Estimating the turning point location in shifted exponential model of time series

We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we provide a formula for computing the distribution of the turning point location and consequently to estimate a confidence interval for the location. We test this formula in simulated data series having a trend with asymmetric minimum, investigating the coverage rate as a function of a bandwidth parameter. The method is applied to estimate the confidence interval of the minimum location of the time series of RT intervals extracted from the electrocardiogram recorded during the exercise test. We discuss the connection with stochastic ordering

Trend extraction in functional data of R and T waves amplitudes of exercise electrocardiogram

The R and T waves amplitudes of the electrocardiogram recorded during the exercise test undergo strong modifications in response to stress. We analyze the time series of these amplitudes in a group of normal subjects in the framework of functional data, performing reduction of dimensionality, smoothing and principal component analysis. These methods show that the R and T amplitudes have opposite responses to stress, consisting respectively in a bump and a dip at the early recovery stage. We test these features computing a confidence band for the trend of the population mean and analyzing the zero crossing of its derivative. Our findings support the existence of a relationship between R and T wave amplitudes and respectively diastolic and systolic ventricular volumes

The difference-sign runs length distribution in testing for serial independence

Abstract We investigate the sequence of difference-sign runs lengths of a time series in the context of non parametric tests for serial independence. This sequence is under suitable conditioning a stationary sequence and we prove that the normalized correlation of two consecutive runs lengths is small (≈ 0.0427). We use this result in a test based on the relative entropy of the empirical distribution of the runs lengths. We investigate the performance of the test in simulated series and test serial independence of cardiac data series in atrial fibrillation

Alcune applicazioni della Matematica all'analisi dell'elettrocardiogramma

Questo lavoro si propone di far conoscere due importanti applicazioni della Matematica all'analisi dell'elettrocardiogramma(ECG). La prima è quella del riconoscimento delle principali caratteristiche dell'ECG e in particolare del picco R, che corrisponde alla sistole. Si considerano due metodi: i filtri lineari e l'analisi multiscala basata sulle wavelet. La seconda riguarda l'analisi della serie temporale degli intervalli che separano due picchi R consecutivi dell'ECG (sequenza RR), che descrive l'andamento nel tempo della frequenza cardiaca. Qui i metodi considerati sono quelli dell'analisi spettrale e dell'analisi simbolica. Di quest'ultima si illustra un'applicazione all'analisi di sequenze RR di fibrillazione atriale

THE LARGE BLOCK SPIN INTERACTION

We consider the block spin variables for the two-dimensional Ising model out of the critical point. We prove that the block spin interaction tends in norm to a one-body quadratic potential if the side of the blocks tends to infinity. This result, that is a sharp form of the central limit theorem, is achieved by means of a renormalization of the diverging interaction between two adjacent blocks. © 1986 Società Italiana di Fisica

Positive and negative correlations for conditional Ising distributions

In the Ising model at zero external field with ferromagnetic first neighbors interaction the Gibbs measure is investigated using the group properties of the contours configurations. Correlation inequalities expressing positive dependence among groups and comparison among groups and cosets are used. An improved version of the Griffiths' inequalities is proved for the Gibbs measure conditioned to a subgroup. Examples of positive and negative correlations among the spin variables are proved under conditioning to a contour or to a separation line

The difference-sign runs length distribution in testing for serial independence

We investigate the sequence of difference-sign runs length of a time series in the context of non-parametric tests for serial independence. This sequence is, under suitable conditioning, a stationary sequence and we prove that the normalized correlation of two consecutive runs length is small (≈0.0427).We use this result in a test based on the relative entropy of the empirical distribution of the runs length. We investigate the performance of the test in simulated series and test serial independence of cardiac data series in atrial fibrillation. © 2011 Taylor & Francis

Decay of correlations for infinite range interactions in unbounded spin systems

In unbounded spin systems at high temperature with two-body potential we prove, using the associated polymer model, that the two-point truncated correlation function decays exponentially (respectively with a power law) if the potential decays exponentially (respectively with a power law). We also give a new proof of the convergence of the Mayer series for the general polymer model. © 1982 Springer-Verlag

Estimating the turning point location in shifted exponential model of time series

We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we provide a formula for computing the distribution of the turning point location and consequently to estimate a confidence interval for the location. We test this formula in simulated data series having a trend with asymmetric minimum, investigating the coverage rate as a function of a bandwidth parameter. The method is applied to estimate the confidence interval of the minimum location of two types of real-time series: the RT intervals extracted from the electrocardiogram recorded during the exercise test and an economic indicator, the current account balance. We discuss the connection with stochastic ordering