# parcorr

Sample partial autocorrelation

## Syntax

## Description

`[`

returns the sample partial autocorrelation function
(PACF) `pacf`

,`lags`

] = parcorr(`y`

)`pacf`

and associated lags `lags`

of the
univariate time series `y`

.

returns the table `PACFTbl`

= parcorr(`Tbl`

)`PACFTbl`

containing variables for the sample PACF
and associated lags of the last variable in the input table or timetable
`Tbl`

. To select a different variable in `Tbl`

,
for which to compute the PACF, use the `DataVariable`

name-value
argument.

`[___,`

uses any input-argument combination in the previous syntaxes, and returns the
output-argument combination for the corresponding input arguments and the approximate
upper and lower confidence bounds `bounds`

]
= parcorr(___)`bounds`

on the PACF.

`[___] = parcorr(___,`

uses additional options specified by one or more name-value arguments. For example,
`Name=Value`

)`parcorr(Tbl,DataVariable="RGDP",NumLags=10,NumSTD=1.96)`

returns 10
lags of the sample PACF of the table variable `"RGDP"`

in
`Tbl`

and 95% confidence bounds.

`parcorr(___)`

plots the sample PACF of the input
series with confidence bounds.

`parcorr(`

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.

`[___,`

plots the sample PACF of the input series and additionally returns handles to plotted
graphics objects. Use elements of `h`

]
= parcorr(___)`h`

to modify properties of the plot
after you create it.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

To plot the PACF without confidence bounds, set

`NumSTD=0`

.

## Algorithms

`parcorr`

plots the PACF when you do not request any output or when
you request the fourth output `h`

.

## References

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

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

## Version History

**Introduced before R2006a**