Autoregressive spectral analysis when observations are missing

Broersen, P.M.T.; Waele, S. de; Bos, R.

doi:10.1016/j.automatica.2004.04.011

Cited by 50 publications

(60 citation statements)

References 19 publications

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“…Models for irregular observations cannot be estimated recursively, in contrast with equidistant observations with efficient recursive algorithms [18]. The estimated parameters of the lower order models have an extra missing-data bias as long as the current model order is lower than the true order and can only serve as non-linear starting values for higher order models [13].…”

Section: Benchmark Data Typementioning

confidence: 99%

“…In equidistant AR estimation, reflection coefficients for increasing model orders are estimated successively, where all previous reflection coefficients remain the same [18]. In missing-data or irregular sampling problems, all reflection coefficients are estimated simultaneously and vary for increasing orders [13]. The AR(2) model has been estimated for the whole frequency range.…”

Section: Benchmark Data Typementioning

confidence: 99%

“…In practical computations, that has much more favorable properties than his continuous algorithm [7]. An automatic time series algorithm with AR, moving average (MA) and combined ARMA models outperformed all other methods that have been described for missing-data problems [13]. This best performing method for missing data, with AR, MA and ARMA models as candidates for selection, can be applied to irregular data, if they are resampled with the multi-shift slotting principle [8].…”

Section: Introductionmentioning

confidence: 99%

“…The discretetime spectral density has a finite frequency interval, until half the resampling frequency. Equidistant missing-data problems have been investigated recently [13]. For missing data, Jones described an efficient method to calculate the true likelihood for autoregressive (AR) processes [14].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Spectral Analysis of Irregularly Sampled Data with Time Series Models

Broersen¹

2009

TOSIGPJ

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Abstract:Slotted resampling transforms an irregularly sampled process into an equidistant missing-data problem. Equidistant resampling inevitably causes bias, due to aliasing and the shift of the irregular observation times to an equidistant grid. Taking a slot width smaller than the resampling time can diminish the shift bias. A dedicated estimator for time series models of multiple slotted data sets with missing observations has been developed for the estimation of the power spectral density and of the autocorrelation function. The algorithm estimates time series models and selects the order and type from a number of candidates. It is tested with benchmark data. Spectra can be estimated until frequencies higher than 100 times the mean data rate.

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Section: Benchmark Data Typementioning

confidence: 99%

Section: Benchmark Data Typementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spectral Analysis of Irregularly Sampled Data with Time Series Models

Broersen¹

2009

TOSIGPJ

Self Cite

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“…This computes Fourier coefficients as the least squares fit of sines and cosines to the available remaining observations. The Lomb-Scargle spectrum is accu- rate in detecting strong spectral peaks, but this assumption biases the description of slopes and background shapes in the spectrum [3], [4]. A second group of methods relies on estimation algorithms that have been developed for uninterrupted equidistant data.…”

Section: Introductionmentioning

confidence: 99%

Time-Series Analysis if Data Are Randomly Missing

Broersen

Bos

2006

IEEE Trans. Instrum. Meas.

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Abstract-Maximum-likelihood (ML) theory presents an elegant asymptotic solution for the estimation of the parameters of time-series models. Unfortunately, the performance of ML algorithms in finite samples is often disappointing, especially in missing-data problems. The likelihood function is symmetric with respect to the unit circle for the estimated zeros of time-series models. As a consequence, the unit circle is either a local maximum or a local minimum in the likelihood of moving-average (MA) models. This is a trap for nonlinear optimization algorithms that often converge to poor models, with estimated zeros precisely on the unit circle. With ML estimation, it is much easier to estimate a long autoregressive (AR) model with only poles. The parameters of that long AR model can then be used to estimate MA and autoregressive moving-average (ARMA) models for different model orders. The accuracy of the estimated AR, MA, and ARMA spectra is very good. The robustness is excellent as long as the AR order is less than 10 or 15. For still-higher AR orders until about 60, the possible convergence to a useful model will depend on the missing fraction and on the specific properties of the data at hand.

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A physics‐informed Bayesian framework for characterizing ground motion process in the presence of missing data

Chen

Patelli

Edwards

et al. 2023

Earthq Engng Struct Dyn

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A Bayesian framework to characterize ground motions even in the presence of missing data is developed. This approach features the combination of seismological knowledge (a priori knowledge) with empirical observations (even incomplete) via Bayesian inference. At its core is a Bayesian neural network model that probabilistically learns temporal patterns from ground motion data. Uncertainties are accounted for throughout the framework. Performance of the approach has been quantitatively demonstrated via various missing data scenarios. This framework provides a general solution to dealing with missing data in ground motion records by providing various forms of representation of ground motions in a probabilistic manner, allowing it to be adopted for numerous engineering and seismological applications. Notably, it is compatible with the versatile Monte Carlo simulation scheme, such that stochastic dynamic analyses are still achievable even with missing data. Furthermore, it serves as a complementary approach to current stochastic ground‐motion models in data‐scarce regions under the growing interests of PBEE (performance‐based earthquake engineering), mitigating the data‐model dependence dilemma due to the paucity of data, and ultimately, as a fundamental solution to the limited data problem in data scarce regions.

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Autoregressive spectral analysis when observations are missing

Cited by 50 publications

References 19 publications

Spectral Analysis of Irregularly Sampled Data with Time Series Models

Spectral Analysis of Irregularly Sampled Data with Time Series Models

Time-Series Analysis if Data Are Randomly Missing

A physics‐informed Bayesian framework for characterizing ground motion process in the presence of missing data

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