# Auto- and Cross- Covariance and Correlation Function Estimation for Panel Series

`psacf.Rd`

`psacf`

, `pspacf`

and `psccf`

compute (and by default plot) estimates of the auto-, partial auto- and cross- correlation or covariance functions for panel series. They are analogues to `acf`

, `pacf`

and `ccf`

.

## Usage

```
psacf(x, ...)
pspacf(x, ...)
psccf(x, y, ...)
# Default S3 method
psacf(x, g, t = NULL, lag.max = NULL, type = c("correlation", "covariance","partial"),
plot = TRUE, gscale = TRUE, ...)
# Default S3 method
pspacf(x, g, t = NULL, lag.max = NULL, plot = TRUE, gscale = TRUE, ...)
# Default S3 method
psccf(x, y, g, t = NULL, lag.max = NULL, type = c("correlation", "covariance"),
plot = TRUE, gscale = TRUE, ...)
# S3 method for class 'data.frame'
psacf(x, by, t = NULL, cols = is.numeric, lag.max = NULL,
type = c("correlation", "covariance","partial"), plot = TRUE, gscale = TRUE, ...)
# S3 method for class 'data.frame'
pspacf(x, by, t = NULL, cols = is.numeric, lag.max = NULL,
plot = TRUE, gscale = TRUE, ...)
# Methods for indexed data / compatibility with plm:
# S3 method for class 'pseries'
psacf(x, lag.max = NULL, type = c("correlation", "covariance","partial"),
plot = TRUE, gscale = TRUE, ...)
# S3 method for class 'pseries'
pspacf(x, lag.max = NULL, plot = TRUE, gscale = TRUE, ...)
# S3 method for class 'pseries'
psccf(x, y, lag.max = NULL, type = c("correlation", "covariance"),
plot = TRUE, gscale = TRUE, ...)
# S3 method for class 'pdata.frame'
psacf(x, cols = is.numeric, lag.max = NULL,
type = c("correlation", "covariance","partial"), plot = TRUE, gscale = TRUE, ...)
# S3 method for class 'pdata.frame'
pspacf(x, cols = is.numeric, lag.max = NULL, plot = TRUE, gscale = TRUE, ...)
```

## Arguments

- x, y
a numeric vector, 'indexed_series' ('pseries'), data frame or 'indexed_frame' ('pdata.frame').

- g
a factor,

`GRP`

object, or atomic vector / list of vectors (internally grouped with`group`

) used to group`x`

.- by
*data.frame method*: Same input as`g`

, but also allows one- or two-sided formulas using the variables in`x`

, i.e.`~ idvar`

or`var1 + var2 ~ idvar1 + idvar2`

.- t
a time vector or list of vectors. See

`flag`

.- cols
*data.frame method*: Select columns using a function, column names, indices or a logical vector.*Note*:`cols`

is ignored if a two-sided formula is passed to`by`

.- lag.max
integer. Maximum lag at which to calculate the acf. Default is

`2*sqrt(length(x)/ng)`

where`ng`

is the number of groups in the panel series / supplied to`g`

.- type
character. String giving the type of acf to be computed. Allowed values are "correlation" (the default), "covariance" or "partial".

- plot
logical. If

`TRUE`

(default) the acf is plotted.- gscale
logical. Do a groupwise scaling / standardization of

`x, y`

(using`fscale`

and the groups supplied to`g`

) before computing panel-autocovariances / correlations. See Details.- ...
further arguments to be passed to

`plot.acf`

.

## Details

If `gscale = TRUE`

data are standardized within each group (using `fscale`

) such that the group-mean is 0 and the group-standard deviation is 1. This is strongly recommended for most panels to get rid of individual-specific heterogeneity which would corrupt the ACF computations.

After scaling, `psacf`

, `pspacf`

and `psccf`

compute the ACF/CCF by creating a matrix of panel-lags of the series using `flag`

and then computing the covariance of this matrix with the series (`x, y`

) using `cov`

and pairwise-complete observations, and dividing by the variance (of `x, y`

). Creating the lag matrix may require a lot of memory on large data, but passing a sequence of lags to `flag`

and thus calling `flag`

and `cov`

one time is generally much faster than calling them `lag.max`

times. The partial ACF is computed from the ACF using a Yule-Walker decomposition, in the same way as in `pacf`

.

## Value

An object of class 'acf', see `acf`

. The result is returned invisibly if `plot = TRUE`

.

## Examples

```
## World Development Panel Data
head(wlddev) # See also help(wlddev)
#> country iso3c date year decade region income OECD PCGDP
#> 1 Afghanistan AFG 1961-01-01 1960 1960 South Asia Low income FALSE NA
#> 2 Afghanistan AFG 1962-01-01 1961 1960 South Asia Low income FALSE NA
#> 3 Afghanistan AFG 1963-01-01 1962 1960 South Asia Low income FALSE NA
#> 4 Afghanistan AFG 1964-01-01 1963 1960 South Asia Low income FALSE NA
#> 5 Afghanistan AFG 1965-01-01 1964 1960 South Asia Low income FALSE NA
#> LIFEEX GINI ODA POP
#> 1 32.446 NA 116769997 8996973
#> 2 32.962 NA 232080002 9169410
#> 3 33.471 NA 112839996 9351441
#> 4 33.971 NA 237720001 9543205
#> 5 34.463 NA 295920013 9744781
#> [ reached 'max' / getOption("max.print") -- omitted 1 rows ]
psacf(wlddev$PCGDP, wlddev$country, wlddev$year) # ACF of GDP per Capita
psacf(wlddev, PCGDP ~ country, ~year) # Same using data.frame method
psacf(wlddev$PCGDP, wlddev$country) # The Data is sorted, can omit t
pspacf(wlddev$PCGDP, wlddev$country) # Partial ACF
psccf(wlddev$PCGDP, wlddev$LIFEEX, wlddev$country) # CCF with Life-Expectancy at Birth
psacf(wlddev, PCGDP + LIFEEX + ODA ~ country, ~year) # ACF and CCF of GDP, LIFEEX and ODA
psacf(wlddev, ~ country, ~year, c(9:10,12)) # Same, using cols argument
pspacf(wlddev, ~ country, ~year, c(9:10,12)) # Partial ACF
## Using indexed data:
wldi <- findex_by(wlddev, iso3c, year) # Creating a indexed frame
PCGDP <- wldi$PCGDP # Indexed Series of GDP per Capita
LIFEEX <- wldi$LIFEEX # Indexed Series of Life Expectancy
psacf(PCGDP) # Same as above, more parsimonious
pspacf(PCGDP)
psccf(PCGDP, LIFEEX)
psacf(wldi[c(9:10,12)])
pspacf(wldi[c(9:10,12)])
```