Observed univariate time series for which the software computes
or plots the PACF, specified as a vector. The last element of `y`

contains
the most recent observation.

**Data Types: **`double`

Number of lags of the PACF that the software returns or plots,
specified as a positive integer.

For example, `parcorr(y,10)`

plots the PACF
for lags 0 through 10.

**Data Types: **`double`

AR order that specifies the number of lags beyond which the
theoretical PACF is effectively 0, specified as a nonnegative integer.

`numAR`

must be less than `numLags`

.

Specify `numAR`

to assess whether
the PACF is effectively 0 beyond lag `numAR`

. Specifically,
if `y`

is an AR(`numAR`

) process,
then:

The PACF coefficient estimates at lags greater than `numAR`

are
approximately mean 0, independently distributed Gaussian variates.

The standard errors of the estimated PACF coefficients
for lags greater than `numAR`

of a length *T* series
are $$1/\sqrt{T}$$ [1].

**Example: **`[~,~,bounds] = parcorr(y,[],5)`

**Data Types: **`double`

Number of standard deviations for the sample PACF estimation
error assuming that `y`

is an AR(`numAR`

),
specified as a positive scalar. For example, `parcorr(y,[],[],1.5)`

plots
the PACF with estimation error bounds 1.5 standard deviations away
from 0.

If the software estimates the PACF coefficient at of lag `numAR`

using `T`

observations,
then the confidence bounds are:

$$\pm \frac{numSTD}{\sqrt{T}}.$$

The default (`numSTD`

= 2) corresponds to approximate
95% confidence bounds.

**Data Types: **`double`