Gamma stochastic volatility models

This paper presents gamma stochastic volatility models and investigates its distributional and time series properties. The parameter estimators obtained by the method of moments are shown analytically to be consistent and asymptotically normal. The simulation results indicate that the estimators behave well. The insample analysis shows that return models with gamma autoregressive stochastic volatility processes capture the leptokurtic nature of return distributions and the slowly decaying autocorrelation functions of squared stock index returns for the USA and UK. In comparison with GARCH and EGARCH models, the gamma autoregressive model picks up the persistence in volatility for the US and UK index returns but not the volatility persistence for the Canadian and Japanese index returns. The out-of-sample analysis indicates that the gamma autoregressive model has a superior volatility forecasting performance compared to GARCH and EGARCH models.

SPATIAL CLUSTERING ALGORITHMS-AN OVERVIEW.

An Overview of known spatial clustering algorithms The space of interest can be the two-dimensional abstraction of the surface of the earth or a man-made space like the layout of a VLSI design, a volume containing a model of the human brain, or another 3d-space representing the arrangement of chains of protein molecules. The data consists of geometric information and can be either discrete or continuous. The explicit location and extension of spatial objects define implicit relations of spatial neighborhood (such as topological, distance and direction relations) which are used by spatial data mining algorithms. Therefore, spatial data mining algorithms are required for spatial characterization and spatial trend analysis. Spatial data mining or knowledge discovery in spatial databases differs from regular data mining in analogous with the differences between non-spatial data and spatial data. The attributes of a spatial object stored in a database may be affected by the attributes of the spatial neighbors of that object. In addition, spatial location, and implicit information about the location of an object, may be exactly the information that can be extracted through spatial data mining

Detection of Flock Movement in Spatio-Temporal Database using Clustering Techniques - an Experience

In this paper, moving flock patterns are mined from spatio- temporal datasets by incorporating a clustering algorithm. A flock is defined as the set of data that move together for a certain continuous amount of time. Finding out moving flock patterns using clustering algorithms is a potential method to find out frequent patterns of movement in large trajectory datasets. In this approach, SPatial clusteRing algoRithm thrOugh sWarm intelligence (SPARROW) is the clustering algorithm used. The advantage of using SPARROW algorithm is that it can effectively discover clusters of widely varying sizes and shapes from large databases. Variations of the proposed method are addressed and also the experimental results show that the problem of scalability and duplicate pattern formation is addressed. This method also reduces the number of patterns produced

Spectral clustering independent component analysis for tissue classification from brain MRI

A spectral angle based feature extraction method, Spectral Clustering Independent Component Analysis (SC-ICA), is proposed in this work to improve the brain tissue classification from Magnetic Resonance Images (MRI). SC-ICA provides equal priority to global and local features; thereby it tries to resolve the inefficiency of conventional approaches in abnormal tissue extraction. First, input multispectral MRI is divided into different clusters by a spectral distance based clustering. Then, Independent Component Analysis (ICA) is applied on the clustered data, in conjunction with Support Vector Machines (SVM) for brain tissue analysis. Normal and abnormal datasets, consisting of real and synthetic T1-weighted, T2-weighted and proton density/fluid-attenuated inversion recovery images, were used to evaluate the performance of the new method. Comparative analysis with ICA based SVM and other conventional classifiers established the stability and efficiency of SC-ICA based classification, especially in reproduction of small abnormalities. Clinical abnormal case analysis demonstrated it through the highest Tanimoto Index/accuracy values, 0.75/98.8%, observed against ICA based SVM results, 0.17/96.1%, for reproduced lesions. Experimental results recommend the proposed method as a promising approach in clinical and pathological studies of brain diseases

Development of Hierarchical Clustering Techniques for Gridded Data from Mixed Data Sequences

Knowledge discovery in databases is the non-trivial process of identifying valid, novel potentially useful and ultimately understandable patterns from data. The term Data mining refers to the process which does the exploratory analysis on the data and builds some model on the data. To infer patterns from data, data mining involves different approaches like association rule mining, classification techniques or clustering techniques. Among the many data mining techniques, clustering plays a major role, since it helps to group the related data for assessing properties and drawing conclusions. Most of the clustering algorithms act on a dataset with uniform format, since the similarity or dissimilarity between the data points is a significant factor in finding out the clusters. If a dataset consists of mixed attributes, i.e. a combination of numerical and categorical variables, a preferred approach is to convert different formats into a uniform format. The research study explores the various techniques to convert the mixed data sets to a numerical equivalent, so as to make it equipped for applying the statistical and similar algorithms. The results of clustering mixed category data after conversion to numeric data type have been demonstrated using a crime data set. The thesis also proposes an extension to the well known algorithm for handling mixed data types, to deal with data sets having only categorical data. The proposed conversion has been validated on a data set corresponding to breast cancer. Moreover, another issue with the clustering process is the visualization of output. Different geometric techniques like scatter plot, or projection plots are available, but none of the techniques display the result projecting the whole database but rather demonstrate attribute-pair wise analysis

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis