Key points are not available for this paper at this time.
Let Yₜ satisfy the stochastic difference equation Yₜ = ᵖ₉ = ₁ⱼYₓ - ₉ + eₜ for t = 1, 2, , where the eₜ are independent identically distributed (0, ²) random variables and the initial conditions (Y- + ₁, Y- + ₂, , Y₀) are fixed constants. It is assumed the true, but unknown, roots m₁, m₂, , mₚ of mᵖ - ᵖ₉ = ₁ⱼm^p - j = 0 satisfy m₁ = m₂ = 1 and |mⱼ| < 1 for j = 3, 4, , p. Let denote the least squares estimator of = (₁, ₂, , ₚ) ' obtained by the least squares regression of Yₜ on Yₓ - ₁, Yₓ - ₂, , Yₓ - for t = 1, 2, , n. The asymptotic distributions of and of a test statistic designed to test the hypothesis that m₁ = m₂ = 1 are characterized. Analogous distributional results are obtained for models containing time trend and intercept terms. Estimated percentiles for these distributions are obtained by the Monte Carlo method.
Hasza et al. (Sat,) studied this question.