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Keywords:

  • Simultaneous confidence tubes;
  • time-varying AR models;
  • Gaussian approximation;
  • locally stationary approximation

The article considers simultaneous inference for a class of non-stationary autoregressive models where the model parameters are allowed to vary smoothly over time. Simultaneous confidence tubes with asymptotically correct coverage probabilities are constructed to assess the overall patterns and magnitudes of the parameter functions over time. Simulation studies are conducted, and a real time-series dataset is analyzed to demonstrate the usefulness of the proposed methodology.