On Time Series Analysis of Public Health and Biomedical Data

A time series is a sequence of observations made over time. Examples in public health include daily ozone concentrations, weekly admissions to an emergency department or annual expenditures on health care in the United States. Time series models are used to describe the dependence of the response at each time on predictor variables including covariates and possibly previous values in the series. Time series methods are necessary to account for the correlation among repeated responses over time. This paper gives an overview of time series ideas and methods used in public health research.

Primary production at time series station DYFAMED

Phytoplankton carbon assimilation has been measured near monthly using the 14C method at DYFAMED France JGOFS time-series station from 1993 to 1999. Data were obtained using the "LET GO" technique, which allowed in situ injection of bicarbonate and incubation in enclosures at 10 depths. Incubation duration was 4 h around noon, from which daily production was estimated. The seasonal variation of the depth-integrated carbon assimilation exhibits a marked cycle. Maximum values reach 1.8 g C/m**2/d in March or April; constant lower values were observed from August to January, in the range 100-300 mg C/m**2/d. The annual primary production vary in the range 86-232 g C/m**2/yr, in the upper range of older estimations. Primary production normalized to chlorophyll a shows maximum values in the period of oligotrophy. This increase of carbon assimilation rate per unit of chlorophyll a appears as linked to the period of phosphorus-limited ecosystem, and vertical distribution of taxonomic pigments suggests a possible role of cyanobacteria. Potential export production has been estimated from primary production data and Fp ratio based on pigments concentrations. These estimates (which imply biological steady state conditions) vary in a wide range, from 19 to 71 g C/m**2/yr. There is a decoupling between years with high potential export production and years with high measured particulate fluxes, which highlights the question of balance by resupply of the limiting nutrients and the role of dissolved organic carbon. A possible shift of primary production towards a more regeneration-dominated system is suggested for recent years.

Oxygen concentration at time series station DYNAPROC

Continuous measurements between 0 and 200 m depth were performed every 2 h over two separate periods of four days at a station in the open northwestern Mediterranean Sea (Dyfamed Station) during the Dynaproc cruise in May 1995. Estimates of the daily variations in profiles of temperature, partial pressure of CO2, oxygen, chlorophyll a and nutrients were obtained. The distributions of the various physical and chemical properties were clearly different during the two time series, which were separated by a period of 11 days during which a wind event occurred. The mean daily utilization or production due to biological processes of dissolved inorganic carbon (DIC), nitrate+nitrite and oxygen were calculated along isopycnals using a vertical diffusion model. Between the surface and about 20 m depth, DIC was consumed and O2 released during the two time series while the nitrate+nitrite concentrations as well as supplies were zero. After the wind event, the O2 : C : N ratios of consumption (or production) were, on average, near the Redfield ratios, but during the first time series, the C : N utilization ratio between 20 and 35 m was two to three times that of Redfield stoichiometry and the oxygen release was low. The integrated net community production (NCP) in terms of carbon was equivalent during the two time series, whereas the chlorophyll a biomass was twice as high, on average, during the first time series but did decrease. These results imply that the production systems were different during the two periods. The first time series corresponds to a period at the end of production, due to the nutrient depletion in the euphotic layer. The formation of degradation products of the living material in dissolved organic form is probably important as indicated by the high C : N utilization ratios. The second time series corresponds to a reactivation of the primary production due to the upward shift of nutrients after the wind event.

Surface time series of nitrate, silicate and chlorophyll a (1999-2011) and CTD profiles (1999) at the PhytoCly station, Bay of Calvi, Corsica, Mediterranean Sea

