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

psacf, pspacf and psccf compute (and by default plot) estimates of the auto-, partial auto- and cross- correlation or covariance functions for panel-vectors and plm::pseries. They are analogues to acf, pacf and ccf.

psacf(x, ...)
pspacf(x, ...)
psccf(x, y, ...)

# S3 method for default
psacf(x, g, t = NULL, lag.max = NULL, type = c("correlation", "covariance","partial"),
      plot = TRUE, gscale = TRUE, ...)
# S3 method for default
pspacf(x, g, t = NULL, lag.max = NULL, plot = TRUE, gscale = TRUE, ...)
# S3 method for default
psccf(x, y, g, t = NULL, lag.max = NULL, type = c("correlation", "covariance"),
      plot = TRUE, gscale = TRUE, ...)

# S3 method for pseries
psacf(x, lag.max = NULL, type = c("correlation", "covariance","partial"),
      plot = TRUE, gscale = TRUE, ...)
# S3 method for pseries
pspacf(x, lag.max = NULL, plot = TRUE, gscale = TRUE, ...)
# S3 method for pseries
psccf(x, y, lag.max = NULL, type = c("correlation", "covariance"),
      plot = TRUE, gscale = TRUE, ...)

# S3 method for 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 data.frame
pspacf(x, by, t = NULL, cols = is.numeric, lag.max = NULL,
       plot = TRUE, gscale = TRUE, ...)

 # S3 method for pdata.frame
psacf(x, cols = is.numeric, lag.max = NULL,
      type = c("correlation", "covariance","partial"), plot = TRUE, gscale = TRUE, ...)
# S3 method for pdata.frame
pspacf(x, cols = is.numeric, lag.max = NULL, plot = TRUE, gscale = TRUE, ...)

Arguments

x, y

a numeric vector, panel series (plm::pseries), data frame or panel data-frame (plm::pdata.frame).
g

a factor, GRP object, atomic vector (internally converted to factor) or a list of vectors / factors (internally converted to a GRP object) used to group x, y.
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

same input as g, to indicate the time-variable(s). For secure computations on unordered panel-vectors. Data frame method also allows one-sided formula i.e. ~time.
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 correlating this matrix with the series (x, y) using cor and pairwise-complete observations. This may require a lot of memory on large data, but is done because passing a sequence of lags to flag and thus calling flag and cor one time is 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.

Note

For plm::pseries and plm::pdata.frame, the first index variable is assumed to be the group-id and the second the time variable. If more than 2 index variables are attached to plm::pseries, the last one is taken as the time variable and the others are taken as group-id's and interacted.

The pdata.frame method only works for properly subsetted objects of class 'pdata.frame'. A list of 'pseries' will not work.

See also

Time Series and Panel Series, Collapse Overview

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
#> 6 Afghanistan   AFG 1966-01-01 1965   1960 South Asia Low income FALSE    NA
#>   LIFEEX GINI       ODA
#> 1 32.292   NA 114440000
#> 2 32.742   NA 233350000
#> 3 33.185   NA 114880000
#> 4 33.624   NA 236450000
#> 5 34.060   NA 302480000
#> 6 34.495   NA 370250000
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

#> Panel Series ACF computed without timevar: Assuming ordered data
pspacf(wlddev$PCGDP, wlddev$country)                            # Partial ACF

#> Panel Series ACF computed without timevar: Assuming ordered data
psccf(wlddev$PCGDP, wlddev$LIFEEX, wlddev$country)              # CCF with Life-Expectancy at Birth

#> Panel Series ACF computed without timevar: Assuming ordered data

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 plm:
pwlddev <- plm::pdata.frame(wlddev, index = c("country","year"))# Creating a Panel Data Frame
PCGDP <- pwlddev$PCGDP                                          # Panel Series  of GDP per Capita
LIFEEX <- pwlddev$LIFEEX                                        # Panel Series  of Life Expectancy
psacf(PCGDP)                                                    # Same as above, more parsimonious

pspacf(PCGDP)

psccf(PCGDP, LIFEEX)

psacf(pwlddev[c(9:10,12)])

pspacf(pwlddev[c(9:10,12)])