On Smooth Transition Interval Autoregressive Models

Forecasting interval time series using a fully complex-valued RBF neural network with DPSO and PSO algorithms

This article reports nonlinear analysis of ECG R-R interval time-series obtained from healthy individuals and some cardiac patients. The R-R interval time-series data from 6 healthy individuals and 3 cardiac patients were transformed into multidimensional phase-space vectors by time-delay embedding. The largest Lyapunov exponent and correlation dimension (CD) were calculated. Nonlinearity was tested by comparing the CDs obtained from the original data with those obtained from surrogate data sets. Results are discussed with reference to results obtained in previous studies.

As a paradigm of data processing, granular computation concerns processing complex data entities called granules, which arise from data abstraction and derivation of knowledge from data. This paper addresses granular computation within the framework of interval time series forecasting and evolving intelligent systems. It develops a generalized interval evolving possibilistic fuzzy modeling algorithm as an analytics tool capable to process interval data stream and to produce interval forecasts. The algorithm uses interval arithmetic in its processing steps, employs the notion of data density to adapt the current forecasting model as data are input, and computes (dis)similarity between interval data using the Hausdorff distance. Computational experiments include forecasting of an interval time series data produced by a synthetic time-varying model with parameter drift, and forecasting of financial interval time series using actual daily minimum and maximum values of the US and Brazilian main equity indexes, S&P 500 and IBOVESPA, respectively. The results suggest that the generalized interval evolving possibilistic fuzzy algorithm is highly effective to model and forecast interval time series. It has comparable or better performance than alternative evolving fuzzy and benchmark interval-based approaches.

Financial interval time series (ITS) describe the evolution of the high and low prices of an asset throughout time. Their accurate forecasts play a key role in risk management, derivatives pricing and asset allocation, demanding the development of models able to properly predict these prices. This paper evaluates threshold autoregressive models for financial ITS forecasting as a nonlinear approach for ITS considering as empirical application the main index of the Brazilian stock market, the IBOVESPA. One step ahead interval forecasts are compared against linear and nonlinear time series benchmark methods in terms of traditional accuracy metrics and quality measures designed for ITS. The results indicated the predictability of IBOVESPA ITS and that significant forecast contribution are achieved when nonlinear approaches are considered. Further, nonlinear models do provide higher accuracy when forecasting Brazilian financial ITS.

Financial interval time series (ITS) describe the evolution of the high and low prices of an asset throughout time. Their accurate forecasts play a key role in risk management, derivatives pricing and asset allocation, demanding the development of models able to properly predict these prices. This paper evaluates threshold autoregressive models for financial ITS forecasting as a nonlinear approach for ITS considering as empirical application the main index of the Brazilian stock market, the IBOVESPA. One step ahead interval forecasts are compared against linear and nonlinear time series benchmark methods in terms of traditional accuracy metrics and quality measures designed for ITS. The results indicated the predictability of IBOVESPA ITS and that significant forecast contribution are achieved when nonlinear approaches are considered. Further, nonlinear models do provide higher accuracy when forecasting Brazilian financial ITS.

Wavelet-based fuzzy clustering of interval time series

Analysis of mental workload during the work with computers using R-R intervals time series

In this paper, we investigate similarities of suicide rates in Europe, which are available as interval time series. For this aim, a novel spatio-temporal hierarchical clustering algorithm for interval time-series data is proposed. The spatial dimension is included in the clustering process to account for possible relevant information such as weather conditions, sunlight hours and socio-cultural factors. Our results indicate the presence of six main clusters in Europe, which almost overlap with the sunlight hours distribution. Differences between male and female suicide rates are also investigated.

The application of data classifications in time series analysis and forecasting is rather important. The fuzzy data classification has received much attention recently. It can be applied on various fields such as finance, sociology, biomedicine, electrical engineering and so on. This study is to use the fuzzy data classification to perform an intensive research on the change periods detection and model construction of the interval time series. We use average of the sum of fuzzy entropies to find out interval of the structural changes. Focusing on the time series of intervals, we build a model and make prediction about it. At the end, based on the case study on the population of singles versus, we thoroughly discuss this topic. The result shows that the unemployment rate does significantly correlate with the population of singles, but the ”widow's year” does not.

In this paper we propose a procedure that uses a single-index model to construct interpolation intervals for a general class of linear processes. We present an extensive Monte Carlo experiment which studies the finite sample properties of this procedure. Finally, we illustrate the performance of the proposed method with a real data example.

This paper mainly suggests a new type of interval time series: interval autoregressive (IAR) model. Firstly we state why we should introduce the interval time series models. Then we give necessary definitions about random intervals and interval time series. Thirdly, we introduce some methods of efficiency evaluation for forecasting of interval time series. And then we discuss parameter estimation and forecasting in IAR model, in which the methods of parameter estimation are based on the evaluation forecasting for interval data. Furthermore, we give the simulation results and apply it to real data from Shanghai Stock Index, which is to illustrate our modeling methodology. This model makes it possible for decision makers to forecast the best and worst possible situations based on interval-valued observations.

Time series modeling of histogram-valued data: The daily histogram time series of S&P500 intradaily returns

Autoregressive modeling and power spectral estimate of R-R interval time series in arrhythmic patients

Parametric estimation of sample entropy in heart rate variability analysis

Fractal dimension analysis of the muscle sympathetic nerve activity