Rodney C. Wolff

Methods for Estimating a Conditional Distribution Function

Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the Nadaraya--Watson estimator. It preserves the bias and variance properties of a class of second-order estimators introduced by Yu and Jones but has the added advantage of always being a distribution itself. Our methods also have application outside the time series setting; for example, to quantile estimation for independent data. This problem motivated the work of Yu and Jones.

Ambient temperature and morbidity: a review of epidemiological evidence.

Objective: In this paper, we review the epidemiological evidence on the relationship between ambient temperature and morbidity. We assessed the methodological issues in previous studies and proposed future research directions. Data sources and data extraction: We searched the PubMed database for epidemiological studies on ambient temperature and morbidity of noncommunicable diseases published in refereed English journals before 30 June 2010. Forty relevant studies were identified. Of these, 24 examined the relationship between ambient temperature and morbidity, 15 investigated the short-term effects of heat wave on morbidity, and 1 assessed both temperature and heat wave effects. Data synthesis: Descriptive and time-series studies were the two main research designs used to investigate the temperature–morbidity relationship. Measurements of temperature exposure and health outcomes used in these studies differed widely. The majority of studies reported a significant relationship between ambient temperature and total or cause-specific morbidities. However, there were some inconsistencies in the direction and magnitude of nonlinear lag effects. The lag effect of hot temperature on morbidity was shorter (several days) compared with that of cold temperature (up to a few weeks). The temperature–morbidity relationship may be confounded or modified by sociodemographic factors and air pollution. Conclusions: There is a significant short-term effect of ambient temperature on total and cause-specific morbidities. However, further research is needed to determine an appropriate temperature measure, consider a diverse range of morbidities, and to use consistent methodology to make different studies more comparable.

A time-domain test for some types of nonlinearity

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. We propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.

Climate Variability, Social and Environmental Factors, and Ross River Virus Transmission: Research Development and Future Research Needs

Background Arbovirus diseases have emerged as a global public health concern. However, the impact of climatic, social, and environmental variability on the transmission of arbovirus diseases remains to be determined. Objective Our goal for this study was to provide an overview of research development and future research directions about the interrelationship between climate variability, social and environmental factors, and the transmission of Ross River virus (RRV), the most common and widespread arbovirus disease in Australia. Methods We conducted a systematic literature search on climatic, social, and environmental factors and RRV disease. Potentially relevant studies were identified from a series of electronic searches. Results The body of evidence revealed that the transmission cycles of RRV disease appear to be sensitive to climate and tidal variability. Rainfall, temperature, and high tides were among major determinants of the transmission of RRV disease at the macro level. However, the nature and magnitude of the interrelationship between climate variability, mosquito density, and the transmission of RRV disease varied with geographic area and socioenvironmental condition. Projected anthropogenic global climatic change may result in an increase in RRV infections, and the key determinants of RRV transmission we have identified here may be useful in the development of an early warning system. Conclusions The analysis indicates that there is a complex relationship between climate variability, social and environmental factors, and RRV transmission. Different strategies may be needed for the control and prevention of RRV disease at different levels. These research findings could be used as an additional tool to support decision making in disease control/surveillance and risk management.

Independence in Time Series: Another Look at the BDS Test [and Discussion]

This paper examines a statistical method derived from chaos theory. The correlation integral was proposed over a decade ago as a way of detecting chaos in a possibly partial realization of a dynamical system, because it depends on the spatial arrangement of the reconstructed attractor of the system. We exploit geometrical properties of an embedded time series to establish a test of independence in the original time series. Earlier efforts here have used the Central Limit Theorem to obtain normality as the null distribution; however, the testing procedure was, to an extent, ad hoc. By making moderately weak assumptions about the marginal distribution of the given series, we obtain a Poisson law for the correlation integral under the null hypothesis of independence, and use nonparametric methods to specify the test precisely. We compare the size and power of the present test with its predecessor and with other non-parametric tests for serial dependence.

BL-GARCH models with elliptical distributed innovations

In this work, we discuss the class of bilinear GARCH (BL-GARCH) models that are capable of capturing simultaneously two key properties of non-linear time series: volatility clustering and leverage effects. It has often been observed that the marginal distributions of such time series have heavy tails; thus we examine the BL-GARCH model in a general setting under some non-normal distributions. We investigate some probabilistic properties of this model and we conduct a Monte Carlo experiment to evaluate the small-sample performance of the maximum likelihood estimation (MLE) methodology for various models. Finally, within-sample estimation properties were studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects. The main results suggest that the Student-t BL-GARCH seems highly appropriate to describe the S&P 500 daily returns.

Can the Content of Public News Be Used to Forecast Abnormal Stock Market Behaviour

A popular theory of markets is that they are efficient: all available information is deemed to provide an accurate valuation of an asset at any time. In this paper, we consider how the content of market- related news articles contributes to such information. Specifically, we mine news articles for terms of interest, and quantify this degree of interest. We then incorporate this measure into traditional models for market index volatility with a view to forecasting whether the incidence of interesting news is correlated with a shock in the index, and thus if the information can be captured to value the underlying asset. We illustrate the methodology on stock market indices for the USA, the UK, and Australia.

BINARY TIME SERIES GENERATED BY CHAOTIC LOGISTIC MAPS

This paper examines stochastic pairwise dependence structures in binary time series obtained from discretised versions of standard chaotic logistic maps. It is motivated by applications in communications modelling which make use of so-called chaotic binary sequences. The strength of non-linear stochastic dependence of the binary sequences is explored. In contrast to the original chaotic sequence, the binary version is non-chaotic with non-Markovian non-linear dependence, except in a special case. Marginal and joint probability distributions, and autocorrelation functions are elicited. Multivariate binary and more discretized time series from a single realisation of the logistic map are developed from the binary paradigm. Proposals for extension of the methodology to other cases of the general logistic map are developed. Finally, a brief illustration of the place of chaos-based binary processes in chaos communications is given.

A new approach to spatial data interpolation using higher-order statistics

Abstract Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

Semiparametric Approximation Methods in Multivariate Model Selection

In this paper we propose a cross-validation selection criterion to determine asymptotically the correct model among the family of all possible partially linear models when the underlying model is a partially linear model. We establish the asymptotic consistency of the criterion. In addition, the criterion is illustrated using two real sets of data.