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The Unit-Root Revolution Revisited: Where Do Non-Standard Sampling Distributions and Related Conundrums Stem From?
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Journal Article
The Unit-Root Revolution Revisited: Where Do Non-Standard Sampling Distributions and Related Conundrums Stem From?
2025
Overview
The primary objective of the paper is twofold.
, to answer the question posed in the title by arguing that the conundrums: [C1] the non-standard sampling distributions, [C2] the low power of unit-root tests for
∈ [0.9, 1], and [C3] their size distortions, [C4] issues in handling
, and [C5] the framing of
and
in testing
= 1, as well as [C6] two competing parametrizations for the AR(1) models, (B)
=
+
+
, (C)
=
+
+
+
,
viewing these models as aPriori Postulated (aPP) stochastic difference equations driven by the error process
.
, to use R.A. Fisher’s model-based statistical perspective to unveil the statistical models implicit in each of the AR(1): (B)-(C) models, specified entirely in terms of probabilistic assumptions assigned to the observable process
underlying the data
, which is all that matters for inference. The key culprit behind [C1]–[C6] is the presumption that the AR(1) nests the unit root [UR(1)] model when
= 1, which is shown to belie Kolmogorov’s existence theorem as it relates to
. Fisher’s statistical perspective reveals that the statistical AR(1) and UR(1) models are grounded on (i) two distinct processes
, with (ii) different probabilistic assumptions and (iii) statistical parametrizations, (iv) rendering them
, and (v) their respective likelihood-based inferential components are free from conundrums [C1]–[C6]. The claims (i)–(v) are affirmed by analytical derivations, simulations, as well as proposing a non-stationary AR(1) model that nests the related UR(1) model, where testing
= 1 relies on likelihood-based tests free from conundrums [C1]–[C6].
Publisher
De Gruyter,Walter de Gruyter GmbH
