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Unit Roots

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Macroeconometrics and Time Series Analysis

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Abstract

Economic and financial time series have frequently been successfully modelled by autoregressive moving-average (ARMA) schemes of the type, where ε t is an orthogonal sequence (that is,E(ε t ) = 0, E(ε t ε1 s ) = 0 for all t ≠ s), L is the backshift operator for which Ly t = yt − 1 and a(L) b(L) are finite-order lag polynomials, whose leading coefficients are a0 = b0 = 1. Parsimonious schemes (often with p + q ≤ 3) are usually selected in practice either by informal ‘model identification’ processes such as those described in the text by Box and Jenkins (1976) or more formal order-selection criteria which penalize choices of large p and/or q. Model (1) is assumed to be irreducible, so that a(L) and b(L) have no common factors. The model (1) and the time series y t are said to have an autoregressive unit root if a(L) factors as (1 − L)a1(L) and a moving-average unit root if b(L) factors as (1 − L)a1(L)

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  1. Peter C. B. Phillips
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  1. University of Wisconsin-Madison, USA

    Steven N. Durlauf

  2. Cornell University, USA

    Lawrence E. Blume

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Phillips, P.C.B. (2010). Unit Roots. In: Durlauf, S.N., Blume, L.E. (eds) Macroeconometrics and Time Series Analysis. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280830_37

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