This work is based on a long time series of data collected in the well-preserved Bay of Calvi (Corsica island, Ligurian Sea, NW Mediterranean) between 1979 and 2011, which include physical characteristics (31 years), chlorophyll a (chl a, 15 years), and inorganic nutrients (13 years). Because samples were collected at relatively high frequencies, which ranged from daily to biweekly during the winter-spring period, it was possible to (1) evidence the key role of two interacting physical variables, i.e. water temperature and wind intensity, on nutrient replenishment and phytoplankton dynamics during the winter-spring period, (2) determine critical values of physical factors that explained interannual variability in the replenishment of surface nutrients and the winter-spring phytoplankton bloom, and (3) identify previously unrecognized characteristics of the planktonic ecosystem. Over the >30 year observation period, the main driver of nutrient replenishment and phytoplankton (chl a) development was the number of wind events (mean daily wind speed >5 m s-1) during the cold-water period (subsurface water <13.5°C). According to winter intensity, there were strong differences in both the duration and intensity of nutrient fertilization and phytoplankton blooms (chl a). The trophic character of the Bay of Calvi changed according to years, and ranged from very oligotrophic (i.e. subtropical regime, characterized by low seasonal variability) to mesotrophic (i.e. temperate regime, with a well-marked increase in nutrient concentrations and chl a during the winter-spring period) during mild and moderate winters, respectively. A third regime occurred during severe winters characterized by specific wind conditions (i.e. high frequency of northeasterly winds), when Mediterranean "high nutrient - low chlorophyll" conditions occurred as a result of enhanced crossshore exchanges and associated offshore export of the nutrient-rich water. There was no long-term trend (e.g. climatic) in either nutrient replenishment or the winter-spring phytoplankton bloom between 1979 and 2011, but both nutrients and chl a reflected interannual and decadal changes in winter intensity.

Anundance of phytoplankton at time series station DYNAPROC

A general study of biogeochemical processes (DYNAPROC cruise) was conducted in May 1995 at a time-series station in the open northwestern Mediterranean Sea where horizontal advection was weak. Short-term variations of the vertical distributions of pico- and nanophytoplankton were investigated over four 36-h cycles, along with parallel determinations of metabolic CO2 production rates and amino acid-containing colloid (AACC) concentrations at the chlorophyll maximum depth. The vertical (0-1000-m depth) distributions of (i) AACC, (ii) suspended particles and (iii) metabolic CO2 production rate were documented during the initial and final stages of these 36-h cycles. This study was concerned with diel vertical migration (DVM) of zooplankton, which provided periodic perturbations. Accordingly, the time scale of the experimental work varied from a few hours to a few days. Although all distributions exhibited a periodic behaviour, AACC distributions were generally not linked to diel vertical migrations. In the subsurface layer, Synechococcus made the most abundant population and large variations in concentration were observed both at day and at night. The corresponding integrated (over the upper 90 m) losses of Synechococcus during one night pointed to a potential source of exported organic matter amounting to 534 mg C/m**2. This study stresses the potential importance of organic matter export from the euphotic zone through the daily grazing activity of vertically migrating organisms, which would not be accounted for by measurements at longer time scales. The metabolic CO2 production exhibited a peak of activity below 500 m that was shifted downward, apparently in a recurrent way and independently of the vertical distributions of AACC or of suspended particulate material. To account for this phenomenon, a 'sustained wave train» hypothesis is proposed that combines the effect of the diel superficial faecal pellet production by swarming migrators and the repackaging activity of the nonmigrating midwater populations. Our results confirm the recent finding that the particulate compartment is not the major source of the observed instantaneous remineralisation rate and shed a new light on the fate of organic matter in the aphotic zone.

Land Surface Temperature continuous time series from SSM/I passive microwave radiometers, over northern latitudes (Latitudes > 45°N), during summer snow free period (2000-2011), with links to NetCDF files

Remote sensing instruments are key players to map land surface temperature (LST) at large temporal and spatial scales. In this paper, we present how we combine passive microwave and thermal infrared data to estimate LST during summer snow-free periods over northern high latitudes. The methodology is based on the SSM/I-SSMIS 37 GHz measurements at both vertical and horizontal polarizations on a 25 km × 25 km grid size. LST is retrieved from brightness temperatures introducing an empirical linear relationship between emissivities at both polarizations as described in Royer and Poirier (2010). This relationship is calibrated at pixel scale, using cloud-free independent LST data from MODIS instruments. The SSM/I-SSMIS and MODIS data are synchronized by fitting a diurnal cycle model built on skin temperature reanalysis provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). The resulting temperature dataset is provided at 25 km scale and at an hourly time step during the ten-year analysis period (2000-2011). This new product was locally evaluated at five experimental sites of the EU-PAGE21 project against air temperature measurements and meteorological model reanalysis, and compared to the MODIS LST product at both local and circumpolar scale. The results giving a mean RMSE of the order of 2.2 K demonstrate the usefulness of the microwave product, which is unaffected by clouds as opposed to thermal infrared products and offers a better resolution compared to model reanalysis.

