arXiv 8 Jun 2026 · Econometrics
arXiv:2606.09531 · PDF · DOI · OpenAlex · Extracted main text
We generalize the convergence results of an explosive autoregression, pioneered in Anderson (1959), in three ways: First, we demonstrate that the centered least-squares estimator converges geometrically to a ratio of limits, even in settings where the innovations are correlated and not centered around zero. Secondly, we demonstrate that the requirement of independent innovations in Anderson (1959), Theorem 2.3, can be relaxed to $α$-mixing. Third, we provide an autocorrelation-robust feasible test statistic for the explosive parameter under Gaussian ARMA innovations.
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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 | Anderson, T (1959) On asymptotic distributions of estimates of parameters of stochastic difference equations | 0.928 | 20 | 6 | 80% |
| 2 | B. Nielsen (2005) Strong consistency results for least squares estimators in general vector autoregressions with deterministic terms | 0.928 | 4 | 3 | 100% |
| 3 | T.L. Lai and C.Z. Wei (1983) Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters | 0.644 | 2 | 2 | 100% |
| 4 | T.L. Lai and C.Z. Wei (1985) Asymptotic properties of multivariate weighted sums with applications to stochastic regression in linear dynamic systems | 0.644 | 2 | 2 | 100% |
| 5 | Billingsley, P (1979) Probability and Measure | 0.511 | 2 | 2 | 50% |
| 6 | Breiman, L (1968) Probability. | 0.511 | 2 | 2 | 50% |
| 7 | Doukhan, P (1994) Mixing: Properties and Examples | 0.511 | 2 | 2 | 50% |
| 8 | Fuller, W.A. and Hasza, D.P. and Goebel, J.J (1981) Estimation of the parameters of stochastic difference equations | 0.405 | 1 | 1 | 100% |
| 9 | P. Jeganathan (1988) On the strong approximation of the distributions of estimators in linear stochastic models, I and II: Stationary and explosive A… | 0.405 | 1 | 1 | 100% |
| 10 | B. Nielsen (2010) Analysis of coexplosive processes | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 17 scored citations.