The analysis of indexed astronomical time series – I. Basic methods

Koen, C.; Lombard, F.

doi:10.1093/mnras/263.2.287

Cited by 36 publications

(34 citation statements)

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“…Wood & Zarro (1981) suggested that it was near the first peak in period following the onset of a thermal pulse and that the period change should cease and/or change sign over the next century. Koen & Lombard (1995) and Percy & Colivas (1999) confirmed that the period change in W Dra was real by analyzing times of maximum, and Greaves (2000) used the AMPSCAN (Howarth 1991) procedure to measure the period change in this star. He found that the period increased from about 255 days in the early part of the 20th century to about 280 days in the late 1970s, where it has remained since.…”

Section: W Dramentioning

confidence: 82%

“…Linear trends in period appear as parabolic curves in O À C, making the detection of period changes reasonably straightforward. This method was employed in the earliest work of Eddington and Plakidis in the 1920s and 1930s and continues to be employed today (see the series of papers by Koen & Lombard [1993], Percy & Au [1999], and Percy & Colivas [1999] for more details). The major limitation of such studies is that they require the measurement of times of maxima and minima-in effect, a ''preprocessing'' of the data.…”

Section: The Utility Of Wavelet Analysis For Deriving Rates Of Periodmentioning

confidence: 99%

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Secular Evolution in Mira Variable Pulsations

Templeton

Mattei

Willson

2005

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Stellar evolution theory predicts that asymptotic giant branch (AGB) stars undergo a series of short thermal pulses that significantly change their luminosity and mass on timescales of hundreds to thousands of years. These pulses are confirmed observationally by the existence of the short-lived radioisotope technetium in the spectra of some of these stars, but other observational consequences of thermal pulses are subtle and may only be detected over many years of observations. Secular changes in these stars resulting from thermal pulses can be detected as measurable changes in period if the star is undergoing Mira pulsations. It is known that a small fraction of Mira variables exhibit large secular period changes, and the detection of these changes among a larger sample of stars could therefore be useful in evolutionary studies of these stars. The American Association of Variable Star Observers (AAVSO) International Database currently contains visual data for over 1500 Mira variables. Light curves for these stars span nearly a century in some cases, making it possible to study the secular evolution of the pulsation behavior on these timescales. In this paper we present the results of our study of period change in 547 Mira variables using data from the AAVSO. We use wavelet analysis to measure the period changes in individual Mira stars over the span of available data. By making linear fits to the period versus time measurements, we determine the average rates of period change, d ln P/dt, for each of these stars. We find nonzero d ln P/dt at the 2 significance level in 57 of the 547 stars, at the 3 level in 21 stars, and at the level of 6 or greater in eight stars. The latter eight stars have been previously noted in the literature, and our derived rates of period change largely agree with published values. The largest and most statistically significant d ln P/dt are consistent with the rates of period change expected during thermal pulses on the AGB. A number of other stars exhibit nonmonotonic period change on decades-long timescales, the cause of which is not yet known. In the majority of stars, the period variations are smaller than our detection threshold, meaning the available data are not sufficient to unambiguously measure slow evolutionary changes in the pulsation period. It is unlikely that more stars with large period changes will be found among heretofore well-observed Mira stars in the short term, but continued monitoring of these and other Mira stars may reveal new and serendipitous candidates in the future.

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Section: W Dramentioning

confidence: 82%

Section: The Utility Of Wavelet Analysis For Deriving Rates Of Periodmentioning

confidence: 99%

Secular Evolution in Mira Variable Pulsations

Templeton

Mattei

Willson

2005

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“…The example observations analysed in Section 3 are in fact non‐stationary in variance, but the data can be divided into segments that are stationary.) This innocuous assumption has the important consequence that the sequences of residuals may be modelled as autoregressive moving average (ARMA) processes – see Koen & Lombard (1993, Paper I in this series). The most general form of an ARMA process is…”

Section: Methodsmentioning

confidence: 99%

The analysis of indexed astronomical time series - VI. Covariances of amplitude ratios and phase differences estimated from multicolour photometry of a pulsating star

