A Least Squares Method for Detecting Multiple Change Points in a Univariate Time Series

2018 ◽  
pp. 125-143
Author(s):  
Kyu S. Hahn ◽  
Won Son ◽  
Hyungwon Choi ◽  
Johan Lim
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Change Points ◽  
Univariate Time Series

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.

A Least Squares Method for Spectral Analysis of Space-Time Series

1995 ◽  
Vol 52 (20) ◽  
pp. 3501-3511 ◽  
Author(s):  
Dong L. Wu ◽  
Paul B. Hays ◽  
Wilbert R. Skinner
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Least Squares ◽  
Least Squares Method ◽  
Space Time

Motion Generation for a Sword-Fighting Robot Based on Quick Detection of Opposite Player’s Initial Motions

2015 ◽  
Vol 27 (5) ◽  
pp. 543-551 ◽  
Author(s):  
Akio Namiki ◽  
◽  
Fumiyasu Takahashi
Keyword(s):  
Least Squares ◽  
High Speed ◽  
Least Squares Method ◽  
Vision System ◽  
Experimental Results ◽  
Change Points ◽  
Motion Generation ◽  
Robot System ◽  
The Moment ◽  
Human Player

<div class=""abs_img""> <img src=""[disp_template_path]/JRM/abst-image/00270005/11.jpg"" width=""300"" /> Defensive motion against attack</div> In this paper, we discuss how to generate defensive motions for a sword-fighting robot based on quick detection of the opposite player’s initial motions. Our sword-fighting robot system, which has a stereo high-speed vision system, recognizes both the position of a human player and that of the sword grasped by the robot’s hand. Further, it detects the moment when the human player initiates a move using ChangeFinder, which is a method of detecting change points. Next, using least squares method, it predicts the possible trajectories of the sword of the human player from the moment when the attack starts. Finally, it judges the type of the attack and generates an appropriate defensive motion. The effectiveness of the proposed algorithm is verified by experimental results. </span>

scholarly journals Time series modeling with pruned multi-layer perceptron and 2-stage damped least-squares method

2014 ◽  
Vol 490 ◽  
pp. 012040
Author(s):  
Cyril Voyant ◽  
Wani Tamas ◽  
Christophe Paoli ◽  
Aurélia Balu ◽  
Marc Muselli ◽  
...  
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Time Series Modeling ◽  
Multi Layer Perceptron ◽  
Damped Least Squares

RECONSTRUCTING DIFFERENTIAL EQUATION FROM A TIME SERIES

2003 ◽  
Vol 13 (11) ◽  
pp. 3307-3323 ◽  
Author(s):  
VALKO PETROV ◽  
JUERGEN KURTHS ◽  
NIKOLA GEORGIEV
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Small Error ◽  
Mathematical Algorithm ◽  
Right Hand ◽  
Polynomial Differential Equation ◽  
Observational Noise

This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient.

On the first-order bilinear time series model

1981 ◽  
Vol 18 (03) ◽  
pp. 617-627 ◽  
Author(s):  
Tuan Dinh Pham ◽  
Lanh Tat Tran
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Time Series Model ◽  
First Order ◽  
Strongly Consistent

The paper investigates some properties of the first-order bilinear time series model: stationarity and invertibility. Estimates of the parameters are obtained by a modified least squares method and shown to be strongly consistent.

MEASURING THE PREDICTABILITY OF NOISY RECURRENT TIME SERIES

1993 ◽  
Vol 03 (03) ◽  
pp. 797-802
Author(s):  
R. WAYLAND ◽  
D. PICKETT ◽  
D. BROMLEY ◽  
A. PASSAMANTE
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Additive Noise ◽  
Nearest Neighbor ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Short Time Series ◽  
Forecasting Method ◽  
Noisy Time Series ◽  
Short Time

The effect of the chosen forecasting method on the measured predictability of a noisy recurrent time series is investigated. Situations where the length of the time series is limited, and where the level of corrupting noise is significant are emphasized. Two simple prediction methods based on explicit nearest-neighbor averages are compared to a more complicated, and computationally expensive, local linearization technique based on the method of total least squares. The comparison is made first for noise-free, and then for noisy time series. It is shown that when working with short time series in high levels of additive noise, the simple prediction schemes perform just as well as the more sophisticated total least squares method.

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