scholarly journals Limiting Distributions for Explosive PAR(1) Time Series with Strongly Mixing Innovation

2015 ◽  
pp. 105-129
Author(s):  
Dominique Dehay
Keyword(s):  
Time Series ◽  
Limiting Distributions ◽  
Strongly Mixing

High-quantile regression for tail-dependent time series

Biometrika ◽  
2020 ◽  
Author(s):  
Ting Zhang
Keyword(s):  
Time Series ◽  
Quantile Regression ◽  
Limit Theorems ◽  
Tail Dependence ◽  
Serial Dependence ◽  
Response Distribution ◽  
Tail Region ◽  
Strongly Mixing ◽  
Regression Estimators ◽  
High Quantile

Summary Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly developed for cases in which the quantile level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena, and (ii) the data are no longer independent, but collected as a time series that can exhibit serial dependence in both tail and non-tail regions. To study the asymptotic theory for high-quantile regression estimators in the time series setting, we introduce a tail adversarial stability condition, which had not previously been described, and show that it leads to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial dependence in the tail region, but are not necessarily strongly mixing. Numerical experiments are conducted to illustrate the effect of tail dependence on high-quantile regression estimators, for which simply ignoring the tail dependence may yield misleading $p$-values.

APPROXIMATION TO THE LIMITING DISTRIBUTION OF t- AND F-STATISTICS IN TESTING FOR SEASONAL UNIT ROOTS

2001 ◽  
Vol 17 (4) ◽  
pp. 711-737 ◽  
Author(s):  
Seiji Nabeya
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Unit Roots ◽  
Limiting Distribution ◽  
Limiting Distributions ◽  
Discussion Paper ◽  
Seasonal Unit Roots ◽  
Series Analysis ◽  
The Moment ◽  
F Statistics

Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), Beaulieu and Miron (1993, Journal of Econometrics 55, 305–328), Ghysels, Lee, and Noh (1994, Journal of Econometrics 62, 415–442), Smith and Taylor (1998, Journal of Econometrics 85, 269–288; 1999, Journal of Time Series Analysis 20, 453–476; 1999, Discussion paper 99-15 in economics, University of Birmingham), and Taylor (1998, Journal of Time Series Analysis 19, 349–368) have developed a method of testing for seasonal unit roots of zero and nonzero frequencies. They propose to use t- and F-statistics as criteria that are obtained from an auxiliary regression and find their limiting distributions as the number of observations becomes large. Their limiting distributions are expressed by means of Brownian motions. In this paper the moment generating functions associated with the limiting distributions are derived, and it is shown, as in Nabeya (2000, Econometric Theory 16, 200–230), that the limiting distribution of t is well approximated by a distribution given in Gram–Charlier series. The limiting distribution of F is also well approximated by another type of distribution.

The LDE-Type Flare Occurrence (1969-1993)

1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Sunspot Cycle ◽  
List Type ◽  
Type Number ◽  
Solar Cycles ◽  
Type Iv ◽  
Long Duration ◽  
Cycle Maximum ◽  
Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

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