Measuring Discontinuities in Time Series Obtained with Repeated Sample Surveys

2020 ◽  
Vol 88 (1) ◽  
pp. 155-175
Author(s):  
Jan Brakel ◽  
Xichuan (Mark) Zhang ◽  
Siu‐Ming Tam
Keyword(s):  
Time Series ◽  
Sample Surveys ◽  
Repeated Sample

scholarly journals Time Series Methods and Repeated Sample Surveys

2021 ◽  
Author(s):  
◽  
Stephen John Haslett
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Sample Survey ◽  
Sample Surveys ◽  
Parameter Vector ◽  
Time Period ◽  
Repeated Sample ◽  
Polynomial Models ◽  
Stochastic Properties ◽  
Over Time

<p>When applied to a sequence of repeated surveys, the traditional sample survey estimators of means or totals for one time period only, fail to take advantage of any time series structure. Such structure may result from correlation between successive responses for resampled individuals, or from time series properties in the parameters of interest. Historically, the initial published papers on time series improvement of repeated sample survey estimates allowed only the first possibility, treating the sum over the population of the individual responses as fixed; individual responses were seen as having stochastic properties only with respect to the sampling scheme. The alternative and later development allowed that both individual responses and their sum have stochastic properties with respect to a superpopulation from which the population of individual responses are drawn. Superpopulations allowed the application of mainstream time series techniques, including signal extraction and stochastic least squares, to repeated sample survey data. These developments in their historical perspective are the topic of Chapter 1. Superpopulation models may also be applied to sample surveys from a single time period, and superpopulation and design properties of the one period linear non-homogeneous sample survey estimator form the topic of Chapter 2; this estimator is sufficiently general to subsume almost all single period non-informative sample survey estimators, and Chapter 2 allows systematisation of a wide range of previously disparate results. This linear estimator may also be extended beyond one time period to include the known estimators for repeated surveys, and this topic, together with a consideration of the effects of data agqregation on non-stochastic and stochastic least squares, is the subject of Chapter 3. Given the central role of the general linear model, and the time series nature of repeated surveys, projection and parameter updating formulae for linear models should form an integral part of repeated survey analysis. The correlation of sample survey errors however, invalidates the formulae appropriate to the known iid error case, and Chapters 4 and 5 develop the general formulae to allow correlated error structure. Chapter 4 considers parameter vectors of fixed length, as for example, for polynomial models, and provides formulae for estimating the length of the parameter vector, and for calculating independent recursive residuals and cusums when further data are added to the model. Chapter 5 considers updating and projection formulae in a wider context, and allows that the parameter vector may be stochastic or non-stochastic and that its length may increase with additional data; it consequently provides a general extension of the Kalman filter to the case of coloured noise over time. The paucity of suitable data has limited data analysis to that contained in Chapter 6, where a simulation study and an analysis of medical data gauge the efficacy of polynomial models in time with multiple observations per time point and autocorrelated errors. The formulae of Chapter 4 allow testing for the constancy of the regression relationships over time. The appendix details SAS computer programs for fitting the polynomial models of Chapter 6.</p>

scholarly journals Time Series Methods and Repeated Sample Surveys

2021 ◽  
Author(s):  
◽  
Stephen John Haslett
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Sample Survey ◽  
Sample Surveys ◽  
Parameter Vector ◽  
Time Period ◽  
Repeated Sample ◽  
Polynomial Models ◽  
Stochastic Properties ◽  
Over Time

<p>When applied to a sequence of repeated surveys, the traditional sample survey estimators of means or totals for one time period only, fail to take advantage of any time series structure. Such structure may result from correlation between successive responses for resampled individuals, or from time series properties in the parameters of interest. Historically, the initial published papers on time series improvement of repeated sample survey estimates allowed only the first possibility, treating the sum over the population of the individual responses as fixed; individual responses were seen as having stochastic properties only with respect to the sampling scheme. The alternative and later development allowed that both individual responses and their sum have stochastic properties with respect to a superpopulation from which the population of individual responses are drawn. Superpopulations allowed the application of mainstream time series techniques, including signal extraction and stochastic least squares, to repeated sample survey data. These developments in their historical perspective are the topic of Chapter 1. Superpopulation models may also be applied to sample surveys from a single time period, and superpopulation and design properties of the one period linear non-homogeneous sample survey estimator form the topic of Chapter 2; this estimator is sufficiently general to subsume almost all single period non-informative sample survey estimators, and Chapter 2 allows systematisation of a wide range of previously disparate results. This linear estimator may also be extended beyond one time period to include the known estimators for repeated surveys, and this topic, together with a consideration of the effects of data agqregation on non-stochastic and stochastic least squares, is the subject of Chapter 3. Given the central role of the general linear model, and the time series nature of repeated surveys, projection and parameter updating formulae for linear models should form an integral part of repeated survey analysis. The correlation of sample survey errors however, invalidates the formulae appropriate to the known iid error case, and Chapters 4 and 5 develop the general formulae to allow correlated error structure. Chapter 4 considers parameter vectors of fixed length, as for example, for polynomial models, and provides formulae for estimating the length of the parameter vector, and for calculating independent recursive residuals and cusums when further data are added to the model. Chapter 5 considers updating and projection formulae in a wider context, and allows that the parameter vector may be stochastic or non-stochastic and that its length may increase with additional data; it consequently provides a general extension of the Kalman filter to the case of coloured noise over time. The paucity of suitable data has limited data analysis to that contained in Chapter 6, where a simulation study and an analysis of medical data gauge the efficacy of polynomial models in time with multiple observations per time point and autocorrelated errors. The formulae of Chapter 4 allow testing for the constancy of the regression relationships over time. The appendix details SAS computer programs for fitting the polynomial models of Chapter 6.</p>

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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