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Stationary and integrated autoregressive neural network processes.

A Trapletti1, F Leisch, K Hornik

  • 1Department of Operations Research, Vienna University of Economics and Business Administration, Austria.

Neural Computation
|October 14, 2000
PubMed
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Characteristic roots of autoregressive neural network (AR-NN) processes dictate their stochastic behavior. Roots outside the unit circle ensure stationarity, while roots inside lead to transient processes.

Area of Science:

  • Statistics
  • Machine Learning
  • Time Series Analysis

Background:

  • Autoregressive neural network (AR-NN) processes are increasingly used in time series analysis.
  • Understanding the stochastic behavior of these complex models is crucial for reliable inference.

Purpose of the Study:

  • To determine how the characteristic roots of AR-NN processes influence their stochastic behavior.
  • To analyze the properties of integrated AR-NN (ARI-NN) processes and their convergence.
  • To discuss estimation and nonstationarity testing for AR-NN models.

Main Methods:

  • Analysis of characteristic roots of AR-NN processes.
  • Investigation of conditions for ergodicity, stationarity, and transience.
  • Examination of integrated AR-NN (ARI-NN) processes and their convergence to Wiener processes.

Related Experiment Videos

  • Discussion of least-squares estimation and nonstationarity testing.

    • Main Results:

    • The stochastic behavior of AR-NN processes is determined by their characteristic roots.
    • Roots outside the unit circle imply ergodic and stationary processes.
    • Roots inside the unit circle indicate transient processes.
    • Roots on the unit circle lead to ergodic, random walk, or transient behavior.
    • Standardized ARI-NN processes converge to a Wiener process.
    • Least-squares estimators for stationary AR-NN models are consistent.

    Conclusions:

    • The characteristic roots provide a fundamental tool for understanding AR-NN process dynamics.
    • AR-NN models exhibit diverse behaviors (stationary, transient, random walk) based on root locations.
    • The convergence of ARI-NN processes to Wiener processes offers insights into their long-term behavior.
    • Consistent estimators and limiting distributions are established for stationary AR-NN models.