Imputation of Missing Observations for Heavy Tailed Cyclostationary Time Series

2015 ◽  
pp. 179-187 ◽  
Author(s):  
Christiana Drake ◽  
Jacek Leskow ◽  
Aldo M. Garay
Keyword(s):  
Time Series ◽  
Missing Observations ◽  
Heavy Tailed

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.

AN EVOLUTIONARY APPROACH FOR IMPUTING MISSING DATA IN TIME SERIES

2010 ◽  
Vol 19 (01) ◽  
pp. 107-121 ◽  
Author(s):  
JUAN CARLOS FIGUEROA GARCÍA ◽  
DUSKO KALENATIC ◽  
CESAR AMILCAR LÓPEZ BELLO
Keyword(s):  
Genetic Algorithm ◽  
Time Series ◽  
Missing Data ◽  
Genetic Structure ◽  
Evolutionary Algorithm ◽  
Fitness Function ◽  
Error Function ◽  
Missing Observations ◽  
Mean And Variance ◽  
Methodological Aspects

This paper presents a proposal based on an evolutionary algorithm for imputing missing observations in time series. A genetic algorithm based on the minimization of an error function derived from their autocorrelation function, mean, and variance is presented. All methodological aspects of the genetic structure are presented. An extended description of the design of the fitness function is provided. Four application examples are provided and solved by using the proposed method.

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.

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