Aidan Wardak, Sayar Karmakar
arXiv 24 Sep 2026 · Econometrics
arXiv:2609.30504 · PDF · Extracted main text
We derive the limiting distributions of the $M$-test family of unit root statistics in the nearly integrated nearly white noise (NINW) framework introduced by Nabeya and Perron (1994) in the case of an unknown linear time trend. In the case of known long run variance (LRV), the limiting distributions of the $M^{GLS}$ tests are contaminated by additional noise terms as a result of quasi differencing whereas these terms are less present in the $M^{OLS}$ limiting distributions, both of which display conservative properties under conventional critical values. Furthermore, we prove the Gaussian power envelope in the NINW model is asymptotically equivalent to the standard envelope of Elliott, Rothenberg, and Stock (1996), and that the oracle $M$-tests have inefficient power relative to this benchmark. We then derive the limiting distributions of the feasible statistics and show that the autoregressive estimate of the LRV commonly used overestimates the LRV, creating altered limiting distributions. Finally, finite sample simulations illustrate that, of the procedures considered, no uniformly satisfactory solution exists for handling a series with a large negative moving average coefficient.
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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 | Serena Ng and Pierre Perron (2001) Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power | 0.974 | 13 | 5 | 92% |
| 2 | Pierre Perron and Serena Ng (1996) Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties | 0.946 | 13 | 6 | 85% |
| 3 | Elliott, Graham and Rothenberg, Thomas J. and Stock, James H (1996) Efficient Tests for an Autoregressive Unit Root | 0.928 | 10 | 6 | 80% |
| 4 | Perron, Pierre and Ng, Serena (1998) AN AUTOREGRESSIVE SPECTRAL DENSITY ESTIMATOR AT FREQUENCY ZERO FOR NONSTATIONARITY TESTS | 0.874 | 5 | 2 | 100% |
| 5 | Seiji Nabeya and Pierre Perron (1994) Local asymptotic distribution related to the AR(1) model with dependent errors | 0.843 | 3 | 3 | 100% |
| 6 | Pierre Perron and Zhongjun Qu (2007) A simple modification to improve the finite sample properties of Ng and Perron's unit root tests | 0.811 | 4 | 2 | 100% |
| 7 | G. William Schwert (1989) Tests for Unit Roots: A Monte Carlo Investigation | 0.644 | 2 | 2 | 100% |
| 8 | Stock, James H (1990) A Class of Tests for Integration and Cointegration | 0.644 | 2 | 2 | 100% |
| 9 | Christos Agiakloglou and Paul Newbold (1992) Empirical evidence on Dickey–Fuller-type tests | 0.405 | 1 | 1 | 100% |
| 10 | Christos Agiakloglou and Paul Newbold (1996) The balance between size and power in Dickey–Fuller tests with data-dependent rules for the choice of truncation lag | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 22 scored citations.