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.

TESTING INSTABILITY IN A PREDICTIVE REGRESSION MODEL WITH NONSTATIONARY REGRESSORS

2014 ◽  
Vol 31 (5) ◽  
pp. 953-980 ◽  
Author(s):  
Zongwu Cai ◽  
Yunfei Wang ◽  
Yonggang Wang
Keyword(s):  
Asymptotic Distributions ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Test Statistic ◽  
Predictive Regression ◽  
Testing Method ◽  
Type Test ◽  
Coefficient Vector ◽  
Alternative Hypotheses ◽  
The Stability

It is well known that allowing the coefficients to be time-varying in a predictive model with possibly nonstationary regressors can help to deal with instability in predictability associated with linear predictive models. In this paper, an L2-type test statistic is proposed to test the stability of the coefficient vector, and the asymptotic distributions of the proposed test statistic are developed under both null and alternative hypotheses. A Monte Carlo experiment is conducted to evaluate the finite sample performance of the proposed test statistic and an empirical example is examined to demonstrate the practical application of the proposed testing method.

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 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 Measures of Dispersion and Serial Dependence in Categorical Time Series

Econometrics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 17 ◽  
Author(s):  
Christian H. Weiß
Keyword(s):  
Time Series ◽  
Real Data ◽  
Asymptotic Distributions ◽  
Serial Dependence ◽  
Finite Sample ◽  
Categorical Time Series ◽  
Dispersion Measures ◽  
Measures Of Dispersion ◽  
Dependence Measures ◽  
Economics And Biology

The analysis and modeling of categorical time series requires quantifying the extent of dispersion and serial dependence. The dispersion of categorical data is commonly measured by Gini index or entropy, but also the recently proposed extropy measure can be used for this purpose. Regarding signed serial dependence in categorical time series, we consider three types of κ -measures. By analyzing bias properties, it is shown that always one of the κ -measures is related to one of the above-mentioned dispersion measures. For doing statistical inference based on the sample versions of these dispersion and dependence measures, knowledge on their distribution is required. Therefore, we study the asymptotic distributions and bias corrections of the considered dispersion and dependence measures, and we investigate the finite-sample performance of the resulting asymptotic approximations with simulations. The application of the measures is illustrated with real-data examples from politics, economics and biology.

A CONSISTENT TEST OF CONDITIONAL PARAMETRIC DISTRIBUTIONS

2000 ◽  
Vol 16 (5) ◽  
pp. 667-691 ◽  
Author(s):  
John Xu Zheng
Keyword(s):  
Linear Expansion ◽  
Kernel Estimation ◽  
Nonparametric Test ◽  
Distribution Functions ◽  
Finite Sample ◽  
Information Function ◽  
Test Statistic ◽  
First Order ◽  
Standard Normal ◽  
Leibler Information

This paper proposes a new nonparametric test for conditional parametric distribution functions based on the first-order linear expansion of the Kullback–Leibler information function and the kernel estimation of the underlying distributions. The test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric distribution is correctly specified, whereas asymptotically rejecting the null with probability one if the parametric distribution is misspecified. The test is also shown to have power against any local alternatives approaching the null at rates slower than the parametric rate n−1/2. The finite sample performance of the test is evaluated via a Monte Carlo simulation.

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.

Calculating the Distribution of the Serial Correlation Estimator by Saddlepoint Integration

1996 ◽  
Vol 12 (3) ◽  
pp. 458-480 ◽  
Author(s):  
Carl W. Helstrom
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Probability Distribution ◽  
Finite Number ◽  
Serial Correlation ◽  
Asymptotic Distributions ◽  
Stationary Time Series ◽  
Finite Sample ◽  
Initial Value ◽  
First Order

The efficient method of numerical saddlepoint integration is described and applied to calculating the probability distribution of the maximum likelihood and Yule-Walker estimators of the correlation coefficient a of a first-order autoregressive normal time series with initial value either zero or nonzero when a finite number n of data are at hand. Stationary time series of the same type are also treated. Significance points are computed in a number of examples to show how, as n increases, the finite-sample distributions approach the asymptotic distributions that have appeared in the literature.

