Polarization of forecast densities : a new approach to time series classification

Time series classification has been extensively explored in many fields of study. Most methods are based on the historical or current information extracted from data. However, if interest is in a specific future time period, methods that directly relate to forecasts of time series are much more appropriate. An approach to time series classification is proposed based on a polarization measure of forecast densities of time series. By fitting autoregressive models, forecast replicates of each time series are obtained via the bias-corrected bootstrap, and a stationarity correction is considered when necessary. Kernel estimators are then employed to approximate forecast densities, and discrepancies of forecast densities of pairs of time series are estimated by a polarization measure, which evaluates the extent to which two densities overlap. Following the distributional properties of the polarization measure, a discriminant rule and a clustering method are proposed to conduct the supervised and unsupervised classification, respectively. The proposed methodology is applied to both simulated and real data sets, and the results show desirable properties.

A hypothesis test using bias-adjusted AR estimators for classifying time series in small samples

A new test of hypothesis for classifying stationary time series based on the bias-adjusted estimators of the fitted autoregressive model is proposed. It is shown theoretically that the proposed test has desirable properties. Simulation results show that when time series are short, the size and power estimates of the proposed test are reasonably good, and thus this test is reliable in discriminating between short-length time series. As the length of the time series increases, the performance of the proposed test improves, but the benefit of bias-adjustment reduces. The proposed hypothesis test is applied to two real data sets: the annual real GDP per capita of six European countries, and quarterly real GDP per capita of five European countries. The application results demonstrate that the proposed test displays reasonably good performance in classifying relatively short time series.

The impact of heatwaves on emergency department visits in Brisbane, Australia : a time series study

Introduction The acute health effects of heatwaves in a subtropical climate and their impact on emergency departments (ED) are not well known. The purpose of this study is to examine overt heat-related presentations to EDs associated with heatwaves in Brisbane. Methods Data were obtained for the summer seasons (December to February) from 2000-2012. Heatwave events were defined as two or more successive days with daily maximum temperature >=34[degree sign]C (HWD1) or >=37[degree sign]C (HWD2). Poisson generalised additive model was used to assess the effect of heatwaves on heat-related visits (International Classification of Diseases (ICD) 10 codes T67 and X30; ICD 9 codes 992 and E900.0). Results Overall, 628 cases presented for heat-related illnesses. The presentations significantly increased on heatwave days based on HWD1 (relative risk (RR) = 4.9, 95% confidence interval (CI): 3.8, 6.3) and HWD2 (RR = 18.5, 95% CI: 12.0, 28.4). The RRs in different age groups ranged between 3-9.2 (HWD1) and 7.5-37.5 (HWD2). High acuity visits significantly increased based on HWD1 (RR = 4.7, 95% CI: 2.3, 9.6) and HWD2 (RR = 81.7, 95% CI: 21.5, 310.0). Average length of stay in ED significantly increased by >1 hour (HWD1) and >2 hours (HWD2). Conclusions Heatwaves significantly increase ED visits and workload even in a subtropical climate. The degree of impact is directly related to the extent of temperature increases and varies by socio-demographic characteristics of the patients. Heatwave action plans should be tailored according to the population needs and level of vulnerability. EDs should have plans to increase their surge capacity during heatwaves.

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.

Dengue fever and el nino-southern oscillation in Queensland, Australia : a time series predictive model

Background It remains unclear over whether it is possible to develop an epidemic forecasting model for transmission of dengue fever in Queensland, Australia. Objectives To examine the potential impact of El Niño/Southern Oscillation on the transmission of dengue fever in Queensland, Australia and explore the possibility of developing a forecast model of dengue fever. Methods Data on the Southern Oscillation Index (SOI), an indicator of El Niño/Southern Oscillation activity, were obtained from the Australian Bureau of Meteorology. Numbers of dengue fever cases notified and the numbers of postcode areas with dengue fever cases between January 1993 and December 2005 were obtained from the Queensland Health and relevant population data were obtained from the Australia Bureau of Statistics. A multivariate Seasonal Auto-regressive Integrated Moving Average model was developed and validated by dividing the data file into two datasets: the data from January 1993 to December 2003 were used to construct a model and those from January 2004 to December 2005 were used to validate it. Results A decrease in the average SOI (ie, warmer conditions) during the preceding 3–12 months was significantly associated with an increase in the monthly numbers of postcode areas with dengue fever cases (β=−0.038; p = 0.019). Predicted values from the Seasonal Auto-regressive Integrated Moving Average model were consistent with the observed values in the validation dataset (root-mean-square percentage error: 1.93%). Conclusions Climate variability is directly and/or indirectly associated with dengue transmission and the development of an SOI-based epidemic forecasting system is possible for dengue fever in Queensland, Australia.

The short-term effect of air pollution on cardiovascular mortality in Tianjin, China : comparison of time series and case–crossover analyses

Background: Many studies have illustrated that ambient air pollution negatively impacts on health. However, little evidence is available for the effects of air pollution on cardiovascular mortality (CVM) in Tianjin, China. Also, no study has examined which strata length for the time-stratified case–crossover analysis gives estimates that most closely match the estimates from time series analysis. Objectives: The purpose of this study was to estimate the effects of air pollutants on CVM in Tianjin, China, and compare time-stratified case–crossover and time series analyses. Method: A time-stratified case–crossover and generalized additive model (time series) were applied to examine the impact of air pollution on CVM from 2005 to 2007. Four time-stratified case–crossover analyses were used by varying the stratum length (Calendar month, 28, 21 or 14 days). Jackknifing was used to compare the methods. Residual analysis was used to check whether the models fitted well. Results: Both case–crossover and time series analyses show that air pollutants (PM10, SO2 and NO2) were positively associated with CVM. The estimates from the time-stratified case–crossover varied greatly with changing strata length. The estimates from the time series analyses varied slightly with changing degrees of freedom per year for time. The residuals from the time series analyses had less autocorrelation than those from the case–crossover analyses indicating a better fit. Conclusion: Air pollution was associated with an increased risk of CVM in Tianjin, China. Time series analyses performed better than the time-stratified case–crossover analyses in terms of residual checking.

