Of `Cocktail Parties' and Exoplanets

The characterisation of ever smaller and fainter extrasolar planets requires an intricate understanding of one's data and the analysis techniques used. Correcting the raw data at the 10^-4 level of accuracy in flux is one of the central challenges. This can be difficult for instruments that do not feature a calibration plan for such high precision measurements. Here, it is not always obvious how to de-correlate the data using auxiliary information of the instrument and it becomes paramount to know how well one can disentangle instrument systematics from one's data, given nothing but the data itself. We propose a non-parametric machine learning algorithm, based on the concept of independent component analysis, to de-convolve the systematic noise and all non-Gaussian signals from the desired astrophysical signal. Such a `blind' signal de-mixing is commonly known as the `Cocktail Party problem' in signal-processing. Given multiple simultaneous observations of the same exoplanetary eclipse, as in the case of spectrophotometry, we show that we can often disentangle systematic noise from the original light curve signal without the use of any complementary information of the instrument. In this paper, we explore these signal extraction techniques using simulated data and two data sets observed with the Hubble-NICMOS instrument. Another important application is the de-correlation of the exoplanetary signal from time-correlated stellar variability. Using data obtained by the Kepler mission we show that the desired signal can be de-convolved from the stellar noise using a single time series spanning several eclipse events. Such non-parametric techniques can provide important confirmations of the existent parametric corrections reported in the literature, and their associated results. Additionally they can substantially improve the precision exoplanetary light curve analysis in the future.Comment: ApJ accepte

Multiscale analysis of high frequency exchange rate time series

Imperial Users onl

Time Series Modelling

The analysis and modeling of time series is of the utmost importance in various fields of application. This Special Issue is a collection of articles on a wide range of topics, covering stochastic models for time series as well as methods for their analysis, univariate and multivariate time series, real-valued and discrete-valued time series, applications of time series methods to forecasting and statistical process control, and software implementations of methods and models for time series. The proposed approaches and concepts are thoroughly discussed and illustrated with several real-world data examples

Characterisation and Estimation of Entropy Rate for Long Range Dependent Processes

Much of the theory of random processes has been developed with the assumption that distant time periods are weakly correlated. However, it has been discovered in many real-world phenomena that this assumption is not valid. These findings have resulted in extensive research interest into stochastic processes that have strong correlations that persist over long time periods. This phenomenon is called long range dependence. This phenomena has been defined in the time and frequency domains by the slow decay of their autocorrelation function and the existence of a pole at the origin of the spectral density function, respectively. Information theory has proved very useful in statistics and probability theory. However, there has not been much research into the information theoretic properties and characterisations of this phenomena.This thesis characterises the phenomena of long range dependence, for discrete and continuous-valued stochastic processes in discrete time, by an information theoretic measure, the entropy rate. The entropy rate measures the amount of information contained in a stochastic process on average, per random variable. Common characterisations of long range dependence in the time and frequency domains are given by the slow convergence to quantities of interest, such as the sample mean. We show that this type of behaviour is present in the entropy rate function, by showing that long range dependence also has slow convergence of the conditional entropy to the entropy rate, due to some entropic quantities diverging to infinity. As an extension we show for classes of Gaussian processes and Markov chains that long range dependence by an infinite amount of shared information between the past and future of a stochastic process. The slow convergence has the impact of making accurate estimation of the differential entropy rate on data from long range dependent processes difficult, to the extent that existing techniques either are not accurate or are computationally intensive. We introduce a new estimation technique, that is able to balance these two concerns and make quick and accurate estimates of the differential entropy rate from continuous-valued data. We develop and utilise a connection between the differential entropy rate and the Shannon entropy rate of its quantised process as the basis of the estimation technique. This allows us to draw on the extensive research into Shannon entropy rate estimation on discrete-valued data, and we show that properties for the differential entropy rate estimator can be inherited from the choice of Shannon entropy rate estimator.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 202

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

Higher order asymptotic theory for nonparametric time series analysis and related contributions.

We investigate higher order asymptotic theory in nonparametric time series analysis. The aim of these techniques is to approximate the finite sample distribution of estimates and test statistics. This is specially relevant for smoothed nonparametric estimates in the presence of autocorrelation, which have slow rates of convergence so that inference rules based on first-order asymptotic approximations may not be very precise. First we review the literature on autocorrelation-robust inference and higher order asymptotics in time series. We evaluate the effect of the nonparametric estimation of the variance in the studentization of least squares estimates in linear regression models by means of asymptotic expansions. Then, we obtain an Edgeworth expansion for the distribution of nonparametric estimates of the spectral density and studentized sample mean. Only local smoothness conditions on the spectrum of the time series are assumed, so long range dependence behaviour in the series is allowed at remote frequencies, not necessary only at zero frequency but at possible cyclical and seasonal ones. The nonparametric methods described rely on a bandwidth or smoothing number. We propose a cross-validation algorithm for the choice of the optimal bandwidth, in a mean square sense, at a single point without restrictions on the spectral density at other frequencies. Then, we focus on the performance of the spectral density estimates around a singularity due to long range dependence and we obtain their asymptotic distribution in the Gaussian case. Semiparametric inference procedures about the long memory parameter based on these nonparametric estimates are justified under mild conditions on the distribution of the observed time series. Using a fixed average of periodogram ordinates, we also prove the consistency of the log-periodogram regression estimate of the memory parameter for linear but non-Gaussian time series

Prediction of nonlinear nonstationary time series data using a digital filter and support vector regression

Volatility is a key parameter when measuring the size of the errors made in modelling returns and other nonlinear nonstationary time series data. The Autoregressive Integrated Moving- Average (ARIMA) model is a linear process in time series; whilst in the nonlinear system, the Generalised Autoregressive Conditional Heteroskedasticity (GARCH) and Markov Switching GARCH (MS-GARCH) models have been widely applied. In statistical learning theory, Support Vector Regression (SVR) plays an important role in predicting nonlinear and nonstationary time series data. We propose a new class model comprised of a combination of a novel derivative Empirical Mode Decomposition (EMD), averaging intrinsic mode function (aIMF) and a novel of multiclass SVR using mean reversion and coefficient of variance (CV) to predict financial data i.e. EUR-USD exchange rates. The proposed novel aIMF is capable of smoothing and reducing noise, whereas the novel of multiclass SVR model can predict exchange rates. Our simulation results show that our model significantly outperforms simulations by state-of-art ARIMA, GARCH, Markov Switching generalised Autoregressive conditional Heteroskedasticity (MS-GARCH), Markov Switching Regression (MSR) models and Markov chain Monte Carlo (MCMC) regression.Open Acces