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OLS Limit Theory for Drifting Sequences of Parameters on the Explosive Side of Unity

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Abstract

A limit theory is developed for the least squares estimator for mildly and purely explosive autoregressions under drifting sequences of parameters with autoregressive roots ρn satisfying ρn → ρ ∈ (—∞, —1] ∪ [1, ∞) and n (|ρn| —1) → ∞. Drifting sequences of innovations and initial conditions are also considered. A standard specification of a short memory linear process for the autoregressive innovations is extended to a triangular array formulation both for the deterministic weights and for the primitive innovations of the linear process, which are allowed to be heteroskedastic L1-mixingales. The paper provides conditions that guarantee the validity of Cauchy limit distribution for the OLS estimator and standard Gaussian limit distribution for the t-statistic under this extended explosive and mildly explosive framework.

Suggested Citation

  • Tassos Magdalinos & Katerina Petrova, 2024. "OLS Limit Theory for Drifting Sequences of Parameters on the Explosive Side of Unity," Staff Reports 1113, Federal Reserve Bank of New York.
    • Handle: RePEc:fip:fednsr:98657
    DOI: 10.59576/sr.1113
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    Keywords

    triangular array; explosive autoregression; linear process; conditional heteroskedasticity; mixingale; Cauchy distribution;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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