Common Independent Component Research Articles

Modelling Multivariate Return Volatilities by Independent Components Using Johnson SU Likelihood

Time-varying volatility modelling is crucial in financial econometrics. For multivariate data, time-varying correlations across securities are important to explain the co-movement of the data. Therefore, we need to estimate the covariance matrix. Estimating a large conditional covariance matrix requires the estimation of a large number of parameters, which is a hard task and often leads to convergence difficulties in the estimation algorithm. We introduce a framework for forecasting the conditional covariance matrix of a large data set by employing a factor model to reduce dimensionality, with the factors estimated using independent components. The main contribution of our article is the estimation of the unobserved independent components using Johnson SU likelihood, which captures the skewness and excess kurtosis—stylized facts in stock returns. First, we extract the independent components using the Johnson SU distribution, maximizing their non-Gaussianity. Second, we sorted the independent components in terms of their explained variability and fit a univariate GARCH process on a few common independent components. Next, we approximate the conditional covariance matrix of the data through a linear combination of the conditional variances of those select few independent components. We apply this procedure to 50 stock returns data (listed in Nifty 50) that exhibit excess kurtosis and skewness, and the findings show that our methodology dominates other algorithms in extracting the independent components. This method enables fund managers to accurately forecast a large conditional covariance matrix, facilitating effective risk management and portfolio construction.

To be and not to be: wide-field Ca2+ imaging reveals neocortical functional segmentation combines stability and flexibility.

The stability and flexibility of the functional parcellation of the cerebral cortex is fundamental to how familiar and novel information is both represented and stored. We leveraged new advances in Ca2+ sensors and microscopy to understand the dynamics of functional segmentation in the dorsal cerebral cortex. We performed wide-field Ca2+ imaging in head-fixed mice and used spatial independent component analysis (ICA) to identify independent spatial sources of Ca2+ fluorescence. The imaging data were evaluated over multiple timescales and discrete behaviors including resting, walking, and grooming. When evaluated over the entire dataset, a set of template independent components (ICs) were identified that were common across behaviors. Template ICs were present across a range of timescales, from days to 30seconds, although with lower occurrence probability at shorter timescales, highlighting the stability of the functional segmentation. Importantly, unique ICs emerged at the shorter duration timescales that could act to transiently refine the cortical network. When data were evaluated by behavior, both common and behavior-specific ICs emerged. Each behavior is composed of unique combinations of common and behavior-specific ICs. These observations suggest that cerebral cortical functional segmentation exhibits considerable spatial stability over time and behaviors while retaining the flexibility for task-dependent reorganization.

FMRI BOLD Correlates of EEG Independent Components: Spatial Correspondence With the Default Mode Network

Goal: We aimed to identify electroencephalographic (EEG) signal fluctuations within independent components (ICs) that correlate to spontaneous blood oxygenation level dependent (BOLD) activity in regions of the default mode network (DMN) during eyes-closed resting state.Methods: We analyzed simultaneously acquired EEG and functional magnetic resonance imaging (fMRI) eyes-closed resting state data in a convenience sample of 30 participants. IC analysis (ICA) was used to decompose the EEG time-series and common ICs were identified using data-driven IC clustering across subjects. The IC time courses were filtered into seven frequency bands, convolved with a hemeodynamic response function (HRF) and used to model spontaneous fMRI signal fluctuations across the brain. In parallel, group ICA analysis was used to decompose the fMRI signal into ICs from which the DMN was identified. Frequency and IC cluster associated hemeodynamic correlation maps obtained from the regression analysis were spatially correlated with the DMN. To investigate the reliability of our findings, the analyses were repeated with data collected from the same subjects 1 year later.Results: Our results indicate a relationship between power fluctuations in the delta, theta, beta and gamma frequency range and the DMN in different EEG ICs in our sample as shown by small to moderate spatial correlations at the first measurement (0.234 < |r| < 0.346, p < 0.0001). Furthermore, activity within an EEG component commonly identified as eye movements correlates with BOLD activity within regions of the DMN. In addition, we demonstrate that correlations between EEG ICs and the BOLD signal during rest are in part stable across time.Discussion: We show that ICA source separated EEG signals can be used to investigate electrophysiological correlates of the DMN. The relationship between the eye movement component and the DMN points to a behavioral association between DMN activity and the level of eye movement or the presence of neuronal activity in this component. Previous findings of an association between frontal midline theta activity and the DMN were replicated.

A conditionally heteroskedastic independent factor model with an application to financial stock returns

a b s t r a c t We propose a new conditionally heteroskedastic factor model, the GICA-GARCH model, which combines independent component analysis (ICA) and multivariate GARCH (MGARCH) models. This model assumes that the data are generated by a set of underlying independent components (ICs) that capture the co-movements among the observations, which are assumed to be conditionally heteroskedastic. The GICA-GARCH model separates the estimation of the ICs from their fitting with a univariate ARMA-GARCH model. Here, we will use two ICA approaches to find the ICs: the first estimates the components, maximizing their non-Gaussianity, while the second exploits the temporal structure of the data. After estimating and identifying the common ICs, we fit a univariate GARCH model to each of them in order to estimate their univariate conditional variances. The GICA- GARCH model then provides a new framework for modelling the multivariate conditional heteroskedasticity in which we can explain and forecast the conditional covariances of the observations by modelling the univariate conditional variances of a few common ICs. We report some simulation experiments to show the ability of ICA to discover leading factors in a multivariate vector of financial data. Finally, we present an empirical application to the Madrid stock market, where we evaluate the forecasting performances of the GICA-GARCH and two additional factor GARCH models: the orthogonal GARCH and the conditionally uncorrelated components GARCH.