<p>Hi: The expression tends to 1.0. The intuition is that, as <span class="math-container">$t$</span> gets larger and larger, the <span class="math-container">$h$</span> lags that seperate the two processes become more and more negligible and the processes begin to look the same. This happens because, as <span class="math-container">$t$</span> gets larger and larger, the proportion of observations common to both processes becomes larger and larger.</p>

CC BY-SA 4.0
2020-02-21T00:32:44.163Z
2020-02-21T00:32:44.163Z
mark leeds
<p>Given the random walk process <span class="math-container">$y_{t}=y_{t-1}+e_{t}$</span>, the auto correlation function is given by <span class="math-container">$corr(y_{t}, y_{t-h})=(\frac{t-h}{t})^{1/2}=(1-\frac{h}{t})^{1/2}$</span>, which tends to 0 as t tends to infinity. What is the intuition behind this result? </p>

<econometrics><time-series><stochastic-processes>
Limit of random walk auto correlation function
Bob Charles
# Limit of random walk auto correlation function

(Asked by: username_0 on 2020-02-20)

Given the random walk process $y\_{t}=y\_{t-1}+e\_{t}$, the auto correlation function is given by $corr(y\_{t}, y\_{t-h})=(\frac{t-h}{t})^{1/2}=(1-\frac{h}{t})^{1/2}$, which tends to 0 as t tends to infinity. What is the intuition behind this result?

**Tags:** econometrics, time-series, stochastic-processes


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## 1 answers

### Answer by username_1 on 2020-02-21. Score: 3

Hi: The expression tends to 1.0. The intuition is that, as $t$ gets larger and larger, the $h$ lags that seperate the two processes become more and more negligible and the processes begin to look the same. This happens because, as $t$ gets larger and larger, the proportion of observations common to both processes becomes larger and larger.


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