RESEARCH STUDENT, UNIVERSITY OF IBADAN
To inform economist and financial analyst in choice of model in making decision in risk portfolio.
GARCH models have been developed to account for empirical regularities in financial data. Many financial time series have a number of characteristics in common; asset prices are generally non stationary while returns are usually stationary, some financial time series are fractionally integrated, return series usually show no or little autocorrelation, serial independence between the squared values of the series is often rejected pointing towards the existence of non-linear relationships between subsequent observations, volatility of the return series appears to be clustered, normality has to be rejected in favor of some thick-tailed distribution, some series exhibit so-called leverage effect that is changes in stock prices tend to be negatively correlated with changes in volatility.
An empirical analysis of the mean return and conditional variance of Nigeria Stock Exchange (NSE) index is performed using various error innovations in GARCH models. Conventional GARCH model which assumed normal error term failed to capture volatility clustering, leptokurtosis and leverage effect as a result of zero skewness and kurtosis respectively. We re-modify error distributions of GARCH (p,q) model inference using some thick-tailed distributions. Method of Quasi – Maximum Likelihood Estimation (MLE) was used in parameter estimation,m our result shows that GARCH(1,1) and APARCH(1,1) models with anomalous densities improves overall estimation for measuring conditional variance. The robust model that explained the NSE index is determined by loglikelihood and model selection Criteria. The prediction performance of these conditional changing variance models is compared using Root Mean Square Error(RMSE) and Mean Absolute Percentage Error (MAPE). Generalized Length Biased Scaled-t Innovation using APARCH(1,1) model is the most robust for forecasting Nigeria Stock Exchange Index.
Abstract: An important research area in biomedical signal processing is that of quantifying the relationship between simultaneously observed time series and to reveal interactions between the signals. Since biomedical signals are potentially non-stationary and the measurements may contain outliers and artifacts, we introduce a robust time-varying generalized partial directed coherence (rTV-gPDC) function.The proposed method, which is based on a robust estimator of the timevarying autoregressive (TVAR) parameters, is capable of revealing directed interactions between signals. By definition, the rTV-gPDC only displays the linear relationships between the signals. We therefore suggest to approximate the residuals of the TVAR process, which potentially carry information about the nonlinear causality by a piece-wise linear time-varying moving-average (TVMA) model.The performance of the proposed method is assessed via extensive simulations. To illustrate the method's applicability to real-world problems, it is applied to a neurophysiological study that involves intracranial pressure (ICP), arterial blood pressure (ABP), and brain tissue oxygenation level (PtiO2) measurements.The rTV-gPDC reveals causal patterns that are in accordance with expected cardiosudoral meachanisms and potentially provides new insights regarding traumatic brain injuries (TBI). The rTV-gPDC is not restricted to the above problem but can be useful in revealing interactions in a broad range of applications.
Pub.: 03 Jun '17, Pinned: 01 Aug '17
Abstract: We present a new framework for learning Granger causality networks for multivariate categorical time series, based on the mixture transition distribution (MTD) model. Traditionally, MTD is plagued by a nonconvex objective, non-identifiability, and presence of many local optima. To circumvent these problems, we recast inference in the MTD as a convex problem. The new formulation facilitates the application of MTD to high-dimensional multivariate time series. As a baseline, we also formulate a multi-output logistic autoregressive model (mLTD), which while a straightforward extension of autoregressive Bernoulli generalized linear models, has not been previously applied to the analysis of multivariate categorial time series. We develop novel identifiability conditions of the MTD model and compare them to those for mLTD. We further devise novel and efficient optimization algorithm for the MTD based on the new convex formulation, and compare the MTD and mLTD in both simulated and real data experiments. Our approach simultaneously provides a comparison of methods for network inference in categorical time series and opens the door to modern, regularized inference with the MTD model.
Pub.: 08 Jun '17, Pinned: 01 Aug '17
Abstract: Process monitoring and fault diagnosis using the multivariate statistical methodologies has been extensively used in the process and product development industries for the last several decades. The fault in one process variable readily affects all the other associated variables, which makes the fault detection process not only more difficult but also time-consuming. In this study, principal component analysis (PCA)-based fault amplification algorithm is developed to detect both the root cause of fault and the fault propagation path in the system. The developed algorithm projects the samples on the residual subspace (RS) to determine the disturbance propagation path. Usually, the RS of the fault data is superimposed with the normal process variations, which should be minimized to amplify the fault magnitude. The RS-containing amplified fault is then converted to the covariance matrix, followed by singular value decomposition (SVD) analysis, which, in turn, generates the fault direction matrix corresponding to the largest eigenvalue. The fault variables are then rearranged according to their magnitude of contribution toward a fault, which, in turn, represents the fault propagation path using an absolute descending order function. Moreover, the multivariate Granger causality (MVGC) algorithm is used to analyze the causal relationship among the variables obtained from the developed algorithm. Both the methodologies are tested on the LNG fractionation process train and distillation column operation, where some fault case scenarios are assumed to estimate the fault directions. It is observed that the hierarchy of variables obtained from fault propagation path algorithm are in good agreement with the MVGC algorithm. Therefore, fault amplification methodology can be used in industrial systems for identifying the root cause of fault, as well as the fault propagation path.
Pub.: 02 Jun '17, Pinned: 01 Aug '17