Koen

2000

Monthly Notices of the Royal Astronomical Society

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One of the tools used to identify the pulsation modes of stars is a comparison of the amplitudes and phases as observed photometrically at different wavelengths. Proper application of the method requires that the errors on the measured quantities, and the correlations between them, be known (or at least estimated). It is assumed that contemporaneous measurements of the light intensity of a pulsating star are obtained in several wavebands. It is also assumed that the measurements are regularly spaced in time, although there may be missing observations. The amplitude and phase of the pulsation are estimated separately for each of the wavebands, and amplitude ratios and phase differences are calculated. A general scheme for estimating the covariance matrix of the amplitude ratios and phase differences is described. The first step is to fit a time series to the residuals after pre‐whitening the observations by the best‐fitting sinusoid. The residuals are then cross‐correlated to study the interdependence between the errors in the different wavebands. Once the multivariate time‐series structure can be modelled, the covariance matrix can be found by bootstrapping. An illustrative application is described in detail.

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“…Its mathematical foundations are treated in monographs such as Palma [22]. Autoregressive modeling is reviewed in the astronomical literature by Scargle [23], Koen and Lombard [24], and Caceres et al [submitted for publication].…”

Section: The Arma Arima and Arfima Modelsmentioning

confidence: 99%

Autoregressive Times Series Methods for Time Domain Astronomy

2018

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Celestial objects exhibit a wide range of variability in brightness at different wavebands. Surprisingly, the most common methods for characterizing time series in statistics-parametric autoregressive modeling-are rarely used to interpret astronomical light curves. We review standard ARMA, ARIMA, and ARFIMA (autoregressive moving average fractionally integrated) models that treat short-memory autocorrelation, long-memory 1/f α "red noise," and nonstationary trends. Though designed for evenly spaced time series, moderately irregular cadences can be treated as evenly-spaced time series with missing data. Fitting algorithms are efficient and software implementations are widely available. We apply ARIMA models to light curves of four variable stars, discussing their effectiveness for different temporal characteristics. A variety of extensions to ARIMA are outlined, with emphasis on recently developed continuous-time models like CARMA and CARFIMA designed for irregularly spaced time series. Strengths and weakness of ARIMA-type modeling for astronomical data analysis and astrophysical insights are reviewed.Keywords: time domain astronomy, irregularly sampled time series, variable stars, quasars, statistical methods, time series analysis, autoregressive modeling, ARIMA THE VARIABILITY OF COSMIC POPULATIONSExcept for five roving planets and an occasional comet or nova, the nighttime sky seems immutable to the human eye. The pattern and brightness of stars appears unchanging as from our childhood to old age. Myths from ancient Egyptian, Greek, and Australian Aboriginal cultures suggest that a few stars (such as Algol, Mira, and Aldeberan) were recognized as variables [1,2]. As telescopic studies proliferated from the seventeenth through twenty first centuries, more variable stars were found with a wide range of characteristics. Some are periodic due to pulsations, rotationally modulated spots, or eclipses of binary companions. Others vary in irregular ways from magnetic flares, eruptions, pulsations, accretion of gas from companions, and most spectacularly, nova and supernova explosions. Ten thousand stars in two dozen categories were cataloged by Kukarkin and Parenago [3]; this catalog now has over 50,000 stars with >100 classes [4]. NASA's Kepler mission has recently shown that most ordinary stars are variable when observed with ∼0.001% accuracy and dense cadences [5].The study of celestial objects with variable brightness has broadened hugely in recent decades, emerging as a recognized discipline called "time domain astronomy" [6]. The brightest sources in the X-ray and gamma-ray sky are highly variable, typically from accretion of gas onto neutron stars and black holes. Timescales range from milliseconds to decades with a bewildering range of

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The analysis of indexed astronomical time series – I. Basic methods

Cited by 36 publications

References 0 publications

Secular Evolution in Mira Variable Pulsations

Secular Evolution in Mira Variable Pulsations

The analysis of indexed astronomical time series - VI. Covariances of amplitude ratios and phase differences estimated from multicolour photometry of a pulsating star

Autoregressive Times Series Methods for Time Domain Astronomy

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