<p>Will the impulse response function and autocorrelation function of an AR(2) coincide? I say that they will not, because <span class="math-container">$IRF_{t}(t+k)$</span> (that is, the effect of a unit shock at time <span class="math-container">$t$</span>, on the process at <span class="math-container">$t+k$</span>) will be 1 when <span class="math-container">$k=0$</span>. However, <span class="math-container">$corr(y_{t}, y_{t})$</span> is the variance of the <span class="math-container">$y_t$</span> process, and will not necessarily be 1. Thank you.</p>

CC BY-SA 4.0
2021-05-22T13:31:02.913Z
Hi: The autocorrelation at lag zero is, by definition, the scaled variance   of $y_t$ which is 1.0. Recall that, in general,  the  auo-correlations at any lag are just scaled covariances; i.e: covariance divided by the variance and the covariance at lag zero is the variance.
mark leeds
CC BY-SA 4.0
2021-05-22T13:42:58.007Z
assume that there is no constant, so that the autocovariance at lag 2 is $E[y_{t+2}y_t]$ and verify your claim
Grada Gukovic
<econometrics><time-series>
IRF vs Autocorrelation function of AR(2)
Charles
# IRF vs Autocorrelation function of AR(2)

(Asked by: username_0 on 2021-05-21)

Will the impulse response function and autocorrelation function of an AR(2) coincide? I say that they will not, because $IRF\_{t}(t+k)$ (that is, the effect of a unit shock at time $t$, on the process at $t+k$) will be 1 when $k=0$. However, $corr(y\_{t}, y\_{t})$ is the variance of the $y\_t$ process, and will not necessarily be 1. Thank you.

**Tags:** econometrics, time-series

> **Comments:**
> **username_1**: Hi: The autocorrelation at lag zero is, by definition, the scaled variance   of $y_t$ which is 1.0. Recall that, in general,  the  auo-correlations at any lag are just scaled covariances; i.e: covariance divided by the variance and the covariance at lag zero is the variance.  
> **username_2**: assume that there is no constant, so that the autocovariance at lag 2 is $E[y_{t+2}y_t]$ and verify your claim  

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