One-Dimensional Inference in Autoregressive Models With the Potential Presence of a Unit Root

Mikusheva, Anna

doi:10.3982/ecta9371

Cited by 32 publications

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References 35 publications

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“…We rule out the possibility that the data are generated by an I (2) process or a near-I(2) process or that the process is explosive. This assumption is standard in the literature (e.g., Mikusheva 2012). Assumption (i) also rules out complex near unit roots and roots near −1.…”

Section: Notation and Assumptionsmentioning

confidence: 99%

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The Uniform Validity of Impulse Response Inference in Autoregressions

Inoue

Kilian

2019

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Existing proofs of the asymptotic validity of conventional methods of impulse response inference based on higher-order autoregressions are pointwise only. In this paper, we establish the uniform asymptotic validity of conventional asymptotic and bootstrap inference about individual impulse responses and vectors of impulse responses when the horizon is fixed with respect to the sample size. For inference about vectors of impulse responses based on Wald test statistics to be uniformly valid, lag-augmented autoregressions are required, whereas inference about individual impulse responses is uniformly valid under weak conditions even without lag augmentation. We introduce a new rank condition that ensures the uniform validity of inference on impulse responses and show that this condition holds under weak conditions. Simulations show that the highest finite-sample accuracy is achieved when bootstrapping the lag-augmented autoregression using the bias adjustments of Kilian (1999). The conventional bootstrap percentile interval for impulse responses based on this approach remains accurate even at long horizons. We provide a formal asymptotic justification for this result.

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Section: Notation and Assumptionsmentioning

confidence: 99%

“…The largest process considered byMikusheva (2012) in her simulation analysis is an AR(2) process. Her method does not appear to have been applied to autoregressions with more lags.…”

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confidence: 99%

The Uniform Validity of Impulse Response Inference in Autoregressions

Inoue

Kilian

2019

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A bias-corrected fixed effects estimator in the dynamic panel data model

2021

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Hybrid stochastic local unit roots

Lieberman

Phillips

2020

Journal of Econometrics

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Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The …rst involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) speci…cations where departures shrink to zero as the sample size n ! 1. The second approach allows for stochastic departures from unity, leading to stochastic unit root (STUR) speci…cations. This paper introduces a hybrid local stochastic unit root (LSTUR) speci…cation that has both LUR and STUR components and allows for endogeneity in the time varying coe¢ cient that introduces structural elements to the autoregression. This hybrid model generates trajectories that, upon normalization, have non-linear di¤usion limit processes that link closely to models that have been studied in mathematical …nance, particularly with respect to option pricing. It is shown that some LSTUR parameterizations have a mean and variance which are the same as a random walk process but with a kurtosis exceeding 3, a feature which is consistent with much …nancial data. We develop limit theory and asymptotic expansions for the process and document how inference in LUR and STUR autoregressions is a¤ected asymptotically by ignoring one or the other component in the more general hybrid generating mechanism. In particular, we show how con…dence belts constructed from the LUR model are a¤ected by the presence of a STUR component in the generating mechanism. The import of these …ndings for empirical research are explored in an application to the spreads on US investment grade corporate debt.

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One-Dimensional Inference in Autoregressive Models With the Potential Presence of a Unit Root

Cited by 32 publications

References 35 publications

The Uniform Validity of Impulse Response Inference in Autoregressions

The Uniform Validity of Impulse Response Inference in Autoregressions

A bias-corrected fixed effects estimator in the dynamic panel data model

Hybrid stochastic local unit roots

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