# crosscorr

Sample cross-correlation

## Syntax

## Description

`[`

returns the sample cross-correlation
function (XCF) `xcf`

,`lags`

] = crosscorr(`y1`

,`y2`

)`xcf`

and associated lags
`lags`

between the univariate time series
`y1`

and `y2`

.

returns the table `XCFTbl`

= crosscorr(`Tbl`

)`XCFTbl`

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

. To select different variables in
`Tbl`

, for which to compute the XCF, use the
`DataVariables`

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`

]
= crosscorr(___)`bounds`

on the
XCF.

`[___] = crosscorr(___,`

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

)```
crosscorr(Tbl,DataVariables=["RGDP"
"CPI"],NumLags=10,NumSTD=1.96)
```

returns the sample XCF for lags -10
through 10 of the table variables `"RGDP"`

and
`"CPI"`

in `Tbl`

and 95% confidence
bounds.

`crosscorr(___)`

plots the sample XCF between
the input series with confidence bounds.

`crosscorr(`

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 XCF between the input series and additionally returns handles
to plotted graphics objects. Use elements of `h`

]
= crosscorr(___)`h`

to modify
properties of the plot after you create it.

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

If

`y1`

and`y2`

have different lengths,`crosscorr`

appends enough zeros to the end of the shorter vector to make both vectors the same size.`crosscorr`

uses a Fourier transform (`fft`

) to compute the XCF in the frequency domain, and then`crosscorr`

converts back to the time domain using an inverse Fourier transform (`ifft`

).`NaN`

values in the input series result in`NaN`

values in the output XCF. Unlike`autocorr`

and`parcorr`

,`crosscorr`

does not treat`NaN`

values as*missing completely at random*. Whereas`autocorr`

and`parcorr`

compute coefficients in the time domain,`crosscorr`

uses`fft`

and`ifft`

to compute coefficients in the frequency domain. Therefore, missing data treatments follow`fft`

and`ifft`

defaults.`crosscorr`

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

## 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.

## Version History

**Introduced before R2006a**