• Corpus ID: 251467998

Partial autocorrelation parameterisation of models with unit roots on the unit circle

  title={Partial autocorrelation parameterisation of models with unit roots on the unit circle},
  author={Jamie Halliday and Georgi N. Boshnakov},
Tiao and Tsay (1983) refer to this model as a nonstationary ARMAmodel. Huang and Anh (1990) call this model autoregressive unit root moving average (ARUMA), see also Woodward et al. (2017). Here {εt} is white noise, B is the backward shift operator and all roots of the polynomials φ(z) and θ(z) are outside the unit circle. The nonstationary part is specified by the polynomial U(z) = 1−U1z−U2z −· · ·−Udz d whose all roots have moduli 1 (i.e., lie on the unit circle). Traditionally the polynomial… 



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. Two methods for the estimation of the non-stationary factor in ARUMA models are given. Both methods yield strongly consistent estimators and the roots of the corresponding filters lie on the unit

Digital Processing of Random Signals: Theory and Methods

sarima: Simulation and Prediction with Seasonal ARIMA Models, 2022

  • URL https://CRAN.R-project.org/package=sarima. https://geobosh.github.io/sarima/ (doc)
  • 2022