scholarly journals A similarity measure for second order properties of non-stationary functional time series with applications to clustering and testing

Bernoulli ◽  
2021 ◽  
Vol 27 (1) ◽  
pp. 469-501
Author(s):  
Anne van Delft ◽  
Holger Dette
Keyword(s):  
Time Series ◽  
Similarity Measure ◽  
Second Order ◽  
Functional Time Series

HIGHER ORDER COMPLEXITY OF TIME SERIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2979-2990 ◽  
Author(s):  
FANJI GU ◽  
ENHUA SHEN ◽  
XIN MENG ◽  
YANG CAO ◽  
ZHIJIE CAI
Keyword(s):  
Time Series ◽  
Mental Arithmetic ◽  
Higher Order ◽  
Second Order ◽  
Stationary Time Series ◽  
Eeg Signals ◽  
Eyes Closed ◽  
Logistic Mapping ◽  
Original Time ◽  
Different Order

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed.

Estimation of second-order properties from jittered time series

1996 ◽  
Vol 48 (1) ◽  
pp. 29-48 ◽  
Author(s):  
Peter J. Thomson ◽  
Peter M. Robinson
Keyword(s):  
Time Series ◽  
Second Order

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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