Maria Eduarda Silva

Time Series Analysis of Sea-Level Records: Characterising Long-Term Variability

The characterisation and quantification of long-term sea-level variability is of considerable interest in a climate change context. Long time series from coastal tide gauges are particularly appropriate for this purpose. Long-term variability in tide gauge records is usually expressed through the linear slope resulting from the fit of a linear model to the time series, thus assuming that the generating process is deterministic with a short memory component. However, this assumption needs to be tested, since trend features can also be due to non-deterministic processes such as random walk or long range dependent processes, or even be driven by a combination of deterministic and stochastic processes. Specific methodology is therefore required to distinguish between a deterministic trend and stochastically-driven trend-like features in a time series. In this chapter, long-term sea-level variability is characterised through the application of (i) parametric statistical tests for stationarity, (ii) wavelet analysis for assessing scaling features, and (iii) generalised least squares for estimating deterministic trends. The results presented here for long tide gauge records in the North Atlantic show, despite some local coherency, profound differences in terms of the low frequency structure of these sea-level time series. These differences suggest that the long-term variations are reflecting mainly local/regional phenomena.

Bivariate binomial autoregressive models

This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued GARCH models is proposed. Then, a new bivariate thinning operation is introduced and explained in detail. The new thinning operation has a number of advantages including the fact that marginally it behaves as the usual binomial thinning operation and also that allows for both positive and negative cross-correlations. Based upon this new thinning operation, a bivariate extension of the binomial autoregressive model of order one is introduced. Basic probabilistic and statistical properties of the model are discussed. Parameter estimation and forecasting are also covered. The performance of these models is illustrated through an empirical application to a set of rainy days time series collected from 2000 up to 2010 in the German cities of Bremen and Cuxhaven.

Changing seasonality in North Atlantic coastal sea level from the analysis of long tide gauge records

Sea level is a key variable in the context of global climate change. Climate-induced variability is expected to affect not only the mean sea level but also the amplitude and phase of its seasonal cycle. This study addresses the changes in the amplitude and phase of the annual cycle of coastal sea level in the extra-tropical North Atlantic. The physical causes of these variations are explored by analysing the association between fluctuations in the annual amplitude of sea level and in ancillary parameters [atmospheric pressure, sea-surface temperature and North Atlantic Oscillation (NAO) winter index]. The annual cycle is extracted through autoregressive decomposition, in order to be able to separate variations in seasonality from long-term interannual variations in the mean. The changes detected in the annual sea level cycle are regionally coherent, and related to changes in the analysed forcing parameters. At the northern sites, fluctuations in the annual amplitude of sea level are associated with concurrent changes in temperature, while atmospheric pressure is the dominant influence for most of the sites on the western boundary. The state of the NAO influences the annual variability in the Southern Bight, possibly through NAO-related changes in wind stress and ocean circulation.

Beyond long memory in heart rate variability: An approach based on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity.

Heart Rate Variability (HRV) series exhibit long memory and time-varying conditional variance. This work considers the Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors. ARFIMA-GARCH models may be used to capture and remove long memory and estimate the conditional volatility in 24 h HRV recordings. The ARFIMA-GARCH approach is applied to fifteen long term HRV series available at Physionet, leading to the discrimination among normal individuals, heart failure patients, and patients with atrial fibrillation.

Modelling neuromuscular blockade: a stochastic approach based on clinical data

During surgical interventions, a muscle relaxant drug is frequently administered with the objective of inducing muscle paralysis. Clinical environment and patient safety issues lead to a huge variety of situations that must be taken into account requiring intensive simulation studies. Hence, population models are crucial for research and development in this field. This work develops a stochastic population model for the neuromuscular blockade (NMB) (muscle paralysis) level induced by atracurium based on a deterministic individual model already proposed in the literature. To achieve this goal, a joint Lognormal distribution is considered for the patient-dependent parameters. This study is based on clinical data collected during general anaesthesia. The procedure developed enables to construct a reliable reference bank of parametrized models that not only reproduces the overall features of the NMB, but also the inter-individual variability characteristic of physiological signals. It turns out that this bank constitutes a fundamental tool to support research on identification and control algorithms and is suitable to be integrated in clinical decision support systems.

