### Abstract

© 2014, Springer-Verlag Berlin Heidelberg. Suppose that $$Y_t$$Yt follows a simple AR(1) model, that is, it can be expressed as $$Y_t= \alpha Y_{t-1} + W_t$$Yt=αYt-1+Wt, where $$W_t$$Wt is a white noise with mean equal to $$\mu $$μ and variance $$\sigma ^2$$σ2. There are many examples in practice where these assumptions hold very well. Consider $$X_t = e^{Y_t}$$Xt=eYt. We shall show that the autocorrelation function of $$X_t$$Xt characterizes the distribution of $$W_t$$Wt.

Original language | English |
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Pages (from-to) | 219-225 |

Journal | Metrika |

Volume | 78 |

Issue number | 2 |

DOIs | |

Publication status | Published - 24 Jan 2015 |

### Keywords

- AR(1) models
- Characterization of distributions
- Time series

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## Cite this

Moriña, D., Puig, P., & Valero, J. (2015). A characterization of the innovations of first order autoregressive models.

*Metrika*,*78*(2), 219-225. https://doi.org/10.1007/s00184-014-0497-5