Unit Root Analysis of Traffic Time Series in Toll Highways

Concession contracts in highways often include some kind of clauses (for example, a minimum traffic guarantee) that allow for better management of the business risks. The value of these clauses may be important and should be added to the total value of the concession. However, in these cases, traditional valuation techniques, like the NPV (net present value) of the project, are insufficient. An alternative methodology for the valuation of highway concession is one based on the real options approach. This methodology is generally built on the assumption of the evolution of traffic volume as a GBM (geometric Brownian motion), which is the hypothesis analyzed in this paper. First, a description of the methodology used for the analysis of the existence of unit roots (i.e., the hypothesis of non-stationarity) is provided. The Dickey-Fuller approach has been used, which is the most common test for this kind of analysis. Then this methodology is applied to perform a statistical analysis of traffic series in Spanish toll highways. For this purpose, data on the AADT (annual average daily traffic) on a set of highways have been used. The period of analysis is around thirty years in most cases. The main outcome of the research is that the hypothesis that traffic volume follows a GBM process in Spanish toll highways cannot be rejected. This result is robust, and therefore it can be used as a starting point for the application of the real options theory to assess toll highway concessions.

Detecting and characterising ramp events in wind power time series

In order to implement accurate models for wind power ramp forecasting, ramps need to be previously characterised. This issue has been typically addressed by performing binary ramp/non-ramp classifications based on ad-hoc assessed thresholds. However, recent works question this approach. This paper presents the ramp function, an innovative wavelet- based tool which detects and characterises ramp events in wind power time series. The underlying idea is to assess a continuous index related to the ramp intensity at each time step, which is obtained by considering large power output gradients evaluated under different time scales (up to typical ramp durations). The ramp function overcomes some of the drawbacks shown by the aforementioned binary classification and permits forecasters to easily reveal specific features of the ramp behaviour observed at a wind farm. As an example, the daily profile of the ramp-up and ramp-down intensities are obtained for the case of a wind farm located in Spain

Therapeutic Assessment for an individual with Binge Eating Disorder: A single-case time-series design .

Therapeutic Assessment (TA) is a treatment approach that combines psychological assessment and psychotherapy. The study examines the efficacy of this approach with an individual with Binge Eating Disorder. A replicated single-case time-series design with daily measures is used to assess the effects of TA and to track the process of change during the TA. The individual experienced inconclusive benefits after participation in TA. Significant change occurred in all variables measured, though none of the changes occurred in the hypothesized direction. Further research is needed to determine if TA is an effective treatment for individuals diagnosed with Binge Eating Disorder.

Detection and mapping of burnt areas from time series of MODIS-derived NDVI data in a Mediterranean region

Moderate resolution remote sensing data, as provided by MODIS, can be used to detect and map active or past wildfires from daily records of suitable combinations of reflectance bands. The objective of the present work was to develop and test simple algorithms and variations for automatic or semiautomatic detection of burnt areas from time series data of MODIS biweekly vegetation indices for a Mediterranean region. MODIS-derived NDVI 250m time series data for the Valencia region, East Spain, were subjected to a two-step process for the detection of candidate burnt areas, and the results compared with available fire event records from the Valencia Regional Government. For each pixel and date in the data series, a model was fitted to both the previous and posterior time series data. Combining drops between two consecutive points and 1-year average drops, we used discrepancies or jumps between the pre and post models to identify seed pixels, and then delimitated fire scars for each potential wildfire using an extension algorithm from the seed pixels. The resulting maps of the detected burnt areas showed a very good agreement with the perimeters registered in the database of fire records used as reference. Overall accuracies and indices of agreement were very high, and omission and commission errors were similar or lower than in previous studies that used automatic or semiautomatic fire scar detection based on remote sensing. This supports the effectiveness of the method for detecting and mapping burnt areas in the Mediterranean region.

Mesozooplankton and phytoplankton time series of the Baltic Monitoring Program (BMP)

Within the monitoring programme of the Helsinki Commission (HELCOM) the mesozooplankton of the Bornholm Basin (ICES subdivision 25, station BMP-K2) was sampled by the WP-2 net (lOOfJm) 5-8 times a year in 1988-1992. Abundance, biomass, secondary production and productivity (P/B) were given for mesozooplankton groups and copepod species. Environmental factors recorded were temperature, chlorophyll a and primary production. Within copepods, the dominant species were Temora longicornis and Pseudocalanus minutus with yearly peak values of 40-50% of the monthly copepod numbers and biomasses. The annual production of Temora longicornis was highest (6.5g C/m**2/y). The biomass of all copepods was at its maximum in June (mean = 2.25g C/m**2), especially in 1992 (3.65g C/m**2). The differences between results from two methods used to calculate the production of copepods were greatest in June and July. The cladocerans were only important in summer and the appendicularians only in spring. The productivity (P/B) of the appendicularians was highest of all mesozooplankton groups. Numbers and the biomass of the meroplankton were one or two orders of magnitude below the holoplanktic groups.

