Subsampling for Heavy Tailed, Nonstationary and Weakly Dependent Time Series

2019 ◽  
pp. 19-40
Author(s):  
Elżbieta Gajecka-Mirek ◽  
Jacek Leśkow
Keyword(s):  
Time Series ◽  
Heavy Tailed ◽  
Weakly Dependent

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

scholarly journals A robust method for shift detection in time series

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 647-660
Author(s):  
H Dehling ◽  
R Fried ◽  
M Wendler
Keyword(s):  
Time Series ◽  
Nonparametric Test ◽  
Test Statistic ◽  
Moment Conditions ◽  
Limit Theory ◽  
Dependent Observations ◽  
U Statistics ◽  
Shift Detection ◽  
Heavy Tailed ◽  
The Stability

Summary We present a robust and nonparametric test for the presence of a changepoint in a time series, based on the two-sample Hodges–Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes in the case of short-range dependent observations. Using this theory, we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on U-statistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so any transform of the observed process can be used to test the stability of higher-order characteristics such as variability, skewness and kurtosis.

scholarly journals Sample correlations of infinite variance time series models: an empirical and theoretical study

1998 ◽  
Vol 11 (3) ◽  
pp. 255-282 ◽  
Author(s):  
Jason Cohen ◽  
Sidney Resnick ◽  
Gennady Samorodnitsky
Keyword(s):  
Time Series ◽  
Correlation Function ◽  
Random Permutation ◽  
Infinite Variance ◽  
Finite Variance ◽  
More Care ◽  
Sample Correlation ◽  
Heavy Tailed ◽  
Random Limit ◽  
Permutation Scheme

When the elements of a stationary ergodic time series have finite variance the sample correlation function converges (with probability 1) to the theoretical correlation function. What happens in the case where the variance is infinite? In certain cases, the sample correlation function converges in probability to a constant, but not always. If within a class of heavy tailed time series the sample correlation functions do not converge to a constant, then more care must be taken in making inferences and in model selection on the basis of sample autocorrelations. We experimented with simulating various heavy tailed stationary sequences in an attempt to understand what causes the sample correlation function to converge or not to converge to a constant. In two new cases, namely the sum of two independent moving averages and a random permutation scheme, we are able to provide theoretical explanations for a random limit of the sample autocorrelation function as the sample grows.

scholarly journals Extreme value analysis for the sample autocovariance matrices of heavy-tailed multivariate time series

Extremes ◽  
2016 ◽  
Vol 19 (3) ◽  
pp. 517-547 ◽  
Author(s):  
Richard A. Davis ◽  
Johannes Heiny ◽  
Thomas Mikosch ◽  
Xiaolei Xie
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Heavy Tailed ◽  
Autocovariance Matrices ◽  
Sample Autocovariance

Comments on: Subsampling weakly dependent time series and application to extremes

Test ◽  
2011 ◽  
Vol 20 (3) ◽  
pp. 480-482
Author(s):  
Carlos Velasco
Keyword(s):  
Time Series ◽  
Weakly Dependent

scholarly journals Polymodeling of time series structures, neighborhood of residuals distribution, wavelet transformation for meso-dynamics assessment

2021 ◽  
Vol 20 (10) ◽  
pp. 1951-1972
Author(s):  
Valerii K. SEMENYCHEV ◽  
Galina A. KHMELEVA ◽  
Anastasiya A. KOROBETSKAYA
Keyword(s):  
Time Series ◽  
Structural Changes ◽  
Middle Term ◽  
Monthly Data ◽  
Russian Economy ◽  
Regular Time ◽  
Modeling And Forecasting ◽  
Heavy Tailed ◽  
Auto Regression ◽  
Adequate Analysis

Subject. The article provides the results of meso-dynamics analysis of main twelve industries, based on monthly data for 82 Russian regions, from January 2005 till December 2020. Objectives. The purpose of the study is to address the problem of balanced and stable spatial development of Russia’s regions and Russia, which requires modeling of adequate tools and forecasting nonlinear mesodynamics. Methods. The study follows the econophysics methodology. Results. We consider additive and multiplicative interactions of regular time series components between each other and the residuals, thus expanding the scope of tools application for the variety of considered industries and their models. Using the common and new trend models, we analyze structural changes, introduce the topological measure of proximity to the neighborhood of residuals with heavy-tailed distribution, which is estimated by median values of trends and cycles for regular components. The traditional time series decomposition (by trend, cycle, seasonality, and residual) is supplemented by our unique complex of wavelet transformations, which forms the models of cycles, using auto regression. We obtained representative and time-synchronized analytical estimates of regular components of industries’ dynamics for meso- and macro-indicators of the Russian economy that have higher accuracy than the known results for the accuracy of modeling and forecasting. Conclusions. The offered methodology and tools enable a more adequate analysis of non-linear dynamics of regions’ middle-term development. They help shift to growth point identification, create the atlas of economic industrial cycles, analyze stages of bifurcations and scenario predictive planning.

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