A characterization of the innovations of first order autoregressive models

D. Moriña (), P. Puig and J. Valero

Metrika: International Journal for Theoretical and Applied Statistics, 2015, vol. 78, issue 2, 219-225

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

Keywords: Time series; AR(1) models; Characterization of distributions (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00184-014-0497-5

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