An application of two techniques for the analysis of short, multivariate non-stationary time-series of Mauritanian trawl survey data

Min/max autocorrelation factor analysis (MAFA) and dynamic factor analysis (DFA) are complementary techniques for analysing short (> 15-25 y), non-stationary, multivariate data sets. We illustrate the two techniques using catch rate (cpue) time-series (1982-2001) for 17 species caught during trawl surveys off Mauritania, with the NAO index, an upwelling index, sea surface temperature, and an index of fishing effort as explanatory variables. Both techniques gave coherent results, the most important common trend being a decrease in cpue during the latter half of the time-series, and the next important being an increase during the first half. A DFA model with SST and UPW as explanatory variables and two common trends gave good fits to most of the cpue time-series. (c) 2004 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

One-year delayed effect of fog on malaria transmission : a time-series analysis in the rain forest area of Mengla County, south-west China

Background: Malaria is a major public health burden in the tropics with the potential to significantly increase in response to climate change. Analyses of data from the recent past can elucidate how short-term variations in weather factors affect malaria transmission. This study explored the impact of climate variability on the transmission of malaria in the tropical rain forest area of Mengla County, south-west China. Methods: Ecological time-series analysis was performed on data collected between 1971 and 1999. Auto-regressive integrated moving average (ARIMA) models were used to evaluate the relationship between weather factors and malaria incidence. Results: At the time scale of months, the predictors for malaria incidence included: minimum temperature, maximum temperature, and fog day frequency. The effect of minimum temperature on malaria incidence was greater in the cool months than in the hot months. The fog day frequency in October had a positive effect on malaria incidence in May of the following year. At the time scale of years, the annual fog day frequency was the only weather predictor of the annual incidence of malaria. Conclusion: Fog day frequency was for the first time found to be a predictor of malaria incidence in a rain forest area. The one-year delayed effect of fog on malaria transmission may involve providing water input and maintaining aquatic breeding sites for mosquitoes in vulnerable times when there is little rainfall in the 6-month dry seasons. These findings should be considered in the prediction of future patterns of malaria for similar tropical rain forest areas worldwide.

Regression and hypothesis tests for multivariate GNSS state time series

A satellite based observation system can continuously or repeatedly generate a user state vector time series that may contain useful information. One typical example is the collection of International GNSS Services (IGS) station daily and weekly combined solutions. Another example is the epoch-by-epoch kinematic position time series of a receiver derived by a GPS real time kinematic (RTK) technique. Although some multivariate analysis techniques have been adopted to assess the noise characteristics of multivariate state time series, statistic testings are limited to univariate time series. After review of frequently used hypotheses test statistics in univariate analysis of GNSS state time series, the paper presents a number of T-squared multivariate analysis statistics for use in the analysis of multivariate GNSS state time series. These T-squared test statistics have taken the correlation between coordinate components into account, which is neglected in univariate analysis. Numerical analysis was conducted with the multi-year time series of an IGS station to schematically demonstrate the results from the multivariate hypothesis testing in comparison with the univariate hypothesis testing results. The results have demonstrated that, in general, the testing for multivariate mean shifts and outliers tends to reject less data samples than the testing for univariate mean shifts and outliers under the same confidence level. It is noted that neither univariate nor multivariate data analysis methods are intended to replace physical analysis. Instead, these should be treated as complementary statistical methods for a prior or posteriori investigations. Physical analysis is necessary subsequently to refine and interpret the results.

Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.

Shrinkage empirical likelihood estimator in longitudinal analysis with time-dependent covariates-application to modeling the health of Filipino children

The method of generalized estimating equations (GEE) is a popular tool for analysing longitudinal (panel) data. Often, the covariates collected are time-dependent in nature, for example, age, relapse status, monthly income. When using GEE to analyse longitudinal data with time-dependent covariates, crucial assumptions about the covariates are necessary for valid inferences to be drawn. When those assumptions do not hold or cannot be verified, Pepe and Anderson (1994, Communications in Statistics, Simulations and Computation 23, 939–951) advocated using an independence working correlation assumption in the GEE model as a robust approach. However, using GEE with the independence correlation assumption may lead to significant efficiency loss (Fitzmaurice, 1995, Biometrics 51, 309–317). In this article, we propose a method that extracts additional information from the estimating equations that are excluded by the independence assumption. The method always includes the estimating equations under the independence assumption and the contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries. We apply the method to a longitudinal study of the health of a group of Filipino children.

