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The Adjustment of Prediction Intervals to Account for Errors in Parameter Estimation
Paul Kabaila,Zhisong He +1 more
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In this article, the authors measure the closeness of the coverage probability, conditional on all of the data, of the adjusted PI and 1-a by measuring the mean square of the difference between this conditional coverage probability and the standard approximate PI.Abstract:
Standard approximate 1-a prediction intervals (PIs) need to be adjusted to take account of the error in estimating the parameters This adjustment may be aimed at setting the (unconditional) probability that the PI includes the value being predicted equal to 1-a Alternatively, this adjustment may be aimed at setting the probability that the PI includes the value being predicted equal to 1-a, conditional on an appropriate statistic T For an autoregressive process of order p, it has been suggested that T consist of the last p observations We provide a new criterion by which both forms of adjustment can be compared on an equal footing This new criterion of performance is the closeness of the coverage probability, conditional on all of the data, of the adjusted PI and 1-a In this paper, we measure this closeness by the mean square of the difference between this conditional coverage probability and 1-a We illustrate the application of this new criterion to a Gaussian zero-mean autoregressive process of order 1-a and one-step-ahead prediction For this example, this comparison shows that the adjustment which is aimed at setting the coverage probability equal to 1-a conditional on the last observation is the better of the two adjustmentsread more
Citations
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The adjustment of prediction intervals to account for errors in parameter estimation
Paul Kabaila,Zhisong He +1 more
TL;DR: In this paper, the authors measure the closeness of the coverage probability, conditional on all of the data, of the adjusted PI and 1−−-α, by the mean square of the difference between this conditional coverage probability and 1 −−α.
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References
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Bootstrap Prediction Intervals for Autoregression
TL;DR: In this article, the nonparametric bootstrap is applied to the problem of prediction in autoregression, where an alternative representation for AR(p) series is used, allowing for bootstrap replicates generated backward in time.
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Wayne A. Fuller,David P. Hasza +1 more
TL;DR: In this paper, the prediction of the (n + s)th observation of the pth order autoregressive process is investigated and the mean square of the predictor error through terms of order n −1, conditional on Yn, Y n 1, 1, ε, δ n − p + 1, is obtained for the stationary normal process.
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The sampling distribution of forecasts from a first-order autoregression
TL;DR: In this paper, the conditional distribution of forecast errors given the final period observation is skewed towards the origin and this skewness is accentuated in the majority of cases by the statistical dependence between the parameter estimates and the tinal period observation.
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The adjustment of prediction intervals to account for errors in parameter estimation
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