A Kolmogorov-Smirnov Type Statistic with Application to Test for Nonlinearity in Time Series

1991 ◽  
Vol 59 (3) ◽  
pp. 287 ◽  
Author(s):  
Cheng Bing
Keyword(s):  
Time Series ◽  
Type Statistic ◽  
Kolmogorov Smirnov

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 TISSBERT: A benchmark for the validation and comparison of NDVI time series reconstruction methods

2018 ◽  
pp. 19 ◽  
Author(s):  
Y. Julien ◽  
J. A. Sobrino
Keyword(s):  
Time Series ◽  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Global Scale ◽  
Remotely Sensed Data ◽  
Reconstruction Methods ◽  
Ndvi Time Series ◽  
Kolmogorov Smirnov ◽  
Time Series Simulation

<p>This paper introduces the Time Series Simulation for Benchmarking of Reconstruction Techniques (TISSBERT) dataset, intended to provide a benchmark for the validation and comparison of time series reconstruction methods. Such methods are routinely used to estimate vegetation characteristics from optical remotely sensed data, where the presence of clouds decreases the usefulness of the data. As for their validation, these methods have been compared with previously published ones, although with different approaches, which sometimes lead to contradictory results. We designed the TISSBERT dataset to be generic so that it could simulate realistic reference and cloud-contaminated time series at global scale. To that end, we estimated both cloud-free and cloud-contaminated Normalized Difference Vegetation Index (NDVI) statistics for randomly selected control points and each day of the year from the Long Term Data Record Version 4 (LTDR-V4) dataset by assuming different statistical distributions. The best approach was then applied to the whole dataset, and validity of the results were estimated through the Kolmogorov-Smirnov statistic. The dataset elaboration is described thoroughly along with how to use it. The advantages and drawbacks of this dataset are then discussed, which emphasize the realistic simulation of the cloud-contaminated and reference time series. This dataset can be obtained from the authors upon demand. It will be used in a next paper to compare widely used NDVI time series reconstruction methods.</p>

scholarly journals Evaluation gridded precipitation datasets in Indonesia

2021 ◽  
Vol 893 (1) ◽  
pp. 012056
Author(s):  
T Wati ◽  
T W Hadi ◽  
A Sopaheluwakan ◽  
L M Hutasoit
Keyword(s):  
Time Series ◽  
Data Use ◽  
Rain Gauge ◽  
Annual Time Scale ◽  
Error Coefficient ◽  
Kolmogorov Smirnov ◽  
Preliminary Study ◽  
Relative Change ◽  
Annual Time ◽  
Smirnov Test

Abstract This preliminary study evaluates ten gridded precipitation datasets in Indonesia, namely APHRODITE, CMORPH, CHIRPS, GFD, SA-OBS, TMPA 3B42 v7, PERSIAN-CDR at 0.25°, moreover GSMaP_NRT V06, GPM-IMERG (Early-Run) V06, and MSWEP V2 at 0.1» in the period of 2003 to 2015. The evaluation focuses on time series bias using metrics such as Mean Error, Coefficient of Variation, Relative Change (Variability), and Kolmogorov-Smirnov test (KS-test) at daily, monthly, seasonal, and annual time scales. The statistical relationship between the precipitation datasets with reference observational data use Taylor diagrams for evaluating the relative skill of the precipitation dataset. The study aims to evaluate the uncertainty of the precipitation datasets compared to rain gauge datasets. Time series bias of SA-OBS and MSWEP have the nearest value to zero as the best score. The relative skill of monthly rainfall based on rainfall typical shows that MSWEP outperformed in regions A and B, GPM-IMERG in C region. GPM-IMERG's relative skill is outperformed than other datasets at annual time scale in Region A and B, while TMPA 3B42 in Region C. The application of existing precipitation datasets is essential to cope with the limitation of rain gauge observations. This study implicates the development of precipitation products in the Indonesia region.

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