Socio-demographic vulnerability to heatwave impacts in Brisbane, Australia : a time series analysis

Objective: Examining the association between socioeconomic disadvantage and heat-related emergency department (ED) visits during heatwave periods in Brisbane, 2000–2008. Methods: Data from 10 public EDs were analysed using a generalised additive model for disease categories, age groups and gender. Results: Cumulative relative risks (RR) for non-external causes other than cardiovascular and respiratory diseases were 1.11 and 1.05 in most and least disadvantaged areas, respectively. The pattern persisted on lags 0–2. Elevated risks were observed for all age groups above 15 years in all areas. However, with RRs of 1.19–1.28, the 65–74 years age group in more disadvantaged areas stood out, compared with RR=1.08 in less disadvantaged areas. This pattern was observed on lag 0 but did not persist. The RRs for male presentations were 1.10 and 1.04 in most and less disadvantaged areas; for females, RR was 1.04 in less disadvantaged areas. This pattern persisted across lags 0–2. Conclusions: Heat-related ED visits increased during heatwaves. However, due to overlapping confidence intervals, variations across socioeconomic areas should be interpreted cautiously. Implications: ED data may be utilised for monitoring heat-related health impacts, particularly on the first day of heatwaves, to facilitate prompt interventions and targeted resource allocation.

A time series analysis of presentations to Queensland health facilities for alcohol-related conditions, following the increase in 'alcopops' tax

Objective: In response to concerns about the health consequences of high-risk drinking by young people, the Australian Government increased the tax on pre-mixed alcoholic beverages ('alcopops') favoured by this demographic. We measured changes in admissions for alcohol-related harm to health throughout Queensland, before and after the tax increase in April 2008. Methods: We used data from the Queensland Trauma Register, Hospitals Admitted Patients Data Collection, and the Emergency Department Information System to calculate alcohol-related admission rates per 100,000 people, for 15 - 29 year-olds. We analysed data over 3 years (April 2006 - April 2009), using interrupted time-series analyses. This covered 2 years before, and 1 year after, the tax increase. We investigated both mental and behavioural consequences (via F10 codes), and intentional/unintentional injuries (S and T codes). Results: We fitted an auto-regressive integrated moving average (ARIMA) model, to test for any changes following the increased tax. There was no decrease in alcohol-related admissions in 15 - 29 year-olds. We found similar results for males and females, as well as definitions of alcohol-related harms that were narrow (F10 codes only) and broad (F10, S and T codes). Conclusions: The increased tax on 'alcopops' was not associated with any reduction in hospital admissions for alcohol-related harms in Queensland 15 - 29 year-olds.

Simulation-based density estimation for time series using covariate data

This paper proposes a simulation-based density estimation technique for time series that exploits information found in covariate data. The method can be paired with a large range of parametric models used in time series estimation. We derive asymptotic properties of the estimator and illustrate attractive finite sample properties for a range of well-known econometric and financial applications.

Efficient use of correlation entropy for analysing time series data

The correlation dimension D 2 and correlation entropy K 2 are both important quantifiers in nonlinear time series analysis. However, use of D 2 has been more common compared to K 2 as a discriminating measure. One reason for this is that D 2 is a static measure and can be easily evaluated from a time series. However, in many cases, especially those involving coloured noise, K 2 is regarded as a more useful measure. Here we present an efficient algorithmic scheme to compute K 2 directly from a time series data and show that K 2 can be used as a more effective measure compared to D 2 for analysing practical time series involving coloured noise.

Contributions to time series data mining departing from the problem of road travel time modeling

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Removing observational noise from fisheries-independent time series data using ARIMA models

Abundance indices derived from fishery-independent surveys typically exhibit much higher interannual variability than is consistent with the within-survey variance or the life history of a species. This extra variability is essentially observation noise (i.e. measurement error); it probably reflects environmentally driven factors that affect catchability over time. Unfortunately, high observation noise reduces the ability to detect important changes in the underlying population abundance. In our study, a noise-reduction technique for uncorrelated observation noise that is based on autoregressive integrated moving average (ARIMA) time series modeling is investigated. The approach is applied to 18 time series of finfish abundance, which were derived from trawl survey data from the U.S. northeast continental shelf. Although the a priori assumption of a random-walk-plus-uncorrelated-noise model generally yielded a smoothed result that is pleasing to the eye, we recommend that the most appropriate ARIMA model be identified for the observed time series if the smoothed time series will be used for further analysis of the population dynamics of a species.