TESTING CHAOS OF TIME SERIES: PORTMANTEAU STATISTICS UNDER AN ORDER TRANSFORMATION

2001 ◽  
Vol 11 (06) ◽  
pp. 1761-1769 ◽  
Author(s):  
DEJIAN LAI
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Random Variable ◽  
Asymptotic Distributions ◽  
Test Statistics ◽  
Chi Square ◽  
Gaussian Series ◽  
Low Dimensional ◽  
Portmanteau Statistics ◽  
Direct Use

This paper studies several portmanteau test statistics with a nonparametric order transformation for distinguishing independent and identically distributed (i.i.d.) random processes from noisy chaotic time series. These portmanteau test statistics are asymptotically distributed as a chi-square random variable under the null hypothesis of i.i.d. Gaussian series. In this Letter, we show that the asymptotic distributions of these portmanteau test statistics on the transformed series are still chi-square under the null hypothesis. The simulations indicate that direct use of these portmanteau test statistics yields low power in identifying chaos. However, with the proposed order transformation, the simulations show that these test statistics are still effective for identifying noisy low dimensional chaos in some cases.

scholarly journals SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL

2009 ◽  
Vol 26 (4) ◽  
pp. 965-993 ◽  
Author(s):  
Christian Francq ◽  
Lajos Horvath ◽  
Jean-Michel Zakoïan
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Null Hypothesis ◽  
Nuisance Parameter ◽  
Time Series Models ◽  
Ratio Test ◽  
Finite Sample ◽  
Chi Square ◽  
Finite Sample Properties ◽  
Linearity Testing

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite-sample properties of the sup-tests are studied by simulations.

scholarly journals Structural change detection in ordinal time series

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0256128
Author(s):  
Fuxiao Li ◽  
Mengli Hao ◽  
Lijuan Yang
Keyword(s):  
Time Series ◽  
Structural Change ◽  
Change Point ◽  
Null Hypothesis ◽  
Change Point Detection ◽  
Complex Data ◽  
Test Statistics ◽  
Efficient Score ◽  
Score Vector ◽  
Ordinal Time Series

Change-point detection in health care data has recently obtained considerable attention due to the increased availability of complex data in real-time. In many applications, the observed data is an ordinal time series. Two kinds of test statistics are proposed to detect the structural change of cumulative logistic regression model, which is often used in applications for the analysis of ordinal time series. One is the standardized efficient score vector, the other one is the quadratic form of the efficient score vector with a weight function. Under the null hypothesis, we derive the asymptotic distribution of the two test statistics, and prove the consistency under the alternative hypothesis. We also study the consistency of the change-point estimator, and a binary segmentation procedure is suggested for estimating the locations of possible multiple change-points. Simulation results show that the former statistic performs better when the change-point occurs at the centre of the data, but the latter is preferable when the change-point occurs at the beginning or end of the data. Furthermore, the former statistic could find the reason for rejecting the null hypothesis. Finally, we apply the two test statistics to a group of sleep data, the results show that there exists a structural change in the data.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

scholarly journals Facial Profile Shape, Malocclusion and Palatal Morphology in Malay Obstructive Sleep Apnea Patients

2010 ◽  
Vol 80 (1) ◽  
pp. 37-42 ◽  
Author(s):  
S. M. Banabilh ◽  
A. R. Samsudin ◽  
A. H. Suzina ◽  
Sidek Dinsuhaimi
Keyword(s):  
Obstructive Sleep Apnea ◽  
Null Hypothesis ◽  
Control Group ◽  
Class Ii Malocclusion ◽  
Chi Square ◽  
Facial Profile ◽  
Obstructive Sleep ◽  
Significant Difference ◽  
Chi Square Test ◽  
The Mean

Abstract Objective: To test the null hypothesis that there is no difference in facial profile shape, malocclusion class, or palatal morphology in Malay adults with and without obstructive sleep apnea (OSA). Materials and Methods: Subjects were 120 adult Malays aged 18 to 65 years (mean ± standard deviation [SD], 33.2 ± 13.31) divided into two groups of 60. Both groups underwent clinical examination and limited channel polysomnography (PSG). The mean OSA and control values were subjected to t-test and the chi square test. Results: Physical examination showed that 61.7% of the OSA patients were obese, and 41.7% of those obese patients had severe OSA. The mean body mass index (BMI) was significantly greater for the OSA group (33.2 kg/m2 ± 6.5) than for the control group (22.7 kg/m2 ± 3.5; P < .001). The mean neck size and systolic blood pressure were greater for the OSA group (43.6 cm ± 6.02; 129.1 mm Hg ± 17.55) than for the control group (35.6 cm ± 3.52; 114.1 mm Hg ± 13.67; P < .001). Clinical examination showed that the most frequent findings among OSA groups when compared with the control group were convex profiles (71.7%), Class II malocclusion (51.7%), and V palatal shape (53.3%), respectively; the chi square test revealed a significant difference in terms of facial profile and malocclusion class (P < .05), but no significant difference in palatal shape was found. Conclusion: The null hypothesis is rejected. A convex facial profile and Class II malocclusion were significantly more common in the OSA group. The V palatal shape was a frequent finding in the OSA group.

