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A characterization of the innovations of first order autoregressive models

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  • D. Moriña
  • P. Puig
  • J. Valero

Abstract

Suppose that $$Y_t$$ Y t follows a simple AR(1) model, that is, it can be expressed as $$Y_t= \alpha Y_{t-1} + W_t$$ Y t = α Y t - 1 + W t , where $$W_t$$ W t is a white noise with mean equal to $$\mu $$ μ and variance $$\sigma ^2$$ σ 2 . There are many examples in practice where these assumptions hold very well. Consider $$X_t=e^{Y_t}$$ X t = e Y t . We shall show that the autocorrelation function of $$X_t$$ X t characterizes the distribution of $$W_t$$ W t . Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • D. Moriña & P. Puig & J. Valero, 2015. "A characterization of the innovations of first order autoregressive models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 219-225, February.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:2:p:219-225
    DOI: 10.1007/s00184-014-0497-5
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    References listed on IDEAS

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    1. Anderson, T. W. & Lockhart, R. A. & Stephens, M. A., 2004. "An omnibus test for the time series model AR(1)," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 111-127.
    2. Božidar Popović & Saralees Nadarajah & Miroslav Ristić, 2013. "A new non-linear AR(1) time series model having approximate beta marginals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 71-92, January.
    3. B. Abraham & N. Balakrishna, 1999. "Inverse Gaussian Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(6), pages 605-618, November.
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