Estimation of a time series model from unequally spaced data

By Peter M. Robinson. 1977

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Citations in the corpus

Trend analysis of climate time series: A review of methods (2019, background): “The persistence time, τ≥0, is the parameter of the AR(1) model for uneven spacing (Robinson, 1977; Mudelsee, 2002).”
Estimating Pearson's Correlation Coefficient with Bootstrap Confidence Interval from Serially Dependent Time Series (2003, background): “…Diego, CA, 467 p. APPENDIX A: BIVARIATE GAUSSIAN AND LOGNORMAL AUTOREGRESSIVE PROCESSES Let {X(i )} and {Y′(i )} be strictly stationary Gaussian AR(1) processes at discrete, monotonically increasing timest(i ) with arbitrary spacing (Robinson, 1977): X(1) = ²x(1)∼ N(0, 1), Y′(1) = ²y(1)∼ N(0, 1),”
REDFIT: estimating red-noise spectra directly from unevenly spaced paleoclimatic time series (2002, methodology): “A discrete AR1 process r for times ti ði 1⁄4 1; 2;y;NÞ with arbitrary spacing is given by (Robinson, 1977)”
TAUEST: a computer program for estimating persistence in unevenly spaced weather/climate time series (2002, methodology): “…sediment or ice cores) are usually unevenly spaced in time, a simple estimation of the AR(1) model via the autocorrelation coefficient r has to be replaced by fitting the AR(1) model (Robinson, 1977) xð1ÞBNð0; 1Þ; xðiÞ ¼ xði@1Þ exp @½tðiÞ@tði@1Þ =t þ eðiÞ; i ¼ 2;y; n; ð1Þ to the (scaled) data x.”
Asymptotic theory for nonparametric regression with spatial data (2011, methodology): “…observations from an underlying continuous model can be di¢ cult even in the time series case; from a rst-order stochastic di¤erential equation, Robinson (1977) derived a (time-varying autoregressive) model but this kind of outcome is di¢ cult to extend to higher-order models, or spatial…”
Correlation Testing in Time Series, Spatial and Cross-Sectional Data (2007, background): “The di¢ culties reported above will only be compounded, indeed it seems even hard to extend the model and estimate of Robinson (1977).”