A Radial Basis Function Approach to Financial Time Series Analysis

Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.

Discovering Clusters in Motion Time-Series Data

A new approach is proposed for clustering time-series data. The approach can be used to discover groupings of similar object motions that were observed in a video collection. A finite mixture of hidden Markov models (HMMs) is fitted to the motion data using the expectation-maximization (EM) framework. Previous approaches for HMM-based clustering employ a k-means formulation, where each sequence is assigned to only a single HMM. In contrast, the formulation presented in this paper allows each sequence to belong to more than a single HMM with some probability, and the hard decision about the sequence class membership can be deferred until a later time when such a decision is required. Experiments with simulated data demonstrate the benefit of using this EM-based approach when there is more "overlap" in the processes generating the data. Experiments with real data show the promising potential of HMM-based motion clustering in a number of applications.

Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.

Empirical Evidence of Conditional Heteroskedasticity in Vietnam’s Stock Returns Time Series

This paper confirms presence of GARCH(1,1) effect on stock return time series of Vietnam’s newborn stock market. We performed tests on four different time series, namely market returns (VN-Index), and return series of the first four individual stocks listed on the Vietnamese exchange (the Ho Chi Minh City Securities Trading Center) since August 2000. The results have been quite relevant to previously reported empirical studies on different markets.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

A Dynamic Directional Model for Effective Brain Connectivity using Electrocorticographic (ECoG) Time Series.

We introduce a dynamic directional model (DDM) for studying brain effective connectivity based on intracranial electrocorticographic (ECoG) time series. The DDM consists of two parts: a set of differential equations describing neuronal activity of brain components (state equations), and observation equations linking the underlying neuronal states to observed data. When applied to functional MRI or EEG data, DDMs usually have complex formulations and thus can accommodate only a few regions, due to limitations in spatial resolution and/or temporal resolution of these imaging modalities. In contrast, we formulate our model in the context of ECoG data. The combined high temporal and spatial resolution of ECoG data result in a much simpler DDM, allowing investigation of complex connections between many regions. To identify functionally segregated sub-networks, a form of biologically economical brain networks, we propose the Potts model for the DDM parameters. The neuronal states of brain components are represented by cubic spline bases and the parameters are estimated by minimizing a log-likelihood criterion that combines the state and observation equations. The Potts model is converted to the Potts penalty in the penalized regression approach to achieve sparsity in parameter estimation, for which a fast iterative algorithm is developed. The methods are applied to an auditory ECoG dataset.

An ontological characterization of time-series and state-sequences for data mining

Time-series and sequences are important patterns in data mining. Based on an ontology of time-elements, this paper presents a formal characterization of time-series and state-sequences, where a state denotes a collection of data whose validation is dependent on time. While a time-series is formalized as a vector of time-elements temporally ordered one after another, a state-sequence is denoted as a list of states correspondingly ordered by a time-series. In general, a time-series and a state-sequence can be incomplete in various ways. This leads to the distinction between complete and incomplete time-series, and between complete and incomplete state-sequences, which allows the expression of both absolute and relative temporal knowledge in data mining.

A framework for state-based time-series analysis and prediction

Time-series analysis and prediction play an important role in state-based systems that involve dealing with varying situations in terms of states of the world evolving with time. Generally speaking, the world in the discourse persists in a given state until something occurs to it into another state. This paper introduces a framework for prediction and analysis based on time-series of states. It takes a time theory that addresses both points and intervals as primitive time elements as the temporal basis. A state of the world under consideration is defined as a set of time-varying propositions with Boolean truth-values that are dependent on time, including properties, facts, actions, events and processes, etc. A time-series of states is then formalized as a list of states that are temporally ordered one after another. The framework supports explicit expression of both absolute and relative temporal knowledge. A formal schema for expressing general time-series of states to be incomplete in various ways, while the concept of complete time-series of states is also formally defined. As applications of the formalism in time-series analysis and prediction, we present two illustrating examples.

