A use of the Stein-Chen method in time series analysis

2000 ◽  
Vol 37 (04) ◽  
pp. 1129-1136 ◽  
Author(s):  
Sun-Tsung Kim
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
White Noise ◽  
Null Hypothesis ◽  
Functional Dependence ◽  
Autoregressive Process ◽  
Time Correlation ◽  
Main Difficulty ◽  
Continuous Functional ◽  
Reasonable Choice

In this paper, a statistic that has been introduced to test for space-time correlation is considered in a time series context. The null hypothesis is white noise; the alternative is any kind of continuous functional dependence. For an autoregressive process close to the null hypothesis, a bound on the distance between the distribution of the statistic and a Poisson distribution is proved, using the Stein-Chen method. The main difficulty in the proof is that the dependence in the time series is not locally restricted. The result implies asymptotically certain discrimination for a reasonable choice of the thresholds.

A use of the Stein-Chen method in time series analysis

2000 ◽  
Vol 37 (4) ◽  
pp. 1129-1136 ◽  
Author(s):  
Sun-Tsung Kim
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
White Noise ◽  
Null Hypothesis ◽  
Functional Dependence ◽  
Autoregressive Process ◽  
Time Correlation ◽  
Main Difficulty ◽  
Continuous Functional ◽  
Reasonable Choice

In this paper, a statistic that has been introduced to test for space-time correlation is considered in a time series context. The null hypothesis is white noise; the alternative is any kind of continuous functional dependence. For an autoregressive process close to the null hypothesis, a bound on the distance between the distribution of the statistic and a Poisson distribution is proved, using the Stein-Chen method. The main difficulty in the proof is that the dependence in the time series is not locally restricted. The result implies asymptotically certain discrimination for a reasonable choice of the thresholds.

scholarly journals Strong indications for nonlinear dynamics during Dansgaard-Oeschger events

2009 ◽  
Vol 5 (4) ◽  
pp. 1751-1762 ◽  
Author(s):  
H. Braun
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Null Hypothesis ◽  
Linear Time ◽  
Ice Core ◽  
Nonlinear Methods ◽  
Future Studies ◽  
Series Analysis ◽  
Ice Core Record ◽  
Glacial Climate

Abstract. Many climate records show the occurrence of large amplitude (10–15 K), millennial-scale warming events during glacial times, the Dansgaard-Oeschger (DO) events. So far these events have almost exclusively been investigated by means of linear time series analysis. The scope of this paper is to test if the assumption of linearity is fulfilled during DO events. By means of a surrogate-based Monte Carlo method, I here demonstrate that the 60 000-year long δ18O-record from the NGRIP ice core from Greenland allows to reject the null hypothesis of linearity beyond any reasonable level of doubt. Instead, the ice core record supports the interpretation that the events represent regime switches between different states of operation of glacial climate. As a conclusion, future studies on DO events should focus on the development and the application of more adequate (i.e., nonlinear) methods of time series analysis.

Research on Chaotic Characteristics of Diary Return Water Time Series in Qingtongxia Irrigation Area

2014 ◽  
Vol 998-999 ◽  
pp. 1429-1434
Author(s):  
Xin Yu Zhao ◽  
Jin Long Gao ◽  
Peng Fei Gu ◽  
Pei Huang
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Time Series Analysis ◽  
White Noise ◽  
Correlation Dimension ◽  
Stationary Time Series ◽  
Irrigation Area ◽  
Research Results ◽  
Analysis Phase ◽  
Return Water

For the problems that the characteristics of diary return water time series in Ningxia Qingtongxia Irrigation area ,this issue studied it by using time series analysis, phase space reconstruction and saturation correlation dimension and other methods.The research results showed that diary return water time series in Qingtongxia irrigation area is a non-white noise stationary time series, and it has the chaotic characteristics, the saturation correlation dimension of it is 1.81, the embedding dimensionality of it is 9.

