scholarly journals Distribution-Based Entropy Weighting Clustering of Skewed and Heavy Tailed Time Series

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 959
Author(s):  
Raffaele Mattera ◽  
Massimiliano Giacalone ◽  
Karina Gibert
Keyword(s):  
Time Series ◽  
Power Distribution ◽  
Heavy Tails ◽  
Financial Time Series ◽  
Economic Time Series ◽  
Data Set ◽  
Exponential Power Distribution ◽  
Economic Time ◽  
Heavy Tailed ◽  
Exponential Power

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series motivated the development of classes of distributions that can accommodate properties, such as heavy tails and skewness. Thanks to its flexibility, the skewed exponential power distribution (also called skewed generalized error distribution) ensures a unified and general framework for clustering possibly skewed and heavy tailed time series. This paper develops a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine the estimated parameters to form the clusters with an entropy weighing k-means approach. The usefulness of the proposal is shown by means of application to financial time series, demonstrating also how the obtained clusters can be used to form portfolio of stocks.

scholarly journals Distribution-Based Entropy Weighting Clustering of Skewed Time Series

2021 ◽  
Author(s):  
Raffaele Mattera ◽  
MassimilIano Giacalone ◽  
Karina Gibert Oliveiras
Keyword(s):  
Time Series ◽  
Power Distribution ◽  
Heavy Tails ◽  
Financial Time Series ◽  
Parameter Estimates ◽  
Economic Time Series ◽  
Data Set ◽  
Exponential Power Distribution ◽  
Economic Time ◽  
Exponential Power

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series have motivated the development of classes of distributions that can accommodate properties such as heavy tails and skewness. Thanks to its flexibility, the Skew Exponential Power Distribution (also called Skew Generalized Error Distribution) ensures a unified and general framework for clustering possibly skewed time series. This paper develop a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine all the parameter estimates to form the clusters with an entropy weighing k-means approach. The usefulness of the proposal is showed by means of an application to financial time series, showing also how the obtained clusters can be used to form portfolio of stocks.

Mathematical and Quantitative Methods: Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series

2013 ◽  
Vol 51 (4) ◽  
pp. 1190-1192
Author(s):  
Timo Teräsvirta
Keyword(s):  
Time Series ◽  
Quantitative Methods ◽  
Heavy Tails ◽  
Dynamic Models ◽  
Economic Time Series ◽  
Corpus Christi ◽  
Economic Time ◽  
Heavy Tailed ◽  
The University ◽  
Changes Over Time

Timo Terasvirta of Aarhus University reviews, “Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series” by Andrew C. Harvey. The Econlit abstract of this book begins: “Presents a theory for a class of nonlinear time series models that can deal with dynamic distributions, with an emphasis on models in which the conditional distribution of an observation may be heavy-tailed and the location and/or scale changes over time. Discusses statistical distributions and asymptotic theory; location; scale; location/scale models for nonnegative variables; dynamic kernel density estimation and time-varying quantiles; multivariate models, correlation, and association; and further directions in dynamic models. Harvey is Professor of Econometrics at the University of Cambridge and Fellow of Corpus Christi College, the Econometric Society, and the British Academy.”

scholarly journals The Application of Random Noise Reduction By Nearest Neighbor Method To Forecasting of Economic Time Series

2014 ◽  
Vol 13 (2) ◽  
pp. 96-108
Author(s):  
Monika Miśkiewicz-Nawrocka
Keyword(s):  
Time Series ◽  
Nearest Neighbor ◽  
Financial Time Series ◽  
Random Noise ◽  
Time Series Prediction ◽  
Deterministic Chaos ◽  
Largest Lyapunov Exponent ◽  
Economic Time Series ◽  
Economic Time

Abstract Since the deterministic chaos appeared in the literature, we have observed a huge increase in interest in nonlinear dynamic systems theory among researchers, which has led to the creation of new methods of time series prediction, e.g. the largest Lyapunov exponent method and the nearest neighbor method. Real time series are usually disturbed by random noise, which can complicate the problem of forecasting of time series. Since the presence of noise in the data can significantly affect the quality of forecasts, the aim of the paper will be to evaluate the accuracy of predicting the time series filtered using the nearest neighbor method. The test will be conducted on the basis of selected financial time series.

scholarly journals Bayesian Estimation and Prediction of Three-Parameter Complementary Exponential Power Distribution using MCMC Technique

2020 ◽  
Vol 10 (2) ◽  
pp. 164-174
Keyword(s):  
Power Distribution ◽  
Real Data ◽  
Credible Interval ◽  
Simulation Method ◽  
Complete Sample ◽  
Unknown Parameters ◽  
Data Set ◽  
Exponential Power Distribution ◽  
Exponential Power ◽  
Bayesian Estimators

The Markov chain Monte Carlo (MCMC) technique is applied for estimating the Complementary Exponential Power (CEP) distribution's parameters through the analysis of complete sample in this article. With the help of the Bayesian and the Maximum Likelihood techniques, the unknown parameters of the model are estimated. To find Complementary Exponential Power distribution's parameters' Bayesian estimates, a new methodology is developed, via simulation method of MCMC through the application of OpenBUGS platform. To demonstrate under the gamma and uniform sets of priors, a real data set is taken. The generations of posterior MCMC samples is conducted with OpenBUGS software. For analyzing the output of so generated MCMC samples, and studying the statistical properties, distribution's comparison tools and model validation the functions of R have been used. The credible interval and predicted of the reliability, hazard and modal parameters' values are also estimated. We have shown that Bayesian estimators are more efficient than classical estimators for any real data set.

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