Inference for the Lagged Cross‐Covariance Operator Between Functional Time Series

2019 ◽  
Vol 40 (5) ◽  
pp. 665-692 ◽  
Author(s):  
Gregory Rice ◽  
Marco Shum
Keyword(s):  
Time Series ◽  
Covariance Operator ◽  
Functional Time Series ◽  
Cross Covariance

scholarly journals Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces

2021 ◽  
Author(s):  
Sebastian Kühnert
Keyword(s):  
Time Series ◽  
Hilbert Spaces ◽  
Upper Bounds ◽  
Estimation Errors ◽  
Cartesian Products ◽  
Major Task ◽  
Functional Time Series ◽  
Cross Covariance ◽  
Covariance Operators ◽  
Practical Tool

A major task in Functional Time Series Analysis is measuring the dependence within and between processes, for which lagged covariance and cross-covariance operators have proven to be a practical tool in well-established spaces. This article deduces estimators and asymptotic upper bounds of the estimation errors for lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces for fixed and increasing lag and Cartesian powers. We allow the processes to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, we discuss features of estimators for the principle components of our covariance operators.

scholarly journals An Enhanced Joint Hilbert Embedding-Based Metric to Support Mocap Data Classification with Preserved Interpretability

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4443
Author(s):  
Cristian Kaori Valencia-Marin ◽  
Juan Diego Pulgarin-Giraldo ◽  
Luisa Fernanda Velasquez-Martinez ◽  
Andres Marino Alvarez-Meza ◽  
German Castellanos-Dominguez
Keyword(s):  
Time Series ◽  
Reproducing Kernel ◽  
Probability Distributions ◽  
Reproducing Kernel Hilbert Space ◽  
Joint Probability ◽  
Principal Component ◽  
Human Movement ◽  
Human Action ◽  
Covariance Operator ◽  
Cross Covariance

Motion capture (Mocap) data are widely used as time series to study human movement. Indeed, animation movies, video games, and biomechanical systems for rehabilitation are significant applications related to Mocap data. However, classifying multi-channel time series from Mocap requires coding the intrinsic dependencies (even nonlinear relationships) between human body joints. Furthermore, the same human action may have variations because the individual alters their movement and therefore the inter/intraclass variability. Here, we introduce an enhanced Hilbert embedding-based approach from a cross-covariance operator, termed EHECCO, to map the input Mocap time series to a tensor space built from both 3D skeletal joints and a principal component analysis-based projection. Obtained results demonstrate how EHECCO represents and discriminates joint probability distributions as kernel-based evaluation of input time series within a tensor reproducing kernel Hilbert space (RKHS). Our approach achieves competitive classification results for style/subject and action recognition tasks on well-known publicly available databases. Moreover, EHECCO favors the interpretation of relevant anthropometric variables correlated with players’ expertise and acted movement on a Tennis-Mocap database (also publicly available with this work). Thereby, our EHECCO-based framework provides a unified representation (through the tensor RKHS) of the Mocap time series to compute linear correlations between a coded metric from joint distributions and player properties, i.e., age, body measurements, and sport movement (action class).

scholarly journals Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces

2021 ◽  
Author(s):  
Sebastian Kühnert
Keyword(s):  
Time Series ◽  
Hilbert Spaces ◽  
Upper Bounds ◽  
Estimation Errors ◽  
Cartesian Products ◽  
Major Task ◽  
Functional Time Series ◽  
Cross Covariance ◽  
Covariance Operators ◽  
Practical Tool

A major task in Functional Time Series Analysis is measuring the dependence within and between processes, for which lagged covariance and cross-covariance operators have proven to be a practical tool in well-established spaces. This article deduces estimators and asymptotic upper bounds of the estimation errors for lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces for fixed and increasing lag and Cartesian powers. We allow the processes to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, we discuss features of estimators for the principle components of our covariance operators.

scholarly journals Functional time series analysis of age-specific fertility rates: visualizing the change in the age-pattern of fertility in India

2016 ◽  
Vol 4 (2) ◽  
pp. 79
Author(s):  
Mallika Deb ◽  
Tapan Kumar Chakrabarty
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Rural Women ◽  
Age Groups ◽  
Reproductive Age ◽  
Data Series ◽  
Fertility Rates ◽  
Registration System ◽  
Series Analysis ◽  
Functional Time Series

Functional Time Series Analysis (FTSA) is carried out in this article to uncover the temporal variations in the age pattern of fertility in India. Attempt is made to find whether there is any typical age pattern in the nation’s fertility across the reproductive age groups. If so, how do we characterize the role of changing age pattern of fertility across reproductive age groups in the nation’s fertility transition? We have used region-specific (rural-urban) and country level data series on Age-Specific Fertility Rates (ASFRs) available from Sample Registration System (SRS), India during 1971-2013. Findings of this study are very impressive. It is observed that the youngest age group of women in 15-19 years has contributed to the maximum decline in fertility with a substantially accelerated pace during the period of study. The major changes in fertility rates among Indian women dominated by the rural representation occur at the ages after 30. Further, the study also suggests that the future course of demographic transition in India from third phase to the fourth phase of replacement fertility would depend on the degree and pace of decline among the rural women aged below 30 years.

Sign in / Sign up

Export Citation Format

Share Document