Estimation of Trigonometric Components in Time Series

Damsleth, Eivind; Spjøtvoll, Emil

doi:10.2307/2287255

Cited by 14 publications

(26 citation statements)

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“…This problem may be overcome with "non-harmonic frequency domain" analysis where dependence of periodicities of cyclical components on series length is relaxed. Here the following procedure, as proposed in [19], is used for identifying true cyclical components: after log transformation to stabilise variances, and de-trending, using a deterministic function of time, the true frequency of a cyclical component, denoted by λ, was estimated, as in [19], by minimising, with respect to λ , the quantity…”

Section: Methodsmentioning

confidence: 99%

The pre-vaccination regional epidemiological landscape of measles in Italy: contact patterns, effort needed for eradication, and comparison with other regions of Europe

Manfredi

Cleur

Williams

et al. 2005

Popul Health Metrics

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BACKGROUND: Strong regional heterogeneity and generally sub-optimal rates of measles vaccination in Italy have, to date, hampered attainment of WHO targets for measles elimination, and have generated the need for the new Italian National Measles Elimination Plan. Crucial to success of the plan is the identification of intervention priorities based upon a clear picture of the regional epidemiology of measles derived from the use of data to estimate basic parameters. Previous estimates of measles force of infection for Italy have appeared anomalously low. It has been argued elsewhere that this results from Italian selective under-reporting by age of cases and that the true measles force of infection in Italy is probably similar to that of other European countries. A deeper examination of the evidence for this conjecture is undertaken in the present paper. METHODS: Using monthly regional case notifications data from 1949 to the start of vaccination in 1976 and notifications by age from 1971-76, summary equilibrium parameters (force of infection (FOI), basic reproductive ratio (R0) and critical vaccination coverage (pc)) are calculated for each region and for each of 5 plausible contact patterns. An analysis of the spectra of incidence profiles is also carried out. Finally a transmission dynamics model is employed to explore the correspondence between projections using different estimates of force of infection and data on seroprevalence in Italy. RESULTS: FOI estimates are lower than comparable European FOIs and there is substantial regional heterogeneity in basic reproductive ratios; certain patterns of contact matrices are demonstrated to be unfeasible. Most regions show evidence of 3-year epidemic cycles or longer, and compared with England & Wales there appears to be little synchronisation between regions. Modelling results suggest that the lower FOI estimated from corrected aggregate national data matches serological data more closely than that estimated from typical European data. CONCLUSION: Results suggest forces of infection in Italy, though everywhere remaining below the typical European level, are historically higher in the South where currently vaccination coverage is lowest. There appears to be little evidence to support the suggestion that a higher true force of infection is masked by age bias in reporting.

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Section: Methodsmentioning

confidence: 99%

The pre-vaccination regional epidemiological landscape of measles in Italy: contact patterns, effort needed for eradication, and comparison with other regions of Europe

Manfredi

Cleur

Williams

et al. 2005

Popul Health Metrics

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“…This is a major difference with the stepwise procedure of [13], which involves Schuster's unifrequential periodogram, and the implications of this difference are discussed in Sections 4.1, 4.3 and 5.1. KÀ1 !…”

Section: Reprintsmentioning

confidence: 99%

“…Comparison is made with the stepwise procedure of [13]. In the first one, the stepwise procedure of Section 2 is assessed for its performance in what it is designed for, the estimation of the number of periodic components of a time series.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…When this is the case, it means the experimenter chose a series length that coincided, by chance, with a multiple of the hidden periodicity. k ) [12] and a stepwise procedure based on Schuster's periodogram analysis of the residual series after fitting the periodic component detected at the previous step [13] were proposed to investigate K 0 hidden periodicities. However, it is then approximately equal to the sum of squares of the corresponding trigonometric regression model fitted to the time series by unweighted least squares [11].…”

Section: Introductionmentioning

confidence: 99%

“…I do so here from the perspective of a user of the multi-frequential periodogram, who would like to know its accuracy, precision and distribution for a given series length and MULTI-FREQUENTIAL PERIODOGRAM ANALYSIS 1065 ORDER REPRINTS a given covariance structure of the random errors in the trigonometric regression model. The stepwise procedure of Section 2 is compared to another, based on Schuster's periodogram [13], in Sections 4.1 and 5.1. Simulations are used as a complement, for aspects that could not be studied otherwise.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Frequential Periodogram Analysis and the Detection of Periodic Components in Time Series