scholarly journals Noise characteristics in Zenith Total Delay from homogeneously reprocessed GPS time series

2016 ◽  
Author(s):  
Anna Klos ◽  
Addisu Hunegnaw ◽  
Felix Norman Teferle ◽  
Kibrom Ebuy Abraha ◽  
Furqan Ahmed ◽  
...  
Keyword(s):  
Time Series ◽  
White Noise ◽  
Autoregressive Process ◽  
Noise Model ◽  
Total Delay ◽  
Tropical Zone ◽  
Climate Zones ◽  
Zenith Total Delay ◽  
Noise Characteristics ◽  
Gps Time Series

Abstract. Zenith Total Delay (ZTD) time series, derived from the re-processing of Global Positioning System (GPS) data, provide valuable information for the evaluation of global atmospheric reanalysis products such as ERA-Interim. Identifying the correct noise characteristics in the ZTD time series is an important step to assess the "true" magnitude of ZTD trend uncertainties. The ZTD residual time series for 1995–2015 are generated from our homogeneously re-processed and homogenized GPS time series from over 700 globally distributed stations classified into five major climate zones. The annual peak of ZTD data ranges between 10 and 150 mm with the smallest values for the polar and Alpine zone. The amplitudes of daily curve fall between 0 and 12 mm with the greatest variations for the dry zone. The autoregressive process of fourth order plus white noise model were found to be optimal for ZTD series. The tropical zone has the largest amplitude of autoregressive noise (9.59 mm) and the greatest amplitudes of white noise (13.00 mm). All climate zones have similar median coefficients of AR(1) (0.80 ± 0.05) with a minimum for polar and Alpine, which has the highest coefficients of AR(2) (0.27 ± 0.01) and AR(3) (0.11 ± 0.01) and clearly different from the other zones considered. We show that 53 of 120 examined trends became insignificant, when the optimum noise model was employed, compared to 11 insignificant trends for pure white noise. The uncertainty of the ZTD trends may be underestimated by a factor of 3 to 12 compared to the white noise only assumption.

scholarly journals A MAX-CORRELATION WHITE NOISE TEST FOR WEAKLY DEPENDENT TIME SERIES

2020 ◽  
Vol 36 (5) ◽  
pp. 907-960
Author(s):  
Jonathan B. Hill ◽  
Kaiji Motegi
Keyword(s):  
Time Series ◽  
White Noise ◽  
Null Hypothesis ◽  
Gaussian Approximation ◽  
Value Theory ◽  
Parametric Models ◽  
Test Statistic ◽  
Sample Correlation ◽  
Noise Test ◽  
Weakly Dependent

This article presents a bootstrapped p-value white noise test based on the maximum correlation, for a time series that may be weakly dependent under the null hypothesis. The time series may be prefiltered residuals. The test statistic is a normalized weighted maximum sample correlation coefficient $ \max _{1\leq h\leq \mathcal {L}_{n}}\sqrt {n}|\hat {\omega }_{n}(h)\hat {\rho }_{n}(h)|$, where $\hat {\omega }_{n}(h)$ are weights and the maximum lag $ \mathcal {L}_{n}$ increases at a rate slower than the sample size n. We only require uncorrelatedness under the null hypothesis, along with a moment contraction dependence property that includes mixing and nonmixing sequences. We show Shao’s (2011, Annals of Statistics 35, 1773–1801) dependent wild bootstrap is valid for a much larger class of processes than originally considered. It is also valid for residuals from a general class of parametric models as long as the bootstrap is applied to a first-order expansion of the sample correlation. We prove the bootstrap is asymptotically valid without exploiting extreme value theory (standard in the literature) or recent Gaussian approximation theory. Finally, we extend Escanciano and Lobato’s (2009, Journal of Econometrics 151, 140–149) automatic maximum lag selection to our setting with an unbounded lag set that ensures a consistent white noise test, and find it works extremely well in controlled experiments.

Sign in / Sign up

Export Citation Format

Share Document