scholarly journals Asymptotic Distributions of M-Estimates for Parameters of Multivariate Time Series with Strong Mixing Property

2021 ◽  
Vol 5 (1) ◽  
pp. 19
Author(s):  
Alexander Kushnir ◽  
Alexander Varypaev
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Multivariate Time Series ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Stationary Time Series ◽  
Strong Mixing ◽  
Statistical Estimates ◽  
Distribution Parameters ◽  
M Estimates

The publication is devoted to studying asymptotic properties of statistical estimates of the distribution parameters u∈Rq of a multidimensional random stationary time series zt∈Rm, t∈ℤ satisfying the strong mixing conditions. We consider estimates u^nδ(z¯n), z¯n=(z1T,…,znT)T∈Rmn that provide in asymptotic n→∞ the maximum values for some objective functions Qn(z¯n;u), which have properties similar to the well-known property of local asymptotic normality. These estimates are constructed by solving the equations δn(z¯n;u)=0, where δn(z¯n;u) are arbitrary functions for which δn(z¯n;u)−gradhQn(z¯n;u+n−1/2h)→0(n→∞) in Pn,u(z¯n)-probability uniformly on u∈U, were U is compact in Rq. In many cases, the estimates u^nδ(z¯n) have the same asymptotic properties as well-known M-estimates defined by equations u^nQ(z¯n)=arg maxu∈UQn(z¯n;u) but often can be much simpler computationally. We consider an algorithmic method for constructing estimates u^nδ(z¯n), which is similar to the accumulation method first proposed by R. Fischer and rigorously developed by L. Le Cam. The main theoretical result of the article is the proof of the theorem, in which conditions of the asymptotic normality of estimates u^nδ(z¯n) are formulated, and the expression is proposed for their matrix of asymptotic mean-square deviations limn→∞nEn,u{(u^δ(z¯n)−u)(u^δ(z¯n)−u)T}.

scholarly journals LSTM-Guided Coaching Assistant for Table Tennis Practice

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4112 ◽  
Author(s):  
Se-Min Lim ◽  
Hyeong-Cheol Oh ◽  
Jaein Kim ◽  
Juwon Lee ◽  
Jooyoung Park
Keyword(s):  
Time Series ◽  
State Space ◽  
Time Series Data ◽  
State Space Model ◽  
Skill Assessment ◽  
Series Data ◽  
High Dimensional ◽  
Table Tennis ◽  
Space Model ◽  
Low Dimensional

Recently, wearable devices have become a prominent health care application domain by incorporating a growing number of sensors and adopting smart machine learning technologies. One closely related topic is the strategy of combining the wearable device technology with skill assessment, which can be used in wearable device apps for coaching and/or personal training. Particularly pertinent to skill assessment based on high-dimensional time series data from wearable sensors is classifying whether a player is an expert or a beginner, which skills the player is exercising, and extracting some low-dimensional representations useful for coaching. In this paper, we present a deep learning-based coaching assistant method, which can provide useful information in supporting table tennis practice. Our method uses a combination of LSTM (Long short-term memory) with a deep state space model and probabilistic inference. More precisely, we use the expressive power of LSTM when handling high-dimensional time series data, and state space model and probabilistic inference to extract low-dimensional latent representations useful for coaching. Experimental results show that our method can yield promising results for characterizing high-dimensional time series patterns and for providing useful information when working with wearable IMU (Inertial measurement unit) sensors for table tennis coaching.

On the estimation of a harmonic component in a time series with stationary dependent residuals

1973 ◽  
Vol 5 (02) ◽  
pp. 217-241 ◽  
Author(s):  
A. M. Walker
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Harmonic Component ◽  
Asymptotic Distributions ◽  
Finite Variance ◽  
Rigorous Derivation ◽  
Image Position ◽  
Vector Valued ◽  
Special Case

Let observations (X 1, X 2, …, Xn ) be obtained from a time series {Xt } such that where the ɛt are independently and identically distributed random variables each having mean zero and finite variance, and the gu (θ) are specified functions of a vector-valued parameter θ. This paper presents a rigorous derivation of the asymptotic distributions of the estimators of A, B, ω and θ obtained by an approximate least-squares method due to Whittle (1952). It is a sequel to a previous paper (Walker (1971)) in which a similar derivation was given for the special case of independent residuals where gu (θ) = 0 for u > 0, the parameter θ thus being absent.

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