Analysis of temperature time-series: embedding dynamics into the MDS method

Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic and health aspects of the human life. Surface temperature time-series characterise Earth as a slow dynamics spatiotemporal system, evidencing long memory behaviour, typical of fractional order systems. Such phenomena are difficult to model and analyse, demanding for alternative approaches. This paper studies the complex correlations between global temperature time-series using the Multidimensional scaling (MDS) approach. MDS provides a graphical representation of the pattern of climatic similarities between regions around the globe. The similarities are quantified through two mathematical indices that correlate the monthly average temperatures observed in meteorological stations, over a given period of time. Furthermore, time dynamics is analysed by performing the MDS analysis over slices sampling the time series. MDS generates maps describing the stations’ locus in the perspective that, if they are perceived to be similar to each other, then they are placed on the map forming clusters. We show that MDS provides an intuitive and useful visual representation of the complex relationships that are present among temperature time-series, which are not perceived on traditional geographic maps. Moreover, MDS avoids sensitivity to the irregular distribution density of the meteorological stations.

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Time series morphological analysis applied to biomedical signals events detection

Dissertation submitted in the fufillment of the requirements for the Degree of Master in Biomedical Engineering

Chagas disease in the State of Pernambuco, Brazil: analysis of admissions and mortality time series

INTRODUCTION: A time series study of admissions, deaths and acute cases was conducted in order to evaluate the context of Chagas disease in Pernambuco. METHODS: Data reported to the Information Technology Department of the Brazilian National Health Service between 1980 and 2008 was collected for regions and Federal Units of Brazil; and microregions and municipalities of Pernambuco. Rates (per 100,000 inhabitants) of hospitalization, mortality and acute cases were calculated using a national hospital database (SIH), a national mortality database (SIM) and the national Information System for Notifiable Diseases (SINAN), respectively. RESULTS: The national average for Chagas disease admissions was 0.99 from 1995 to 2008. Pernambuco obtained a mean of 0.39 in the same period, with the highest rates being concentrated in the interior of the state. The state obtained a mean mortality rate of 1.56 between 1980 and 2007, which was lower than the national average (3.66). The mortality rate has tended to decline nationally, while it has remained relatively unchanged in Pernambuco. Interpolating national rates of admissions and deaths, mortality rates were higher than hospitalization rates between 1995 and 2007. The same occurred in Pernambuco, except for 2003. Between 2001 and 2006, rates for acute cases were 0.56 and 0.21 for Brazil and Pernambuco, respectively. CONCLUSIONS: Although a decrease in Chagas mortality has occurred in Brazil, the disease remains a serious public health problem, especially in the Northeast region. It is thus essential that medical care, prevention and control regarding Chagas disease be maintained and improved.

Analysis of patterns in mining time series using Qlucore

Raw measurement data does not always immediately convey useful information, but applying mathematical statistical analysis tools into measurement data can improve the situation. Data analysis can offer benefits like acquiring meaningful insight from the dataset, basing critical decisions on the findings, and ruling out human bias through proper statistical treatment. In this thesis we analyze data from an industrial mineral processing plant with the aim of studying the possibility of forecasting the quality of the final product, given by one variable, with a model based on the other variables. For the study mathematical tools like Qlucore Omics Explorer (QOE) and Sparse Bayesian regression (SB) are used. Later on, linear regression is used to build a model based on a subset of variables that seem to have most significant weights in the SB model. The results obtained from QOE show that the variable representing the desired final product does not correlate with other variables. For SB and linear regression, the results show that both SB and linear regression models built on 1-day averaged data seriously underestimate the variance of true data, whereas the two models built on 1-month averaged data are reliable and able to explain a larger proportion of variability in the available data, making them suitable for prediction purposes. However, it is concluded that no single model can fit well the whole available dataset and therefore, it is proposed for future work to make piecewise non linear regression models if the same available dataset is used, or the plant to provide another dataset that should be collected in a more systematic fashion than the present data for further analysis.

MCMC Analysis Of Classical Time Series Algorithms

Identification of order of an Autoregressive Moving Average Model (ARMA) by the usual graphical method is subjective. Hence, there is a need of developing a technique to identify the order without employing the graphical investigation of series autocorrelations. To avoid subjectivity, this thesis focuses on determining the order of the Autoregressive Moving Average Model using Reversible Jump Markov Chain Monte Carlo (RJMCMC). The RJMCMC selects the model from a set of the models suggested by better fitting, standard deviation errors and the frequency of accepted data. Together with deep analysis of the classical Box-Jenkins modeling methodology the integration with MCMC algorithms has been focused through parameter estimation and model fitting of ARMA models. This helps to verify how well the MCMC algorithms can treat the ARMA models, by comparing the results with graphical method. It has been seen that the MCMC produced better results than the classical time series approach.

