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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.
fdiff(x, n = 1, diff = 1, …)
D(x, n = 1, diff = 1, …)
Dlog(x, n = 1, diff = 1, …)# S3 method for default
fdiff(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, log = FALSE, rho = 1,
stubs = TRUE, …)
# S3 method for default
D(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1,
stubs = TRUE, …)
# S3 method for default
Dlog(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1, stubs = TRUE, …)
# S3 method for 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 matrix
D(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1,
stubs = TRUE, …)
# S3 method for matrix
Dlog(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1, stubs = TRUE, …)
# S3 method for 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 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 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 pseries
fdiff(x, n = 1, diff = 1, fill = NA, log = FALSE, rho = 1, stubs = TRUE, …)
# S3 method for pseries
D(x, n = 1, diff = 1, fill = NA, rho = 1, stubs = TRUE, …)
# S3 method for pseries
Dlog(x, n = 1, diff = 1, fill = NA, rho = 1, stubs = TRUE, …)
# S3 method for pdata.frame
fdiff(x, n = 1, diff = 1, fill = NA, log = FALSE, rho = 1,
stubs = length(n) + length(diff) > 2L, …)
# S3 method for pdata.frame
D(x, n = 1, diff = 1, cols = is.numeric, fill = NA, rho = 1, stubs = TRUE,
keep.ids = TRUE, …)
# S3 method for 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 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 grouped_df
D(x, n = 1, diff = 1, t = NULL, fill = NA, rho = 1, stubs = TRUE,
keep.ids = TRUE, …)
# S3 method for grouped_df
Dlog(x, n = 1, diff = 1, t = NULL, fill = NA, rho = 1, stubs = TRUE,
keep.ids = TRUE, …)
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').
integer. A vector indicating the number of lags or leads.
integer. A vector of integers > 1 indicating the order of differencing / log-differencing.
data.frame method: Same as g, but also allows one- or two-sided formulas i.e. ~ group1 or var1 + var2 ~ group1 + group2. See Examples.
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).
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.
value to insert when vectors are shifted. Default is NA.
logical. TRUE computes log-differences instead. See Details.
double. Autocorrelation parameter. Set to a value between 0 and 1 for quasi-differencing. Any numeric value can be supplied.
logical. TRUE will rename all differenced columns by adding prefixes "LnDdiff." / "FnDdiff." for differences "LnDlogdiff." / "FnDlogdiff." for log-differences and replacing "D" / "Dlog" with "QD" / "QDlog" for quasi-differences.
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.
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.
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.
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.
flag/L/F, fgrowth/G, Time Series and Panel Series, Collapse Overview
# NOT RUN {
## 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$country) # Omitting t and precomputing g allows for
summary(lm(D(PCGDP,1,1,g) ~ L(PCGDP,1,g) + # a bit more parsimonious specification
D(LIFEEX,1,1,g), wlddev))
summary(lm(D1.PCGDP ~., # Now adding level and lagged level of
L(D(wlddev,0:1,1, ~ country, ~year,9:10),0:1, # LIFEEX and lagged differences rates
~ country, ~year, keep.ids = FALSE)[-1]))
# }
# NOT RUN {
<!-- % No code relying on suggested package -->
## Using plm can make things easier, but avoid attaching or 'with' calls:
pwlddev <- plm::pdata.frame(wlddev, index = c("country","year"))
head(D(pwlddev, 0:1, 1, 9:10)) # Again differences of LIFEEX and PCGDP
PCGDP <- pwlddev$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)
# }
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