Time series of air chemistry measurements at Georg-von-Neumayer station, Dronning Maud Land, Antarctica in the years 1982 to 1991

The first Air Chemistry Observatory at the German Antarctic station Georg von Neumayer (GvN) was operated for 10 years from 1982 to 1991. The focus of the established observational programme was on characterizing the physical properties and chemical composition of the aerosol, as well as on monitoring the changing trace gas composition of the background atmosphere, especially concerning greenhouse gases. The observatory was designed by the Institut für Umweltphysik, University of Heidelberg (UHEIIUP). The experiments were installed inside the bivouac lodge, mounted on a sledge and put upon a snow hill to prevent snow accumulation during blizzards. All experiments were under daily control and daily performance protocols were documented. A ventilated stainless steel inlet stack (total height about 3-4 m above the snow surface) with a 50% aerodynamic cut-off diameter around 7-10 µm at wind velocities between 4-10 m/s supplied all experiments with ambient air. Contamination free sampling was realized by several means: (i) The Air Chemistry Observatory was situated in a clean air area about 1500 m south of GvN. Due to the fact that northern wind directions are very rare, contamination from the base can be excluded for most of the time. (ii) The power supply (20 kW) is provided by a cable from the main station, thus no fuel-driven generator is operated in the very vicinity. (iii) Contamination-free sampling is controlled by the permanently recorded wind velocity, wind direction and by condensation particle concentration. Contamination was indicated if one of the following criteria were given: Wind direction within a 330°-30° sector, wind velocity <2.2 m/s or >17.5 m/s, or condensation particle concentrations >2500/cm**3 during summer, >800/cm**3 during spring/autumn and >400/cm**3 during winter. If one or a definable combination of these criteria were given, high volume aerosol sampling and part of the trace gas sampling were interrupted. Starting at 1982 through 1991-01-14 surface ozone was measured with an electrochemical concentration cell (ECC). Surface ozone mixing ratio are given in ppbv = parts per 10**9 by volume. The averaging time corresponds to the given time intervals in the data sheet. The accuracy of the values are better than ±1 ppbv and the detection limit is around 1.0 ppbv. Aerosols were sampled on two Whatman 541 cellulose filters in series and analyzed by ion chromatography at the UHEI-IUP. Generally, the sampling period was seven days but could be up to two weeks on occasion. The air flow was around 100 m**3/h and typically 10000-20000 m**3 of ambient air was forced through the filters for one sample. Concentration values are given in nanogram (ng) per 1 m**3 air at standard pressure and temperature (1013 mbar, 273.16 K). Uncertainties of the values were approximately ±10% to ±15% for the main components MSA, chloride, nitrate, sulfate and sodium, and between ±20% and ±30% for the minor species bromide, ammonium, potassium, magnesium and calcium.

Tourism time series forecast

In this chapter four combinations of input features and the feedforward, cascade forward and recurrent architectures are compared for the task of forecast tourism time series. The input features of the ANNs consist in the combination of the previous 12 months, the index time modeled by two nodes used to the year and month and one input with the daily hours of sunshine (insolation duration). The index time features associated to the previous twelve values of the time series proved its relevance in this forecast task. The insolation variable can improved results with some architectures, namely the cascade forward architecture. Finally, the experimented ANN models/architectures produced a mean absolute percentage error between 4 and 6%, proving the ability of the ANN models based to forecast this time series. Besides, the feedforward architecture behaved better considering validation and test sets, with 4.2% percentage error in test set.

The Effect of Spatial Scale on Predicting Time Series: A Study on Epidemiological System Identification

A susceptible-infective-recovered (SIR) epidemiological model based on probabilistic cellular automaton (PCA) is employed for simulating the temporal evolution of the registered cases of chickenpox in Arizona, USA, between 1994 and 2004. At each time step, every individual is in one of the states S, I, or R. The parameters of this model are the probabilities of each individual (each cell forming the PCA lattice ) passing from a state to another state. Here, the values of these probabilities are identified by using a genetic algorithm. If nonrealistic values are allowed to the parameters, the predictions present better agreement with the historical series than if they are forced to present realistic values. A discussion about how the size of the PCA lattice affects the quality of the model predictions is presented. Copyright (C) 2009 L. H. A. Monteiro et al.