Detecting departures from meta-ellipticity for multivariate stationary time series

2021 ◽  
Vol 9 (1) ◽  
pp. 121-140
Author(s):  
Axel Bücher ◽  
Miriam Jaser ◽  
Aleksey Min
Keyword(s):  
Time Series ◽  
Simulation Study ◽  
Large Scale ◽  
Stationary Time Series ◽  
Serial Dependence ◽  
Finite Sample ◽  
Test Statistic ◽  
Stationary Time ◽  
Theoretical Results

Abstract A test for detecting departures from meta-ellipticity for multivariate stationary time series is proposed. The large sample behavior of the test statistic is shown to depend in a complicated way on the underlying copula as well as on the serial dependence. Valid asymptotic critical values are obtained by a bootstrap device based on subsampling. The finite-sample performance of the test is investigated in a large-scale simulation study, and the theoretical results are illustrated by a case study involving financial log returns.

Tests for high-dimensional covariance matrices

2019 ◽  
Vol 09 (03) ◽  
pp. 2050009
Author(s):  
Jing Chen ◽  
Xiaoyi Wang ◽  
Shurong Zheng ◽  
Baisen Liu ◽  
Ning-Zhong Shi
Keyword(s):  
Sample Size ◽  
Matrix Theory ◽  
Covariance Matrices ◽  
Asymptotic Distributions ◽  
High Dimensional ◽  
Frobenius Norm ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Sample Case

In this paper, we propose some new tests for high-dimensional covariance matrices that are applicable to generally distributed populations with finite fourth moments. The proposed test statistics are the maximum of the likelihood ratio test statistic and the statistic based on the Frobenius norm. The advantage of the new tests is the good performance in terms of power for both the traditional case, in which the dimension is much smaller than the sample size, and the high-dimensional case, in which the dimension is large compared to the sample size. In the one-sample case, the new test is proposed for testing the hypothesis that the high-dimensional covariance matrix equals an identity matrix. In the two-sample case, the new test is developed for testing the equality of two high-dimensional covariance matrices. By using the random matrix theory, the asymptotic distributions of the proposed new tests are derived under the assumption that the dimension and the sample size proportionally tend toward infinity. Finally, numerical studies are conducted to investigate the finite sample performance of the proposed new tests.

Residual-Based Tests for the Null of Stationarity with Applications to U.S. Macroeconomic Time Series

1994 ◽  
Vol 10 (3-4) ◽  
pp. 720-746 ◽  
Author(s):  
In Choi
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Distribution Functions ◽  
Asymptotic Distributions ◽  
Cumulative Distribution ◽  
Finite Sample ◽  
Annual Series ◽  
Cumulative Distribution Functions ◽  
Lm Test ◽  
Macroeconomic Time Series

This paper proposes residual-based tests for the null of level- and trend-stationarity, which are analogs of the LM test for an MA unit root. Asymptotic distributions of the tests are nonstandard, but they are expressed in a unified manner by expressing stochastic integrals. In addition, the tests are shown to be consistent. By expressing the distributions expressed as a function of a chi-square variable with one degree of freedom, the exact limiting probability density and cumulative distribution functions are obtained, and the exact limiting cumulative distribution functions are tabulated. Finite sample performance of the proposed tests is studied by simulation. The tests display stable size when the lag truncation number for the long-run variance estimation is chosen appropriately. But the power of the tests is generally not high at selected sample sizes. The test for the null of trend-stationarity is applied to the U.S. macroeconomic time series along with the Phillips-Perron Z(⋯) test. For some monthly and annual series, the two tests provide consistent inferential results. But for most series, the two contradictory nulls of trend-stationarity and a unit root cannot be rejected at the conventional significance levels.

Sign in / Sign up

Export Citation Format

Share Document