Uwe Hassler, Marc-Oliver Pohle, Tanja Zahn
arXiv 24 Mar 2025 · Econometrics
arXiv:2503.18560 · PDF · DOI · OpenAlex · Extracted main text
Sample autocorrelograms typically come with significance bands (non-rejection regions) for the null hypothesis of no temporal correlation. These bands have two shortcomings. First, they build on pointwise intervals and suffer from joint undercoverage (overrejection) under the null hypothesis. Second, if this null is clearly violated one would rather prefer to see confidence bands to quantify estimation uncertainty. We propose and discuss both simultaneous significance bands and simultaneous confidence bands for time series and series of regression residuals. They are as easy to construct as their pointwise counterparts and at the same time provide an intuitive and visual quantification of sampling uncertainty as well as valid statistical inference. For regression residuals, we show that for static regressions the asymptotic variances underlying the construction of the bands are the same as those for observed time series, and for dynamic regressions (with lagged endogenous regressors) we show how they need to be adjusted. We study theoretical properties of simultaneous significance bands and two types of simultaneous confidence bands (sup-t and Bonferroni) and analyse their finite-sample performance in a simulation study. Finally, we illustrate the use of the bands in an application to monthly US inflation and residuals from Phillips curve regressions.
appendix boundary found by appendix_command · 75% of the source is main text. Read the extracted text to check this.
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 | Mélard, G. and R. Roy (1987) On confidence intervals and tests for autocorrelations | 1.000 | 6 | 3 | 100% |
| 2 | Montiel Olea, J. L. and M. Plagborg-Mller (2019) Simultaneous confidence bands: Theory, implementation, and an application to SVARs | 0.941 | 6 | 4 | 83% |
| 3 | Cumby, R. E. and J. Huizinga (1992) Testing the autocorrelation structure of disturbances in ordinary least squares and instrumental variables regressions | 0.843 | 5 | 3 | 60% |
| 4 | Box, G. E. P. and D. A. Pierce (1970) Distribution of residual autocorrelations in autoregressive-integrated moving average time series models | 0.843 | 3 | 3 | 100% |
| 5 | Ljung, G. M. and G. E. P. Box (1978) On a measure of lack of fit in time series models | 0.843 | 3 | 3 | 100% |
| 6 | Lazarus, E., D. J. Lewis, J. H. Stock, and M. W. Watson (2018) HAR inference: Recommendations for practice | 0.843 | 3 | 3 | 100% |
| 7 | Sidák, Z (1967) Rectangular confidence regions for the means of multivariate normal distributions | 0.737 | 3 | 3 | 67% |
| 8 | Brockwell, P. J. and R. A. Davis (1991) Time Series: Theory and Methods\/ (2nd ed.) | 0.737 | 3 | 2 | 100% |
| 9 | Inoue, A., Ò. Jordà, and G. M. Kuersteiner (2025) Inference for local projections | 0.737 | 3 | 2 | 100% |
| 10 | Bartlett, M. S (1946) On the theoretical specification and sampling properties of autocorrelated time-series | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 62 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Uncertainty Quantification in Forecast Comparisons | 0.511 | 2 | 2 |