Unevenly Spaced Time Series Research Articles

Hidden Markov Mixtures for Change Detection in Unevenly Spaced Time Series

This work tackles sequential data change-point detection, a research area with various applications in different fields. It focuses on analyzing sequential data such that the distance between locations of consecutive observations is not fixed. The models developed here for change detection extend a Hidden Markov Mixture approach originally designed to handle irregular spacing to improve the identification of atypical values. These models consider the probability of Markov dependence explained by the distance between locations. Bayesian inference is carried out via Gibbs Sampling. Informative priors for the dependency structure are crucial to identify clusters. The models adapt these priors to enable change identification in a general setting. Two mixture models are formulated: one for mean changes and another for mean or variance changes. Post-processing strategies are suggested to categorize observations among the components to facilitate change identification by the mixtures. These strategies are based on maximum posterior probability and consider the uncertainty associated with classifications. Models and clustering performances are evaluated in simulation studies including a Monte Carlo scheme. The analysis also explores three real illustrations. Finally, the proposed approaches are compared to existing clustering and change detection methods available in the literature.

Classifying unevenly spaced clinical time series data using forecast error approximation based bottom-up (FeAB) segmented time delay neural network

ABSTRACT Clinical time series data contain large set of time-stamped data points that describe the patient’s health. The observations of these data points are done at irregular intervals and hence knowledge mining turns challenging. To overcome this, there is a need to reduce the dimension (length) of time series data into smaller representations with minimal loss of information. The objective of this work is to present a forecast-error approximation-based bottom-up (FeAB) segmentation for segmenting and classifying clinical time series data using time delay neural network (TDNN). The proposed approach includes two functionalities namely temporal data summarisation and classification. In temporal data summarisation, clinical time-series data are divided into sequence of temporal interpreted segments using FeAB segmentation. FeAB adopts a double exponential smoothing technique to derive the growth rate, mean and forecast-error for each clinical observation. The obtained forecast-error is used to compute the merge-cost for FeAB segmentation. TDNN classifier builds classification model for the segmented time series. The classifier is trained using backpropagation with Levenberg-Marquardt algorithm. The time series dataset of hepatitis and thrombosis patients are used for experimentation. The results illustrate that the proposed framework has effectively handled the temporal data irregularities and has shown improvement in classification accuracy.

Price duration versus trading volume in high-frequency data for selected DAX companies

The main goal of this paper is to gain insights into the dependence structure between the duration and trading volume of selected stocks listed on the Frankfurt Stock Exchange. We demonstrate the usefulness of the copula function to describe the dependence of specific unevenly spaced time series. The properties of the time series of price durations and trading volumes under study are in line with common observations from other empirical studies. We observe clustering, overdispersion, and diurnality. For most of the stocks, the seminal model (linear parametrization with exponential or Weibull distribution) can be replaced by a logarithmic specification with more-flexible conditional distributions. The price duration and trading volume associated with this duration exhibit dependence in the tails of distribution. We may conclude that high cumulative trading volumes are associated with long duration. However, changes of price over short times are related to low cumulative volume.

Significance of periodogram peaks and a pulsation mode analysis of the Beta Cephei star V403 Car

We discuss some commonly used methods for determining the significance of peaks in the periodograms of time series. We review methods for constructing the classical significance tests, their corresponding false alarm probability functions and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We discuss the concepts of independent frequencies and oversampling in periodogram analysis. We then compare the results of new Monte Carlo simulations for evenly spaced time series with results obtained previously by other authors, and present the results of Monte Carlo simulations for a specific unevenly spaced time series obtained for V403 Car.

MTIE and TDEV Analysis of Unevenly Spaced Time Series Data

This work investigates how uneven data spacing affects the computations of MTIE (maximum time interval error) and TDEV (time deviation). MTIE and TDEV are evaluated with unevenly spaced data in five different power-law noise types.Each simulated data set has 3600 evenly spaced data points spaced one second apart.Dat a points are then removed from each file according to the parameter p. Each data point in a file is removed with probability p and retained with probability (1 – p). For the unevenly spaced data files, the average spacing is recomputed.Then MTIE and TDEV were calculated for data files with different p values.The simulated results show that the difference among the performance of various p values is not significant when the observation time exceeds 100 seconds. Additionally, the discrepancy between the computation results of evenly (p = 0) and slightly unevenly (0>p>0.1) spaced data files is often negligible.Therefore, the effect of slightly unevenly spaced data on computations of MTIE and TDEV can be ignored.Based on these results, the telecommunications synchronization measurement can be performed using a simple model, which does not require a clock recovery device to recover the timing signal from the data bits.Instead, the network data signal can be input directly to the time interval counter (TIC).The measured data are often unevenly spaced as the data bits of “1” and “0” are not distributed regularly. However, this novel measurement model can still be validated using previous results.

Quantifying the effects of temporal autocorrelation on climatological regression models using geostatistical techniques

When time-dependent data are used in regression models, temporal autocorrelation violates ordinary least squares assumptions and impedes their proper testing and interpretation. The problem of temporal autocorrelation is exacerbated by the uneven temporal spacing inherent in many data sets. Using simple linear regression models of stomatal conductance as examples, we compare the effectiveness of two methods for removing temporal autocorrelation from regression models (first-differencing and Cochrane–Orcutt) and we introduce the geostatistical technique of semivariograms as a method for quantifying temporal autocorrelation in uneven time series. The Cochrane–Orcutt method proved more effective than first-differencing at removing autocorrelation and produced regression models without changing the significance of the independent variables. Semivariograms were used to quantify the time dependence of the unevenly spaced stomatal conductance time series. This technique revealed the dominant autocorrelation at the minimum time lag (0.5 h) and the 24-h periodicity caused by the climatological variables used in the model. We conclude that geostatistical techniques provide a robust method for quantifying temporal structure and periodicity in unevenly spaced time series.