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fdiff

Fast (Quasi-, Log-) Differences for Time Series and Panel Data

Description

fdiff is a S3 generic to compute (sequences of) suitably lagged / leaded and iterated differences, quasi-differences, log-differences or quasi-log-differences. The difference and log-difference operators D and Dlog also exists as parsimonious wrappers around fdiff, providing more flexibility than fdiff when applied to data frames.

Usage

fdiff(x, n = 1, diff = 1, ...)
      D(x, n = 1, diff = 1, ...)
   Dlog(x, n = 1, diff = 1, ...)

## Default S3 method:
fdiff(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, log = FALSE, rho = 1,
      stubs = TRUE, ...)
## Default S3 method:
D(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1,
  stubs = TRUE, ...)
## Default S3 method:
Dlog(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1, stubs = TRUE, ...)

## S3 method for class 'matrix'
fdiff(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, log = FALSE, rho = 1,
      stubs = length(n) + length(diff) > 2L, ...)
## S3 method for class 'matrix'
D(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1,
  stubs = TRUE, ...)
## S3 method for class 'matrix'
Dlog(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1, stubs = TRUE, ...)

## S3 method for class 'data.frame'
fdiff(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, log = FALSE, rho = 1,
      stubs = length(n) + length(diff) > 2L, ...)
## S3 method for class 'data.frame'
D(x, n = 1, diff = 1, by = NULL, t = NULL, cols = is.numeric,
  fill = NA, rho = 1, stubs = TRUE, keep.ids = TRUE, ...)
## S3 method for class 'data.frame'
Dlog(x, n = 1, diff = 1, by = NULL, t = NULL, cols = is.numeric,
     fill = NA, rho = 1, stubs = TRUE, keep.ids = TRUE, ...)

# Methods for compatibility with plm:

## S3 method for class 'pseries'
fdiff(x, n = 1, diff = 1, fill = NA, log = FALSE, rho = 1, stubs = TRUE, ...)
## S3 method for class 'pseries'
D(x, n = 1, diff = 1, fill = NA, rho = 1, stubs = TRUE, ...)
## S3 method for class 'pseries'
Dlog(x, n = 1, diff = 1, fill = NA, rho = 1, stubs = TRUE, ...)

## S3 method for class 'pdata.frame'
fdiff(x, n = 1, diff = 1, fill = NA, log = FALSE, rho = 1,
      stubs = length(n) + length(diff) > 2L, ...)
## S3 method for class 'pdata.frame'
D(x, n = 1, diff = 1, cols = is.numeric, fill = NA, rho = 1, stubs = TRUE,
  keep.ids = TRUE, ...)
## S3 method for class 'pdata.frame'
Dlog(x, n = 1, diff = 1, cols = is.numeric, fill = NA, rho = 1, stubs = TRUE,
     keep.ids = TRUE, ...)

# Methods for grouped data frame / compatibility with dplyr:

## S3 method for class 'grouped_df'
fdiff(x, n = 1, diff = 1, t = NULL, fill = NA, log = FALSE, rho = 1,
      stubs = length(n) + length(diff) > 2L, keep.ids = TRUE, ...)
## S3 method for class 'grouped_df'
D(x, n = 1, diff = 1, t = NULL, fill = NA, rho = 1, stubs = TRUE,
  keep.ids = TRUE, ...)
## S3 method for class 'grouped_df'
Dlog(x, n = 1, diff = 1, t = NULL, fill = NA, rho = 1, stubs = TRUE,
     keep.ids = TRUE, ...)

Arguments

`x`	a numeric vector / time series, (time series) matrix, data frame, panel series (`plm::pseries`), panel data frame (`plm::pdata.frame`) or grouped data frame (class 'grouped_df').
`n`	integer. A vector indicating the number of lags or leads.
`diff`	integer. A vector of integers > 1 indicating the order of differencing / log-differencing.
`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`.
`by`	data.frame method: Same as `g`, but also allows one- or two-sided formulas i.e. `~ group1` or `var1 + var2 ~ group1 + group2`. See Examples.
`t`	same input as `g/by`, to indicate the time-variable(s). For safe computation of differences on unordered time series and panels. Data Frame method also allows one-sided formula i.e. `~time`. grouped_df method supports lazy-evaluation i.e. `time` (no quotes).
`cols`	data.frame method: Select columns to difference using a function, column names, indices or a logical vector. Default: All numeric variables. Note: `cols` is ignored if a two-sided formula is passed to `by`.
`fill`	value to insert when vectors are shifted. Default is `NA`.
`log`	logical. `TRUE` computes log-differences instead. See Details.
`rho`	double. Autocorrelation parameter. Set to a value between 0 and 1 for quasi-differencing. Any numeric value can be supplied.
`stubs`	logical. `TRUE` will rename all differenced columns by adding prefixes "L`n`D`diff`." / "F`n`D`diff`." for differences "L`n`Dlog`diff`." / "F`n`Dlog`diff`." for log-differences and replacing "D" / "Dlog" with "QD" / "QDlog" for quasi-differences.
`keep.ids`	data.frame / pdata.frame / grouped_df methods: Logical. Drop all panel-identifiers from the output (which includes all variables passed to `by` or `t`). Note: For grouped / panel data frames identifiers are dropped, but the 'groups' / 'index' attributes are kept.
`...`	arguments to be passed to or from other methods.