Dutilleul

2001

Communications in Statistics - Theory and Methods

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The spectral analysis of Gaussian linear time-series processes is usually based on uni-frequential tools because the spectral density functions of degree 2 and higher are identically zero and there is no polyspectrum in this case. In finite samples, such an approach does not allow the resolution of closely adjacent spectral lines, except by using autoregressive models of excessively high order in the method of maximum entropy. In this article, multi-frequential periodograms designed for the analysis of discrete and mixed spectra are defined and studied for their properties in finite samples. For a given vector of frequencies !, the sum of squares of the corresponding trigonometric regression model fitted to a time series by unweighted least squares defines the multi-frequential periodogram statistic IM(!). When ! is unknown, it follows from the properties of nonlinear models whose parameters separate (i.e., the frequencies and the cosine and ORDER REPRINTS sine coefficients here) that the least-squares estimator of frequencies is obtained by maximizing I M (!). The first-order, second-order and distribution properties of I M (!) are established theoretically in finite samples, and are compared with those of Schuster's uni-frequential periodogram statistic. In the multi-frequential periodogram analysis, the least-squares estimator of frequencies is proved to be theoretically unbiased in finite samples if the number of periodic components of the time series is correctly estimated. Here, this number is estimated at the end of a stepwise procedure based on pseudo-F likelihood ratio tests. Simulations are used to compare the stepwise procedure involving I M (!) with a stepwise procedure using Schuster's periodogram, to study an approximation of the asymptotic theory for the frequency estimators in finite samples in relation to the proximity and signal-to-noise ratio of the periodic components, and to assess the robustness of I M (!) against autocorrelation in the analysis of mixed spectra. Overall, the results show an improvement of the new method over the classical approach when spectral lines are adjacent. Finally, three examples with real data illustrate specific aspects of the method, and extensions (i.e., unequally spaced observations, trend modeling, replicated time series, periodogram matrices) are outlined.Key Words: Trigonometric regression; Nonlinear models whose parameters separate; Least-squares estimation of frequencies; Finite-sample properties of periodogram statistics and frequency estimators; Analysis of discrete and mixed spectra 1064 DUTILLEUL

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Harmonic Migration Algorithm for Virtual Machine Migration and Switching Strategy in Cloud Computing

Siruvoru,

Aparna

2024

Concurrency and Computation

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Nowadays, cloud computing (CC) has been utilized broadly owing to the services it provides which can be received from any location at any time on the basis of the customer's requirements. A huge amount of data transmission is made from both user to host as well as host to the customer in the cloud environment, but here placing the virtual machine (VM) on a suitable host and data transferring is a challenging task. In this research, a harmonic migration algorithm (HMA) is developed by combining both the migration algorithm (MA) and the harmonic analysis (HA) for migrating a VM from an overloaded to an under‐loaded physical machine (PM) and enabling or disabling the VM through switching strategies in CC. The tasks are allocated to the corresponding VM in a round‐robin (RR) manner and subsequently, the load of the VM is predicted through the gated recurrent unit (GRU). The HMA technique migrates the VM when the predicted load is higher than the value of threshold and also, it enables or disables the VM when necessary. Thus, the performance of the developed HMA is improved over the other previous schemes at tasks 100, 200, 300, and 400 by varying the iterations. Therefore, the predicted load, makespan, and resource utilization of the developed HMA are 0.148, 0.327 s, and 0.482% for task 100 at iteration 100.

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Estimation of Trigonometric Components in Time Series

Cited by 14 publications

References 0 publications

The pre-vaccination regional epidemiological landscape of measles in Italy: contact patterns, effort needed for eradication, and comparison with other regions of Europe

The pre-vaccination regional epidemiological landscape of measles in Italy: contact patterns, effort needed for eradication, and comparison with other regions of Europe

Multi-Frequential Periodogram Analysis and the Detection of Periodic Components in Time Series

Harmonic Migration Algorithm for Virtual Machine Migration and Switching Strategy in Cloud Computing

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