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Sample autocorrelation

`autocorr(y)`

`autocorr(y,Name,Value)`

`acf = autocorr(___)`

```
[acf,lags,bounds]
= autocorr(___)
```

`autocorr(ax,___)`

```
[acf,lags,bounds,h]
= autocorr(___)
```

`autocorr(`

plots
the sample autocorrelation
function (ACF) of the univariate, stochastic time series `y`

)`y`

with
confidence bounds.

`autocorr(`

uses
additional options specified by one or more name-value pair arguments. For
example, `y`

,`Name,Value`

)`autocorr(y,'NumLags',10,'NumSTD',2)`

plots the sample
ACF of `y`

for `10`

lags and displays
confidence bounds consisting of `2`

standard errors.

returns the sample
ACF of `acf`

= autocorr(___)`y`

using any of the input arguments in the previous
syntaxes.

`autocorr(`

plots on the axes specified by `ax`

,___)`ax`

instead
of the current axes (`gca`

). `ax`

can precede any of the input
argument combinations in the previous syntaxes.

To plot the ACF without confidence bounds, set `'NumSTD',0`

.

If

`y`

is a fully observed series (that is, it does not contain any`NaN`

values), then`autocorr`

uses a Fourier transform to compute the ACF in the frequency domain, then converts back to the time domain using an inverse Fourier transform.If

`y`

is not fully observed (that is, it contains at least one`NaN`

value),`autocorr`

computes the ACF at lag*k*in the time domain, and includes in the sample average only those terms for which the cross product*y*_{t}*y*_{t+k}exists. Consequently, the effective sample size is a random variable.`autocorr`

plots the ACF when you do not request any output or when you request the fourth output.

[1] Box, G. E. P., G. M. Jenkins, and G. C.
Reinsel. *Time Series Analysis: Forecasting and Control*.
3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.

[2] Hamilton, J. D. *Time Series Analysis*.
Princeton, NJ: Princeton University Press, 1994.