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1 results

  • On some nonstationary, nonlinear random processes and their stationary approximations

  • Part of
  • Suhasini Subba Rao
  • Journal:
    Advances in Applied Probability / Volume 38 / Issue 4 / December 2006
    Published online by Cambridge University Press:
    08 September 2016, pp. 1155-1172
    Print publication:
    December 2006
    • Article
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  • In this paper our object is to show that a certain class of nonstationary random processes can locally be approximated by stationary processes. The class of processes we are considering includes the time-varying autoregressive conditional heteroscedastic and generalised autoregressive conditional heteroscedastic processes, amongst others. The measure of deviation from stationarity can be expressed as a function of a derivative random process. This derivative process inherits many properties common to stationary processes. We also show that the derivative processes obtained here have alpha-mixing properties.