NONPARAMETRIC SPECIFICATION TESTING FOR NONLINEAR TIME SERIES WITH NONSTATIONARITY

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.

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A robust method for shift detection in time series

Biometrika ◽

10.1093/biomet/asaa004 ◽

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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A CONSISTENT TEST FOR CONDITIONAL HETEROSKEDASTICITY IN TIME-SERIES REGRESSION MODELS

Econometric Theory ◽

10.1017/s0266466601171069 ◽

2001 ◽

Vol 17 (1) ◽

pp. 188-221 ◽

Cited By ~ 17

Author(s):

Cheng Hsiao ◽

Qi Li

Keyword(s):

Time Series ◽

Bootstrap Method ◽

Conditional Heteroskedasticity ◽

Test Statistic ◽

Time Series Regression ◽

Consistent Test ◽

Asymptotic Normal Distribution ◽

Asymptotic Normal ◽

Weakly Dependent Data ◽

Generated Regressors

We show that the standard consistent test for testing the null of conditional homoskedasticity (against conditional heteroskedasticity) can be generalized to a time-series regression model with weakly dependent data and with generated regressors. The test statistic is shown to have an asymptotic normal distribution under the null hypothesis of conditional homoskedastic error. We also discuss extension of our test to the case of testing the null of a parametrically specified conditional variance. We advocate using a bootstrap method to overcome the issue of slow convergence of this test statistic to its limiting distribution.

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A consistent nonparametric test for nonlinear causality—Specification in time series regression

Journal of Econometrics ◽

10.1016/j.jeconom.2011.05.010 ◽

2011 ◽

Vol 165 (1) ◽

pp. 112-127 ◽

Cited By ~ 89

Author(s):

Yoshihiko Nishiyama ◽

Kohtaro Hitomi ◽

Yoshinori Kawasaki ◽

Kiho Jeong

Keyword(s):

Time Series ◽

Nonparametric Test ◽

Time Series Regression

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SIMULTANEOUS SPECIFICATION TESTING OF MEAN AND VARIANCE STRUCTURES IN NONLINEAR TIME SERIES REGRESSION

Econometric Theory ◽

10.1017/s0266466610000502 ◽

2011 ◽

Vol 27 (4) ◽

pp. 792-843 ◽

Cited By ~ 5

Author(s):

Song Xi Chen ◽

Jiti Gao

Keyword(s):

Time Series ◽

Empirical Likelihood ◽

Goodness Of Fit ◽

Test Procedure ◽

Single Pair ◽

Test Statistic ◽

Time Series Regression ◽

Variance Functions ◽

Mean And Variance ◽

The Mean

This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the variance components of the goodness-of-fit measure. To reduce the dependence of the test on a single pair of smoothing bandwidths, we construct an adaptive test by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. The test procedure is based on a bootstrap calibration to the distribution of the empirical likelihood test statistic. We demonstrate that the empirical likelihood test is able to distinguish local alternatives that are different from the null hypothesis at an optimal rate.

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

Econometric Theory ◽

10.1017/s0266466615000018 ◽

2015 ◽

Vol 32 (4) ◽

pp. 988-1022 ◽

Cited By ~ 7

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.

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Model and Variable Selection Procedures for Semiparametric Time Series Regression

Journal of Probability and Statistics ◽

10.1155/2009/487194 ◽

2009 ◽

Vol 2009 ◽

pp. 1-37 ◽

Cited By ~ 2

Author(s):

Risa Kato ◽

Takayuki Shiohama

Keyword(s):

Time Series ◽

Model Selection ◽

Variable Selection ◽

Time Series Data ◽

Selection Procedure ◽

Semiparametric Regression ◽

Information Criteria ◽

Series Data ◽

Unknown Parameters ◽

Time Series Regression

Semiparametric regression models are very useful for time series analysis. They facilitate the detection of features resulting from external interventions. The complexity of semiparametric models poses new challenges for issues of nonparametric and parametric inference and model selection that frequently arise from time series data analysis. In this paper, we propose penalized least squares estimators which can simultaneously select significant variables and estimate unknown parameters. An innovative class of variable selection procedure is proposed to select significant variables and basis functions in a semiparametric model. The asymptotic normality of the resulting estimators is established. Information criteria for model selection are also proposed. We illustrate the effectiveness of the proposed procedures with numerical simulations.

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SPECIFICATION TESTING IN NONLINEAR TIME SERIES WITH LONG-RANGE DEPENDENCE

Econometric Theory ◽

10.1017/s0266466610000241 ◽

2010 ◽

Vol 27 (2) ◽

pp. 260-284 ◽

Cited By ~ 5

Author(s):

Jiti Gao ◽

Qiying Wang ◽

Jiying Yin

Keyword(s):

Time Series ◽

Long Range ◽

Nonlinear Time Series ◽

Testing Procedure ◽

Model Specification ◽

Specification Testing ◽

Asymptotically Normal ◽

Bootstrap Simulation ◽

Normal Test ◽

Mean Function

This paper proposes a model specification testing procedure for parametric specification of the conditional mean function in a nonlinear time series model with long-range dependent. An asymptotically normal test is established even when long-range dependent is involved. To implement the proposed test in practice using a simulated example, a bootstrap simulation procedure is established to find a simulated critical value to compute both the size and power values of the proposed test.

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Der Sommer und Herbst 2003 aus phänologischer Sicht | Summer and autumn 2003 from a phenological point of view

Schweizerische Zeitschrift fur Forstwesen ◽

10.3188/szf.2004.0142 ◽

2004 ◽

Vol 155 (5) ◽

pp. 142-145 ◽

Cited By ~ 2

Author(s):

Claudio Defila

Keyword(s):

Time Series ◽

New Record ◽

Point Of View ◽

Late Spring ◽

Mean Deviation ◽

Leaf Shedding ◽

The Mean ◽

Very High ◽

Selection Of

The record-breaking heatwave of 2003 also had an impact on the vegetation in Switzerland. To examine its influences seven phenological late spring and summer phases were evaluated together with six phases in the autumn from a selection of stations. 30% of the 122 chosen phenological time series in late spring and summer phases set a new record (earliest arrival). The proportion of very early arrivals is very high and the mean deviation from the norm is between 10 and 20 days. The situation was less extreme in autumn, where 20% of the 103 time series chosen set a new record. The majority of the phenological arrivals were found in the class «normal» but the class«very early» is still well represented. The mean precocity lies between five and twenty days. As far as the leaf shedding of the beech is concerned, there was even a slight delay of around six days. The evaluation serves to show that the heatwave of 2003 strongly influenced the phenological events of summer and spring.

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Fluctuations in Influenza Epidemics and Suicide Mortality: A Time-Series Regression of 13-Year Mortality Data

SSRN Electronic Journal ◽

10.2139/ssrn.3441827 ◽

2019 ◽

Author(s):

Sun Jae Jung ◽

Sung-Shil Lim ◽

Jin-Ha Yoon

Keyword(s):

Time Series ◽

Suicide Mortality ◽

Mortality Data ◽

Time Series Regression

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

Engineering Proceedings ◽

10.3390/engproc2021005010 ◽

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.

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