Facilitating needs based cancer care for people with a chronic disease : evaluation of an intervention using a multi-centre interrupted time series design

Background: Palliative care should be provided according to the individual needs of the patient, caregiver and family, so that the type and level of care provided, as well as the setting in which it is delivered, are dependent on the complexity and severity of individual needs, rather than prognosis or diagnosis. This paper presents a study designed to assess the feasibility and efficacy of an intervention to assist in the allocation of palliative care resources according to need, within the context of a population of people with advanced cancer. ---------- Methods/design: People with advanced cancer and their caregivers completed bi-monthly telephone interviews over a period of up to 18 months to assess unmet needs, anxiety and depression, quality of life, satisfaction with care and service utilisation. The intervention, introduced after at least two baseline phone interviews, involved a) training medical, nursing and allied health professionals at each recruitment site on the use of the Palliative Care Needs Assessment Guidelines and the Needs Assessment Tool: Progressive Disease - Cancer (NAT: PD-C); b) health professionals completing the NAT: PD-C with participating patients approximately monthly for the rest of the study period. Changes in outcomes will be compared pre-and post-intervention.---------- Discussion: The study will determine whether the routine, systematic and regular use of the Guidelines and NAT: PD-C in a range of clinical settings is a feasible and effective strategy for facilitating the timely provision of needs based care.

Exposure to hot and cold temperatures and ambulance attendances in Brisbane, Australia: A time series study

ABSTRACT Objectives: To investigate the effect of hot and cold temperatures on ambulance attendances. Design: An ecological time series study. Setting and participants: The study was conducted in Brisbane, Australia. We collected information on 783 935 daily ambulance attendances, along with data of associated meteorological variables and air pollutants, for the period of 2000–2007. Outcome measures: The total number of ambulance attendances was examined, along with those related to cardiovascular, respiratory and other non-traumatic conditions. Generalised additive models were used to assess the relationship between daily mean temperature and the number of ambulance attendances. Results: There were statistically significant relationships between mean temperature and ambulance attendances for all categories. Acute heat effects were found with a 1.17% (95% CI: 0.86%, 1.48%) increase in total attendances for 1 °C increase above threshold (0–1 days lag). Cold effects were delayed and longer lasting with a 1.30% (0.87%, 1.73%) increase in total attendances for a 1 °C decrease below the threshold (2–15 days lag). Harvesting was observed following initial acute periods of heat effects, but not for cold effects. Conclusions: This study shows that both hot and cold temperatures led to increases in ambulance attendances for different medical conditions. Our findings support the notion that ambulance attendance records are a valid and timely source of data for use in the development of local weather/health early warning systems.

Effects of extreme temperatures on years of life lost for cardiovascular deaths : a time series study in Brisbane, Australia

Background: Extreme temperatures are associated with cardiovascular disease (CVD) deaths. Previous studies have investigated the relative CVD mortality risk of temperature, but this risk is heavily influenced by deaths in frail elderly persons. To better estimate the burden of extreme temperatures we estimated their effects on years of life lost due to CVD. Methods and Results: The data were daily observations on weather and CVD mortality for Brisbane, Australia between 1996 and 2004. We estimated the association between daily mean temperature and years of life lost due to CVD, after adjusting for trend, season, day of the week, and humidity. To examine the non-linear and delayed effects of temperature, a distributed lag non-linear model was used. The model’s residuals were examined to investigate if there were any added effects due to cold spells and heat waves. The exposure-response curve between temperature and years of life lost was U-shaped, with the lowest years of life lost at 24 °C. The curve had a sharper rise at extremes of heat than of cold. The effect of cold peaked two days after exposure, whereas the greatest effect of heat occurred on the day of exposure. There were significantly added effects of heat waves on years of life lost. Conclusions: Increased years of life lost due to CVD are associated with both cold and hot temperatures. Research on specific interventions is needed to reduce temperature-related years of life lost from CVD deaths.

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.

Diurnal temperature range and childhood asthma : a time-series study

BACKGROUND: Hot and cold temperatures have been associated with childhood asthma. However, the relationship between daily temperature variation and childhood asthma is not well understood. This study aimed to examine the relationship between diurnal temperature range (DTR) and childhood asthma. METHODS: A Poisson generalized linear model combined with a distributed lag non-linear model was used to examine the relationship between DTR and emergency department admissions for childhood asthma in Brisbane, from January 1st 2003 to December 31st 2009. RESULTS: There was a statistically significant relationship between DTR and childhood asthma. The DTR effect on childhood asthma increased above a DTR of 10[degree sign]C. The effect of DTR on childhood asthma was the greatest for lag 0--9 days, with a 31% (95% confidence interval: 11% -- 58%) increase of emergency department admissions per 5[degree sign]C increment of DTR. Male children and children aged 5--9 years appeared to be more vulnerable to the DTR effect than others. CONCLUSIONS: Large DTR may trigger childhood asthma. Future measures to control and prevent childhood asthma should include taking temperature variability into account. More protective measures should be taken after a day of DTR above10[degree sign]C.