Long-range dependence in heart rate variability data: ARFIMA modelling vs detrended fluctuation analysis

Heart rate variability (HRV) data display non-stationary characteristics and exhibit long-range correlation (memory). Detrended fluctuation analysis (DFA) has become a widely-used technique for long memory estimation in non-stationary HRV data. Recently, we have proposed an alternative approach based on fractional integrated autoregressive moving average (ARFIMA) models. ARFIMA models, combined with selective adaptive segmentation may be used to capture and remove long-range correlation, leading to an improved description and interpretation of the components in 24 hour HRV recordings. In this work estimation of long memory by DFA and selective adaptive ARFIMA modelling is carried out in 24 hour HRV recordings of 17 healthy subjects of two age groups. The two methods give similar information on long-range global characteristics. However, ARFIMA modelling is advantageous, allowing the description of long-range correlation in reduced length segments.

Individualizing propofol dosage: a multivariate linear model approach

In the last decades propofol became established as an intravenous agent for the induction and maintenance of both sedation and general anesthesia procedures. In order to achieve the desired clinical effects appropriate infusion rate strategies must be designed. Moreover, it is important to avoid or minimize associated side effects namely adverse cardiorespiratory effects and delayed recovery. Nowadays, to attain these purposes the continuous propofol delivery is usually performed through target-controlled infusion (TCI) systems whose algorithms rely on pharmacokinetic and pharmacodynamic models. This work presents statistical models to estimate both the infusion rate and the bolus administration. The modeling strategy relies on multivariate linear models, based on patient characteristics such as age, height, weight and gender along with the desired target concentration. A clinical database collected with a RugLoopII device on 84 patients undergoing ultrasonographic endoscopy under sedation-analgesia with propofol and remifentanil is used to estimate the models (training set with 74 cases) and assess their performance (test set with 10 cases). The results obtained in the test set comprising a broad range of characteristics are satisfactory since the models are able to predict bolus, infusion rates and the effect-site concentrations comparable to those of TCI. Furthermore, comparisons of the effect-site concentrations for dosages predicted by the proposed Linear model and the Marsh model for the same target concentration is achieved using Schnider model and a factorial design on the factors (patients characteristics). The results indicate that the Linear model predicts a dosage profile that is faster in leading to an effect-site concentration closer to the desired target concentration.

Detection of Additive Outliers in Poisson INAR(1) Time Series

Outlying observations are commonly encountered in the analysis of time series. In this paper a Bayesian approach is employed to detect additive outliers in order one Poisson integer-valued autoregressive time series. The methodology is informative and allows the identification of the observations which require further inspection. The procedure is illustrated with simulated and observed data sets.

Neuromuscular blockade nonlinear model identification

This paper presents a methodology for parameter estimation of a nonlinear neuromuscular blockade dynamic model to be used as a predictive model for automated control, in general anesthesia. The neuromuscular blockade dynamic model comprises two blocks connected in series, a pharmacokinetic model and the pharmacodynamic model. The pharmacokinetic model is a second order linear dynamic model and describes the redistribution of the drug in the body. The pharmacodynamic model is a nonlinear function, named as the Hill equation, and it describes the interaction between the concentration of the drug in the effect site and the measured patients muscle paralysis state. The identification methodology uses four data points taken from the neuromuscular blockade response obtained with the administration of the first bolus. The four data points are chosen to avoid the identification difficulties caused by the presence of the nonlinear behavior of the Hill equation. This approach enables the identification of the pharmacokinetic dynamics, that is, the two poles of the second order linear dynamic model followed by the estimation of the normalized parameters of the Hill equation. Computer simulations show that the proposed identification methodology is able to provide good results even when the pharmacokinetic dynamics has an order higher that two. This suggests that the methodology may be employed in neuromuscular blockade automated control as a predictive model, to help the initial tuning of the controller parameters or in adaptive control to get a first model that can be improved with online identification using some recursive minimization techniques to adjust the adaptive controller or as an advising mechanism to help the anesthesiologist during the anesthesia.

Modeling volatility in heat rate variability

Modeling Heart Rate Variability (HRV) data has become important for clinical applications and as a research tool. These data exhibit long memory and time-varying conditional variance (volatility). In HRV, volatility is traditionally estimated by recursive least squares combined with short memory AutoRegressive (AR) models. This work considers a parametric approach based on long memory Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with heteroscedastic errors. To model the heteroscedasticity nonlinear Generalized Autoregressive Conditionally Heteroscedastic (GARCH) and Exponential Generalized Autoregressive Conditionally Heteroscedastic (EGARCH) models are considered. The latter are necessary to model empirical characteristics of conditional volatility such as clustering and asymmetry in the response, usually called leverage in time series literature. The ARFIMA-EGARCH models are used to capture and remove long memory and characterize conditional volatility in 24 hour HRV recordings from the Noltisalis database.