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 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 large deviations approach to limit theory for heavy-tailed time series

2015 ◽  
Vol 166 (1-2) ◽  
pp. 233-269 ◽  
Author(s):  
Thomas Mikosch ◽  
Olivier Wintenberger
Keyword(s):  
Time Series ◽  
Large Deviations ◽  
Limit Theory ◽  
Heavy Tailed

A CONSISTENT NONPARAMETRIC TEST ON SEMIPARAMETRIC SMOOTH COEFFICIENT MODELS WITH INTEGRATED TIME SERIES

2015 ◽  
Vol 32 (4) ◽  
pp. 988-1022 ◽  
Author(s):  
Yiguo Sun ◽  
Zongwu Cai ◽  
Qi Li
Keyword(s):  
Time Series ◽  
Nonparametric Test ◽  
Asymptotic Distributions ◽  
Varying Coefficient Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Smooth Coefficients ◽  
Alternative Hypotheses ◽  
Constant Coefficients ◽  
Integrated Time Series

In this paper, we propose a simple nonparametric test for testing the null hypothesis of constant coefficients against nonparametric smooth coefficients in a semiparametric varying coefficient model with integrated time series. We establish the asymptotic distributions of the proposed test statistic under both null and alternative hypotheses. Moreover, we derive a central limit theorem for a degenerate second order U-statistic, which contains a mixture of stationary and nonstationary variables and is weighted locally on a stationary variable. This result is of independent interest and useful in other applications. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed test.

scholarly journals NONPARAMETRIC SPECIFICATION TESTING FOR NONLINEAR TIME SERIES WITH NONSTATIONARITY

2009 ◽  
Vol 25 (6) ◽  
pp. 1869-1892 ◽  
Author(s):  
Jiti Gao ◽  
Maxwell King ◽  
Zudi Lu ◽  
Dag Tjøstheim
Keyword(s):  
Time Series ◽  
Nonparametric Test ◽  
Parametric Form ◽  
Test Statistic ◽  
Specification Testing ◽  
Unknown Parameters ◽  
Time Series Regression ◽  
Bootstrap Simulation ◽  
Simulation Scheme ◽  
Selection Of

This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test statistic. Both the setting and the results differ from earlier work on nonparametric time series regression with stationarity. In addition, we develop a bootstrap simulation scheme for the selection of suitable bandwidth parameters involved in the kernel test as well as the choice of simulated critical values. An example of implementation is given to show that the proposed test works in practice.

scholarly journals NONPARAMETRIC TESTS OF MOMENT CONDITION STABILITY

2012 ◽  
Vol 29 (1) ◽  
pp. 90-114 ◽  
Author(s):  
Ted Juhl ◽  
Zhijie Xiao
Keyword(s):  
Monte Carlo ◽  
Nonparametric Test ◽  
Nonparametric Tests ◽  
Moment Condition ◽  
Monte Carlo Experiment ◽  
Regularity Conditions ◽  
Test Statistic ◽  
Moment Conditions ◽  
The Moment ◽  
Over Time

This paper considers testing for moment condition instability for a wide variety of models that arise in econometric applications. We propose a nonparametric test based on smoothing the moment conditions over time. The resulting test takes the form of a U-statistic and has a limiting normal distribution. The proposed test statistic is not affected by changes in the distribution of the data, so long as certain simple regularity conditions hold. We examine the performance of the test through a small Monte Carlo experiment.

DEVELOPMENT OF STREAMFLOW DROUGHT INDICES IN THE MORAVA RIVER BASIN

2020 ◽  
Author(s):  
Ondrej Ledvinka ◽  
◽  
Pavel Coufal ◽  
Keyword(s):  
Time Series ◽  
Kendall Test ◽  
Drought Indices ◽  
Drought Period ◽  
Left Hand ◽  
Low Flows ◽  
Current Period ◽  
Catchment Size ◽  
Morava River ◽  
The Stability

The territory of Czechia currently suffers from a long-lasting drought period which has been a subject of many studies, including the hydrological ones. Previous works indicated that the basin of the Morava River, a left-hand tributary of the Danube, is very prone to the occurrence of dry spells. It also applies to the development of various hydrological time series that often show decreases in the amount of available water. The purpose of this contribution is to extend the results of studies performed earlier and, using the most updated daily time series of discharge, to look at the situation of the so-called streamflow drought within the basin. 46 water-gauging stations representing the rivers of diverse catchment size were selected where no or a very weak anthropogenic influences are expected and the stability and sensitivity of profiles allow for the proper measurement of low flows. The selected series had to cover the most current period 1981-2018 but they could be much longer, which was considered beneficial for the next determination of the development direction. Various series of drought indices were derived from the original discharge series. Specifically, 7-, 15- and 30-day low flows together with deficit volumes and their durations were tested for trends using the modifications of the Mann– Kendall test that account for short-term and long-term persistence. In order to better reflect the drivers of streamflow drought, the indices were considered for summer and winter seasons separately as well. The places with the situation critical to the future water resources management were highlighted where substantial changes in river regime occur probably due to climate factors. Finally, the current drought episode that started in 2014 was put into a wider context, making use of the information obtained by the analyses.

A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

2020 ◽  
pp. 1-45
Author(s):  
Feng Yao ◽  
Taining Wang
Keyword(s):  
Null Distribution ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Hedonic Price ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Test ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

scholarly journals Subsampling the mean of heavy-tailed dependent observations

2004 ◽  
Vol 25 (2) ◽  
pp. 217-234 ◽  
Author(s):  
Piotr Kokoszka ◽  
Michael Wolf
Keyword(s):  
Dependent Observations ◽  
The Mean ◽  
Heavy Tailed

scholarly journals LIMIT THEORY FOR COINTEGRATED SYSTEMS WITH MODERATELY INTEGRATED AND MODERATELY EXPLOSIVE REGRESSORS

2009 ◽  
Vol 25 (2) ◽  
pp. 482-526 ◽  
Author(s):  
Tassos Magdalinos ◽  
Peter C.B. Phillips
Keyword(s):  
Multivariate Regression ◽  
Cauchy Type ◽  
Tail Behavior ◽  
Least Squares Regression ◽  
Moment Conditions ◽  
Limit Theory ◽  
Asymptotically Normal ◽  
Significant Bias ◽  
Integrated Or ◽  
Special Case

An asymptotic theory is developed for multivariate regression in cointegrated systems whose variables are moderately integrated or moderately explosive in the sense that they have autoregressive roots of the form ρni = 1 + ci/nα, involving moderate deviations from unity when α ∈ (0, 1) and ci ∈ ℝ are constant parameters. When the data are moderately integrated in the stationary direction (with ci < 0), it is shown that least squares regression is consistent and asymptotically normal but suffers from significant bias, related to simultaneous equations bias. In the moderately explosive case (where ci > 0) the limit theory is mixed normal with Cauchy-type tail behavior, and the rate of convergence is explosive, as in the case of a moderately explosive scalar autoregression (Phillips and Magdalinos, 2007, Journal of Econometrics 136, 115–130). Moreover, the limit theory applies without any distributional assumptions and for weakly dependent errors under conventional moment conditions, so an invariance principle holds, unlike the well-known case of an explosive autoregression. This theory validates inference in cointegrating regression with mildly explosive regressors. The special case in which the regressors themselves have a common explosive component is also considered.

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