Analysis of Patterns in Electricity Spot Market Time Series

Due to its non-storability, electricity must be produced at the same time that it is consumed, as a result prices are determined on an hourly basis and thus analysis becomes more challenging. Moreover, the seasonal fluctuations in demand and supply lead to a seasonal behavior of electricity spot prices. The purpose of this thesis is to seek and remove all causal effects from electricity spot prices and remain with pure prices for modeling purposes. To achieve this we use Qlucore Omics Explorer (QOE) for the visualization and the exploration of the data set and Time Series Decomposition method to estimate and extract the deterministic components from the series. To obtain the target series we use regression based on the background variables (water reservoir and temperature). The result obtained is three price series (for Sweden, Norway and System prices) with no apparent pattern.

Early detection of metabolic and energy disorders by thermal time series stochastic complexity analysis

Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile.

Modelling and Analysis of Some Time Series

The thesis deals with some of the non-linear Gaussian and non-Gaussian time models and mainly concentrated in studying the properties and application of a first order autoregressive process with Cauchy marginal distribution. In this thesis some of the non-linear Gaussian and non-Gaussian time series models and mainly concentrated in studying the properties and application of a order autoregressive process with Cauchy marginal distribution. Time series relating to prices, consumptions, money in circulation, bank deposits and bank clearing, sales and profit in a departmental store, national income and foreign exchange reserves, prices and dividend of shares in a stock exchange etc. are examples of economic and business time series. The thesis discuses the application of a threshold autoregressive(TAR) model, try to fit this model to a time series data. Another important non-linear model is the ARCH model, and the third model is the TARCH model. The main objective here is to identify an appropriate model to a given set of data. The data considered are the daily coconut oil prices for a period of three years. Since it is a price data the consecutive prices may not be independent and hence a time series based model is more appropriate. In this study the properties like ergodicity, mixing property and time reversibility and also various estimation procedures used to estimate the unknown parameters of the process.

Comparing meta-analysis and ecological-longitudinal analysis in time-series studies: a case study of the effects of air pollution on mortality in three Spanish cities

The objective of this paper is to introduce a diVerent approach, called the ecological-longitudinal, to carrying out pooled analysis in time series ecological studies. Because it gives a larger number of data points and, hence, increases the statistical power of the analysis, this approach, unlike conventional ones, allows the complementation of aspects such as accommodation of random effect models, of lags, of interaction between pollutants and between pollutants and meteorological variables, that are hardly implemented in conventional approaches. Design—The approach is illustrated by providing quantitative estimates of the short-termeVects of air pollution on mortality in three Spanish cities, Barcelona,Valencia and Vigo, for the period 1992–1994. Because the dependent variable was a count, a Poisson generalised linear model was first specified. Several modelling issues are worth mentioning. Firstly, because the relations between mortality and explanatory variables were nonlinear, cubic splines were used for covariate control, leading to a generalised additive model, GAM. Secondly, the effects of the predictors on the response were allowed to occur with some lag. Thirdly, the residual autocorrelation, because of imperfect control, was controlled for by means of an autoregressive Poisson GAM. Finally, the longitudinal design demanded the consideration of the existence of individual heterogeneity, requiring the consideration of mixed models. Main results—The estimates of the relative risks obtained from the individual analyses varied across cities, particularly those associated with sulphur dioxide. The highest relative risks corresponded to black smoke in Valencia. These estimates were higher than those obtained from the ecological-longitudinal analysis. Relative risks estimated from this latter analysis were practically identical across cities, 1.00638 (95% confidence intervals 1.0002, 1.0011) for a black smoke increase of 10 μg/m3 and 1.00415 (95% CI 1.0001, 1.0007) for a increase of 10 μg/m3 of sulphur dioxide. Because the statistical power is higher than in the individual analysis more interactions were statistically significant,especially those among air pollutants and meteorological variables. Conclusions—Air pollutant levels were related to mortality in the three cities of the study, Barcelona, Valencia and Vigo. These results were consistent with similar studies in other cities, with other multicentric studies and coherent with both, previous individual, for each city, and multicentric studies for all three cities