, such as fastICA, are often used to extract latent series, but they don't utilize any information on temporal dependence. Also financial time series often have periods of low and high volatility. In such settings second order source separation methods, such as SOBI, fail. We review here some classical methods used for time series with stochastic volatility, and suggest modifications of them by proposing a family of vSOBI estimators. These estimators use different nonlinearity functions to capture nonlinear autocorrelation of the time series and extract the independent components. Simulation study shows that the proposed method outperforms the existing methods when latent components follow GARCH and SV models. This paper is an invited extended version of the paper presented at the CDAM 2016 conference.

Financial Data Mining Using Flexible ICA-GARCH Models

2010 ◽  
pp. 255-272
Author(s):  
Philip L.H. Yu ◽  
Edmond H.C. Wu ◽  
W.K. Li
Keyword(s):  
Data Mining ◽  
Time Series ◽  
Risk Management ◽  
Independent Component Analysis ◽  
Value At Risk ◽  
Financial Time Series ◽  
Multivariate Time Series ◽  
Independent Component ◽  
Garch Models ◽  
Financial Time

As a data mining technique, independent component analysis (ICA) is used to separate mixed data signals into statistically independent sources. In this chapter, we apply ICA for modeling multivariate volatility of financial asset returns which is a useful tool in portfolio selection and risk management. In the finance literature, the generalized autoregressive conditional heteroscedasticity (GARCH) model and its variants such as EGARCH and GJR-GARCH models have become popular standard tools to model the volatility processes of financial time series. Although univariate GARCH models are successful in modeling volatilities of financial time series, the problem of modeling multivariate time series has always been challenging. Recently, Wu, Yu, & Li (2006) suggested using independent component analysis (ICA) to decompose multivariate time series into statistically independent time series components and then separately modeled the independent components by univariate GARCH models. In this chapter, we extend this class of ICA-GARCH models to allow more flexible univariate GARCH-type models. We also apply the proposed models to compute the value-at-risk (VaR) for risk management applications. Backtesting and out-of-sample tests suggest that the ICA-GARCH models have a clear cut advantage over some other approaches in value-at-risk estimation.

Time-varying copula models for financial time series

2016 ◽  
Vol 48 (A) ◽  
pp. 159-180
Author(s):  
Rüdiger Kiesel ◽  
Magda Mroz ◽  
Ulrich Stadtmüller
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Multivariate Time Series ◽  
Local Maximum ◽  
Time Varying ◽  
Monte Carlo Simulation Study ◽  
Copula Models ◽  
Copula Theory ◽  
Statistical Homogeneity ◽  
Financial Time

AbstractWe perform an analysis of the potential time inhomogeneity in the dependence between multiple financial time series. To this end, we use the framework of copula theory and tackle the question of whether dependencies in such a case can be assumed constant throughout time or rather have to be modeled in a time-inhomogeneous way. We focus on parametric copula models and suitable inference techniques in the context of a special copula-based multivariate time series model. A recent result due to Chan et al. (2009) is used to derive the joint limiting distribution of local maximum-likelihood estimators on overlapping samples. By restricting the overlap to be fixed, we establish the limiting law of the maximum of the estimator series. Based on the limiting distributions, we develop statistical homogeneity tests, and investigate their local power properties. A Monte Carlo simulation study demonstrates that bootstrapped variance estimates are needed in finite samples. Empirical analyses on real-world financial data finally confirm that time-varying parameters are an exception rather than the rule.

TESTING FOR THE MARKOV PROPERTY IN TIME SERIES

2011 ◽  
Vol 28 (1) ◽  
pp. 130-178 ◽  
Author(s):  
Bin Chen ◽  
Yongmiao Hong
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Multivariate Time Series ◽  
Fundamental Property ◽  
Markov Property ◽  
Transition Density ◽  
Conditional Moment ◽  
Financial Modeling ◽  
Finite Samples ◽  
Frequency Domain Approach

The Markov property is a fundamental property in time series analysis and is often assumed in economic and financial modeling. We develop a new test for the Markov property using the conditional characteristic function embedded in a frequency domain approach, which checks the implication of the Markov property in every conditional moment (if it exists) and over many lags. The proposed test is applicable to both univariate and multivariate time series with discrete or continuous distributions. Simulation studies show that with the use of a smoothed nonparametric transition density-based bootstrap procedure, the proposed test has reasonable sizes and all-around power against several popular non-Markov alternatives in finite samples. We apply the test to a number of financial time series and find some evidence against the Markov property.

Sign in / Sign up

Export Citation Format

Share Document