Details

By default, fdiff/D/Dlog return x with all columns differenced / log-differenced. Differences are computed as repeat(diff) x[i] - rho*x[i-n], and log-differences as repeat(diff) log(x[i]) - rho*log(x[i-n]). If rho < 1, this becomes quasi- (or partial) differencing, which is a technique suggested by Cochrane and Orcutt (1949) to deal with serial correlation in regression models, where rho is typically estimated by running a regression of the model residuals on the lagged residuals. Setting diff = 2 returns differences of differences etc... and setting n = 2 returns simple differences computed by subtracting twice-lagged x from x. It is also possible to compute forward differences by passing negative n values. n also supports arbitrary vectors of integers (lags), and diff supports positive sequences of integers (differences):

If more than one value is passed to n and/or diff, the data is expanded-wide as follows: If x is an atomic vector or time series, a (time series) matrix is returned with columns ordered first by lag, then by difference. If x is a matrix or data frame, each column is expanded in like manor such that the output has ncol(x)*length(n)*length(diff) columns ordered first by column name, then by lag, then by difference.

With groups/panel-identifiers supplied to g/by, fdiff/D/Dlog efficiently compute panel-differences. If t is left empty, the data needs to be ordered such that all values belonging to a group are consecutive and in the right order. It is not necessary that the groups themselves occur in the right order. If time-variable(s) are supplied to t, the panel is fully identified and differences can be securely computed even if the data is unordered.

fdiff/D/Dlog supports balanced panels and unbalanced panels where various individuals are observed for different time-sequences. For computational details and efficiency considerations see the help page for flag.

It is also possible to compute differences on unordered vectors or irregular time series (thus utilizing t but leaving g/by empty).

The methods applying to plm objects (panel series and panel data frames) automatically utilize the panel-identifiers attached to these objects and thus securely compute fully identified panel-differences. If these objects have > 2 panel-identifiers attached to them, the last identifier is assumed to be the time-variable, and the others are taken as grouping-variables and interacted.

Value

x differenced diff times using lags n of itself. Quasi and log-differences are toggled by the rho and log arguments or the Dlog operator. Computations can be grouped by g/by and/or ordered by t. See Details and Examples.

References

Cochrane, D.; Orcutt, G. H. (1949). Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms. Journal of the American Statistical Association. 44 (245): 32-61.

Prais, S. J. & Winsten, C. B. (1954). Trend Estimators and Serial Correlation. Cowles Commission Discussion Paper No. 383. Chicago.

Examples

## Simple Time Series: AirPassengers
D(AirPassengers)                      # 1st difference, same as fdiff(AirPassengers)
D(AirPassengers, -1)                  # Forward difference
Dlog(AirPassengers)                   # Log-difference
D(AirPassengers, 1, 2)                # Second difference
Dlog(AirPassengers, 1, 2)             # Second log-difference
D(AirPassengers, 12)                  # Seasonal difference (data is monthly)
D(AirPassengers,                      # Quasi-difference, see a better example below
  rho = pwcor(AirPassengers, L(AirPassengers)))

head(D(AirPassengers, -2:2, 1:3))     # Sequence of leaded/lagged and iterated differences

# let's do some visual analysis
plot(AirPassengers)                   # Plot the series - seasonal pattern is evident
plot(stl(AirPassengers, "periodic"))  # Seasonal decomposition
plot(D(AirPassengers,c(1,12),1:2))    # Plotting ordinary and seasonal first and second differences
plot(stl(window(D(AirPassengers,12),  # Taking seasonal differences removes most seasonal variation
                1950), "periodic"))