The evaluation of time series: their scientific value and contribution to policy needs. Occasional Publication of the Marine Biological Association 22

In 2000 a Review of Current Marine Observations in relation to present and future needs was undertaken by the Inter-Agency Committee for Marine Science and Technology (IACMST). The Marine Environmental Change Network (MECN) was initiated in 2002 as a direct response to the recommendations of the report. A key part of the current phase of the MECN is to ensure that information from the network is provided to policy makers and other end-users to enable them to produce more accurate assessments of ecosystem state and gain a clearer understanding of factors influencing change in marine ecosystems. The MECN holds workshops on an annual basis, bringing together partners maintaining time-series and long-term datasets as well as end-users interested in outputs from the network. It was decided that the first workshop of the MECN continuation phase should consist of an evaluation of the time series and data sets maintained by partners in the MECN with regard to their ‘fit for purpose’ for answering key science questions and informing policy development. This report is based on the outcomes of the workshop. Section one of the report contains a brief introduction to monitoring, time series and long-term datasets. The various terms are defined and the need for MECN type data to complement compliance monitoring programmes is discussed. Outlines are also given of initiatives such as the United Kingdom Marine Monitoring and Assessment Strategy (UKMMAS) and Oceans 2025. Section two contains detailed information for each of the MECN time series / long-term datasets including information on scientific outputs and current objectives. This information is mainly based on the presentations given at the workshop and therefore follows a format whereby the following headings are addressed: Origin of time series including original objectives; current objectives; policy relevance; products (advice, publications, science and society). Section three consists of comments made by the review panel concerning all the time series and the network. Needs or issues highlighted by the panel with regard to the future of long-term datasets and time-series in the UK are shown along with advice and potential solutions where offered. The recommendations are divided into 4 categories; ‘The MECN and end-user requirements’; ‘Procedures & protocols’; ‘Securing data series’ and ‘Future developments’. Ever since marine environmental protection issues really came to the fore in the 1960s, it has been recognised that there is a requirement for a suitable evidence base on environmental change in order to support policy and management for UK waters. Section four gives a brief summary of the development of marine policy in the UK along with comments on the availability and necessity of long-term marine observations for the implementation of this policy. Policy relating to three main areas is discussed; Marine Conservation (protecting biodiversity and marine ecosystems); Marine Pollution and Fisheries. The conclusion of this section is that there has always been a specific requirement for information on long-term change in marine ecosystems around the UK in order to address concerns over pollution, fishing and general conservation. It is now imperative that this need is addressed in order for the UK to be able to fulfil its policy commitments and manage marine ecosystems in the light of climate change and other factors.

Continuous Plankton Records - Persistence In Time-Series And The Population-Dynamics Of Pseudocalanus-Elongatus And Acartia-Clausi

Rates of population increase in early spring and the sizes of overwintering stocks were calculated for the planktonic copepods Pseudocalanus elongatus and Acartia clausi for a set of areas covering the open waters of the north-east Atlantic Ocean and the North Sea for the period 1948 to 1979. For both species, the rates of population increase were higher in the open ocean than in the North Sea and appear to be related to temperature. The overwintering stocks in the North Sea were larger than those in the open ocean and are probably related to phytoplanton concentration. P. elongatus shows higher overwintering stocks and lower rates of population increase than A. clausi, resulting in different levels of persistence in the stocks of the two species. It is suggested that this difference in persistence is responsible for differences between the two species with respect to geographical distribution in summer and different patterns of year-to-year fluctuations in abundance.

Continuous Plankton Records - Persistence In Time-Series Of Annual Means Of Abundance Of Zooplankton

Time-series of annual means of abundance of zooplankton of the north-east Atlantic Ocean and the North Sea, for the period 1948 to 1977, show considerable associations between successive years. The seasonal dynamics of the stocks appear to be consistent with at least a proportion of this being due to inherent persistence from year-to-year. Experiments with a simple model suggest that the observed properties of the time-series cannot be reproduced as a response to simple random forcing. The extent of trends and long wavelength variations can be simulated by introducing fairly extensive persistence into the perturbations, but this underestimates the extent of shorter wavelength variability in the observed time-series. The effect of persistence is to increase the proportion of trend and long wavelength variability in time-series of annual means, but stocks can respond to short wavelength perturbations provided these have a clearly defined frequency.