# A characterization of the innovations of first order autoregressive models

D. Moriña, P. Puig, J. Valero

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

## 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 219-225 Metrika 78 2 https://doi.org/10.1007/s00184-014-0497-5 Published - 24 Jan 2015

## Keywords

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

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