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 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 Bootstrapping covariance operators of functional time series

2020 ◽  
Vol 32 (3) ◽  
pp. 648-666 ◽  
Author(s):  
Olimjon Sh. Sharipov ◽  
Martin Wendler
Keyword(s):  
Time Series ◽  
Functional Time Series ◽  
Covariance Operators

scholarly journals THE DECAY OF THE WALSH COEFFICIENTS OF SMOOTH FUNCTIONS

2009 ◽  
Vol 80 (3) ◽  
pp. 430-453 ◽  
Author(s):  
JOSEF DICK
Keyword(s):  
Lower Bound ◽  
Fractional Order ◽  
Bounded Variation ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Upper Bounds ◽  
Reproducing Kernel Hilbert Spaces ◽  
Smooth Functions ◽  
Kernel Hilbert Spaces

AbstractWe give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and nonperiodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown.

scholarly journals Learning from Nighttime Observations of Gas Flaring in North Dakota for Better Decision and Policy Making

2021 ◽  
Vol 13 (5) ◽  
pp. 941
Author(s):  
Rong Lu ◽  
Jennifer L. Miskimins ◽  
Mikhail Zhizhin
Keyword(s):  
Time Series ◽  
North Dakota ◽  
Policy Making ◽  
Nearest Neighbor ◽  
Negative Binomial ◽  
Infrared Imaging ◽  
Gaussian Mixture Models ◽  
Data Gathering ◽  
Gaussian Mixture ◽  
Estimation Errors

In today’s oil industry, companies frequently flare the produced natural gas from oil wells. The flaring activities are extensive in some regions including North Dakota. Besides company-reported data, which are compiled by the North Dakota Industrial Commission, flaring statistics such as count and volume can be estimated via Visible Infrared Imaging Radiometer Suite nighttime observations. Following data gathering and preprocessing, Bayesian machine learning implemented with Markov chain Monte Carlo methods is performed to tackle two tasks: flaring time series analysis and distribution approximation. They help further understanding of the flaring profiles and reporting qualities, which are important for decision/policy making. First, although fraught with measurement and estimation errors, the time series provide insights into flaring approaches and characteristics. Gaussian processes are successful in inferring the latent flaring trends. Second, distribution approximation is achieved by unsupervised learning. The negative binomial and Gaussian mixture models are utilized to describe the distributions of field flare count and volume, respectively. Finally, a nearest-neighbor-based approach for company level flared volume allocation is developed. Potential discrepancies are spotted between the company reported and the remotely sensed flaring profiles.

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.

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