A characterization of the innovations of first order autoregressive models
Tóm tắt
Suppose that
$$Y_t$$
follows a simple AR(1) model, that is, it can be expressed as
$$Y_t= \alpha Y_{t-1} + W_t$$
, where
$$W_t$$
is a white noise with mean equal to
$$\mu $$
and variance
$$\sigma ^2$$
. There are many examples in practice where these assumptions hold very well. Consider
$$X_t = e^{Y_t}$$
. We shall show that the autocorrelation function of
$$X_t$$
characterizes the distribution of
$$W_t$$
.
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