fdiff: Fast (Quasi-, Log-) Differences for Time Series and Panel...

In collapse: Advanced and Fast Data Transformation

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 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 = .op[["stub"]], ...)
## Default S3 method:
Dlog(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1, stubs = .op[["stub"]],
     ...)

## 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 = .op[["stub"]], ...)
## S3 method for class 'matrix'
Dlog(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, rho = 1, stubs = .op[["stub"]],
     ...)

## 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 = .op[["stub"]], 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 = .op[["stub"]], keep.ids = TRUE, ...)

# Methods for indexed data / compatibility with plm:

## S3 method for class 'pseries'
fdiff(x, n = 1, diff = 1, fill = NA, log = FALSE, rho = 1,
      stubs = length(n) + length(diff) > 2L, shift = "time", ...)
## S3 method for class 'pseries'
D(x, n = 1, diff = 1, fill = NA, rho = 1, stubs = .op[["stub"]], shift = "time", ...)
## S3 method for class 'pseries'
Dlog(x, n = 1, diff = 1, fill = NA, rho = 1, stubs = .op[["stub"]], shift = "time", ...)

## S3 method for class 'pdata.frame'
fdiff(x, n = 1, diff = 1, fill = NA, log = FALSE, rho = 1,
      stubs = length(n) + length(diff) > 2L, shift = "time", ...)
## S3 method for class 'pdata.frame'
D(x, n = 1, diff = 1, cols = is.numeric, fill = NA, rho = 1, stubs = .op[["stub"]],
  shift = "time", keep.ids = TRUE, ...)
## S3 method for class 'pdata.frame'
Dlog(x, n = 1, diff = 1, cols = is.numeric, fill = NA, rho = 1, stubs = .op[["stub"]],
     shift = "time", 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 = .op[["stub"]],
  keep.ids = TRUE, ...)
## S3 method for class 'grouped_df'
Dlog(x, n = 1, diff = 1, t = NULL, fill = NA, rho = 1, stubs = .op[["stub"]],
     keep.ids = TRUE, ...)

Arguments

x	a numeric vector / time series, (time series) matrix, data frame, 'indexed_series' ('pseries'), 'indexed_frame' ('pdata.frame') or grouped data frame ('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, or atomic vector / list of vectors (internally grouped with group) used to group x. Note that without t, all values in a group need to be consecutive and in the right order. See Details of flag.
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	a time vector or list of vectors. See flag.
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. 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 (default) 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.
shift	pseries / pdata.frame methods: character. "time" or "row". See flag for details.
keep.ids	data.frame / pdata.frame / grouped_df methods: Logical. Drop all identifiers from the output (which includes all variables passed to by or t using formulas). Note: For 'grouped_df' / 'pdata.frame' 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 log(x[i]) - rho*log(x[i-n]) for diff = 1 and repeat(diff-1) x[i] - rho*x[i-n] is used to compute subsequent differences (usually diff = 1 for log-differencing). 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. 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.

For further computational details and efficiency considerations see the help page of flag.

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.

See Also

flag/L/F, fgrowth/G, Time Series and Panel Series, Collapse Overview

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))

## Indexed computations:
wldi <- findex_by(wlddev, iso3c, year)

# Dynamic Panel Data Models:
summary(lm(D(PCGDP) ~ L(PCGDP) + D(LIFEEX), data = wldi))            # Simple case
summary(lm(Dlog(PCGDP) ~ L(log(PCGDP)) + Dlog(LIFEEX), data = wldi)) # In log-differneces
# Adding a lagged difference...
summary(lm(D(PCGDP) ~ L(D(PCGDP, 0:1)) + L(D(LIFEEX), 0:1), data = wldi))
summary(lm(Dlog(PCGDP) ~ L(Dlog(PCGDP, 0:1)) + L(Dlog(LIFEEX), 0:1), data = wldi))
# Same thing:
summary(lm(D1.PCGDP ~., data = L(D(wldi,0:1,1,9:10),0:1,keep.ids = FALSE)[,-1]))
 
## Grouped data
library(magrittr)
wlddev %>% fgroup_by(country) %>%
             fselect(PCGDP,LIFEEX) %>% fdiff(0:1,1:2)       # Adding a first and second difference
wlddev %>% fgroup_by(country) %>%
             fselect(year,PCGDP,LIFEEX) %>% D(0:1,1:2,year) # Also using t (safer)
wlddev %>% fgroup_by(country) %>%                           # Dropping id's
             fselect(year,PCGDP,LIFEEX) %>% D(0:1,1:2,year, keep.ids = FALSE)

collapse documentation built on Nov. 13, 2023, 1:08 a.m.