Eric Beutner, Alexander Heinemann, Stephan Smeekes
arXiv 2 Oct 2017 · Econometrics
arXiv:1710.00643 · PDF · Extracted main text
To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the unrealistic assumption of observing two independent processes, where one is used for parameter estimation, and the other for conditioning upon. Such unrealistic foundation raises the question whether these intervals are theoretically justified in a realistic setting. This paper presents an asymptotic justification for this type of intervals that does not require such an unrealistic assumption, but relies on a sample-split approach instead. By showing that our sample-split intervals coincide asymptotically with the standard intervals, we provide a novel, and realistic, justification for confidence intervals of conditional objects. The analysis is carried out for a rich class of time series models.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Phillips, P. C. B (1979) The sampling distribution of forecasts from a first-order autoregression | 1.000 | 6 | 3 | 100% |
| 2 | Lütkepohl, H (2005) New Introduction to Multiple Time Series Analysis | 0.811 | 4 | 2 | 100% |
| 3 | Kabaila, P (1999) The relevance property for prediction intervals | 0.737 | 3 | 2 | 100% |
| 4 | Kreiss, J.-P (2016) Discussion: bootstrap prediction intervals for linear, nonlinear and nonparametric autoregressions | 0.737 | 3 | 2 | 100% |
| 5 | Pan, L. and D. N. Politis (2016) Bootstrap prediction intervals for linear, nonlinear and nonparametric autoregressions | 0.737 | 3 | 2 | 100% |
| Vidoni | unmatched citation key Vidoni | 0.644 | 4 | 1 | 100% |
| 7 | Pesaran, M. H (2015) Time Series and Panel Data Econometrics | 0.644 | 2 | 2 | 100% |
| 8 | Samaranayake, V. A. and D. P. Hasza (1988) Properties of predictors for multivariate autoregressive models with estimated parameters | 0.644 | 2 | 2 | 100% |
| 9 | Dudley, R. M (2002) Real Analysis and Probability | 0.606 | 9 | 2 | 33% |
| Beutner | unmatched citation key Beutner | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 92 scored citations. 2 of these could not be matched to a bibliography entry, so only the citation key is shown.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Journal of Econometrics | 0.845 | 21 | 2 |
| 2 | A General Framework for Prediction in Time Series Models | 0.737 | 3 | 2 |
| 3 | V1 A Residual Bootstrap for Conditional Expected Shortfall | 0.585 | 3 | 1 |
| 4 | Lasso Inference for High-Dimensional Time Series | 0.405 | 1 | 1 |
| 5 | LASSO Inference for High Dimensional Predictive Regressions | 0.405 | 1 | 1 |