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.

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.

Towards a new recruitment paradigm for fish stocks

1997 ◽  
Vol 54 (4) ◽  
pp. 969-977 ◽  
Author(s):  
D J Gilbert
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Meta Analysis ◽  
Fish Stock ◽  
Test Statistic ◽  
Mean Values ◽  
Fish Stocks ◽  
Independent Events ◽  
Alternative Hypotheses ◽  
Stock Recruitment

The stock recruitment paradigm involves the hypothesis that recruitment (R) to a fish stock is positively related to the spawning stock biomass (SSB) of the stock, at low SSB. I propose a ``recruitment states'' hypothesis wherein R is independent of SSB but has different mean values during successive periods. Meta-analysis was used to test the null hypothesis that recruitment is a series of random, independent events, against these two alternative hypotheses, for 153 marine spawning bony fish stocks and 31 salmonid stocks. A test statistic for the stock recruitment paradigm, based on estimating derivatives from the first differences of the time series, was not significant for the marine stocks. The null hypothesis was rejected for the salmonid stocks. Recruitment states models significantly fitted time series for the marine stocks. Ricker models also significantly fitted these data, conflicting with the derivatives test result. However, because SSB is dependent on R, lagged by the age at maturity, a period in a low recruitment state would tend to lead to a period of low SSB. Therefore, the significance of the fit to the Ricker model may have been spurious. The recruitment states model best explained the meta-dataset for the marine stocks.

TESTING FOR NONLINEARITY IN SHANGHAI STOCK MARKET

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2720-2724 ◽  
Author(s):  
HAIYAN WANG ◽  
LONGKUN TANG
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Null Hypothesis ◽  
Quantitative Method ◽  
Multivariate Time Series ◽  
Surrogate Data ◽  
Significance Test ◽  
Test Statistic ◽  
Gaussian Random Process ◽  
Linear And Nonlinear

In this paper, we apply IAAFT to generate surrogate time series of measured multivariate time series. A quantitative method to detect nonlinearity in multivariate time series is proposed using the generalized redundancy and linear redundancy as the significance test statistic. The null hypothesis of a multivariate linear Gaussian random process is tested using the multivariate surrogate data. The validity of this method is demonstrated using two types models (linear and nonlinear) and applied to Shanghai stock market.

scholarly journals Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models

Risks ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 51
Author(s):  
Anthony Medford
Keyword(s):  
Time Series ◽  
Life Expectancy ◽  
Extreme Value Theory ◽  
Autoregressive Model ◽  
Best Practice ◽  
Gumbel Distribution ◽  
Value Theory ◽  
Model Diagnostics ◽  
Temporal Dependence ◽  
Simulation Results

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework for modeling time series extremes. The Gumbel distribution accounts for the extreme nature of best practice life expectancy, while the AR structure accounts for the temporal dependence in the time series. Model diagnostics and simulation results indicate that these models present a viable alternative to Gaussian AR(1) models when dealing with time series of extremes and merit further exploration.

scholarly journals REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction

2021 ◽  
Author(s):  
Zaheer Ahmed ◽  
Alberto Cassese ◽  
Gerard van Breukelen ◽  
Jan Schepers
Keyword(s):  
Null Hypothesis ◽  
Type I Error ◽  
Type I ◽  
The Novel ◽  
Simulation Studies ◽  
Test Statistic ◽  
Clustering Model ◽  
Novel Method ◽  
Main Effects ◽  
Empirical Case Studies

AbstractWe present a novel method, REMAXINT, that captures the gist of two-way interaction in row by column (i.e., two-mode) data, with one observation per cell. REMAXINT is a probabilistic two-mode clustering model that yields two-mode partitions with maximal interaction between row and column clusters. For estimation of the parameters of REMAXINT, we maximize a conditional classification likelihood in which the random row (or column) main effects are conditioned out. For testing the null hypothesis of no interaction between row and column clusters, we propose a $$max-F$$ m a x - F test statistic and discuss its properties. We develop a Monte Carlo approach to obtain its sampling distribution under the null hypothesis. We evaluate the performance of the method through simulation studies. Specifically, for selected values of data size and (true) numbers of clusters, we obtain critical values of the $$max-F$$ m a x - F statistic, determine empirical Type I error rate of the proposed inferential procedure and study its power to reject the null hypothesis. Next, we show that the novel method is useful in a variety of applications by presenting two empirical case studies and end with some concluding remarks.

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.

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