## Time Series Matrix of 4 EU Stock Market Indicators, recorded 260 days per year
plot(D(EuStockMarkets, c(0, 260)))                      # Plot series and annual differnces
mod <- lm(DAX ~., L(EuStockMarkets, c(0, 260)))         # Regressing the DAX on its annual lag
summary(mod)                                            # and the levels and annual lags others
r <- residuals(mod)                                     # Obtain residuals
pwcor(r, L(r))                                          # Residual Autocorrelation
fFtest(r, L(r))                                         # F-test of residual autocorrelation
                                                        # (better use lmtest::bgtest)
modCO <- lm(QD1.DAX ~., D(L(EuStockMarkets, c(0, 260)), # Cochrane-Orcutt (1949) estimation
                        rho = pwcor(r, L(r))))
summary(modCO)
rCO <- residuals(modCO)
fFtest(rCO, L(rCO))                                     # No more autocorrelation

## World Development Panel Data
head(fdiff(num_vars(wlddev), 1, 1,                      # Computes differences of numeric variables
             wlddev$country, wlddev$year))              # fdiff requires external inputs..
head(D(wlddev, 1, 1, ~country, ~year))                  # Differences of numeric variables
head(D(wlddev, 1, 1, ~country))                         # Without t: Works because data is ordered
head(D(wlddev, 1, 1, PCGDP + LIFEEX ~ country, ~year))  # Difference of GDP & Life Expectancy
head(D(wlddev, 0:1, 1, ~ country, ~year, cols = 9:10))  # Same, also retaining original series
head(D(wlddev, 0:1, 1, ~ country, ~year, 9:10,          # Dropping id columns
       keep.ids = FALSE))

# Dynamic Panel Data Models:
summary(lm(D(PCGDP,1,1,iso3c,year) ~                    # Diff. GDP regressed on it's lagged level
             L(PCGDP,1,iso3c,year) +                    # and the difference of Life Expanctancy
             D(LIFEEX,1,1,iso3c,year), data = wlddev))

g = qF(wlddev$country)                                  # Omitting t and precomputing g allows for
summary(lm(D(PCGDP,1,1,g) ~ L(PCGDP,1,g) +              # a bit more parsimonious specification
                            D(LIFEEX,1,1,g), wlddev))

summary(lm(D1.PCGDP ~.,                                 # Now adding level and lagged level of
L(D(wlddev,0:1,1, ~ country, ~year,9:10),0:1,           # LIFEEX and lagged differences rates
  ~ country, ~year, keep.ids = FALSE)[-1]))
 
## Using plm can make things easier, but avoid attaching or 'with' calls:
pwlddev <- plm::pdata.frame(wlddev, index = c("country","year"))
head(D(pwlddev, 0:1, 1, 9:10))                          # Again differences of LIFEEX and PCGDP
PCGDP <- pwlddev$PCGDP                                  # A panel-Series of GDP per Capita
head(D(PCGDP))                                          # Differencing the panel series
summary(lm(D1.PCGDP ~.,                                 # Running the dynamic model again ->
           data = L(D(pwlddev,0:1,1,9:10),0:1,          # code becomes a bit simpler
                    keep.ids = FALSE)[-1]))

# One could be tempted to also do something like this, but THIS DOES NOT WORK!!:
# -> a pseries is only created when subsetting the pdata.frame using $ or [[
summary(lm(D(PCGDP) ~ L(D(PCGDP,0:1)) + L(D(LIFEEX,0:1),0:1), pwlddev))

# To make it work, one needs to create pseries
LIFEEX <- pwlddev$LIFEEX
summary(lm(D(PCGDP) ~ L(D(PCGDP,0:1)) + L(D(LIFEEX,0:1),0:1))) # THIS WORKS !

## Using dplyr:
library(dplyr)
wlddev %>% group_by(country) %>%
             select(PCGDP,LIFEEX) %>% fdiff(0:1,1:2)       # Adding a first and second difference
wlddev %>% group_by(country) %>%
             select(year,PCGDP,LIFEEX) %>% D(0:1,1:2,year) # Also using t (safer)
wlddev %>% group_by(country) %>%                           # Dropping id's
             select(year,PCGDP,LIFEEX) %>% D(0:1,1:2,year, keep.ids = FALSE)

collapse

Advanced and Fast Data Transformation

v1.5.3

GPL (>= 2) | file LICENSE

Authors

Sebastian Krantz [aut, cre], Matt Dowle [ctb], Arun Srinivasan [ctb], Laurent Berge [ctb], Dirk Eddelbuettel [ctb], Josh Pasek [ctb], Kevin Tappe [ctb], R Core Team and contributors worldwide [ctb], Martyn Plummer [cph], 1999-2016 The R Core Team [cph]

Initial release

2021-03-05