fgrowth is a S3 generic to compute (sequences of) suitably lagged / leaded, iterated and compounded growth rates, obtained with via the exact method of computation or through log differencing. By default growth rates are provided in percentage terms, but any scale factor can be applied. The growth operator G is a parsimonious wrapper around fgrowth, and also provides more flexibility when applied to data frames.

fgrowth(x, n = 1, diff = 1, ...)
      G(x, n = 1, diff = 1, ...)

# S3 method for default
fgrowth(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA,
        logdiff = FALSE, scale = 100, power = 1, stubs = TRUE, ...)
# S3 method for default
G(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, logdiff = FALSE,
  scale = 100, power = 1, stubs = TRUE, ...)

# S3 method for matrix
fgrowth(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA,
        logdiff = FALSE, scale = 100, power = 1,
        stubs = length(n) + length(diff) > 2L, ...)
# S3 method for matrix
G(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA, logdiff = FALSE,
  scale = 100, power = 1, stubs = TRUE, ...)

# S3 method for data.frame
fgrowth(x, n = 1, diff = 1, g = NULL, t = NULL, fill = NA,
        logdiff = FALSE, scale = 100, power = 1,
        stubs = length(n) + length(diff) > 2L, ...)
# S3 method for data.frame
G(x, n = 1, diff = 1, by = NULL, t = NULL, cols = is.numeric,
  fill = NA, logdiff = FALSE, scale = 100, power = 1, stubs = TRUE,
  keep.ids = TRUE, ...)

# Methods for indexed data / compatibility with plm:

# S3 method for pseries
fgrowth(x, n = 1, diff = 1, fill = NA, logdiff = FALSE, scale = 100,
        power = 1, stubs = length(n) + length(diff) > 2L, shift = "time", ...)
# S3 method for pseries
G(x, n = 1, diff = 1, fill = NA, logdiff = FALSE, scale = 100,
  power = 1, stubs = TRUE, shift = "time", ...)

# S3 method for pdata.frame
fgrowth(x, n = 1, diff = 1, fill = NA, logdiff = FALSE, scale = 100,
        power = 1, stubs = length(n) + length(diff) > 2L, shift = "time", ...)
# S3 method for pdata.frame
G(x, n = 1, diff = 1, cols = is.numeric, fill = NA, logdiff = FALSE,
  scale = 100, power = 1, stubs = TRUE, shift = "time", keep.ids = TRUE, ...)

# Methods for grouped data frame / compatibility with dplyr:

# S3 method for grouped_df
fgrowth(x, n = 1, diff = 1, t = NULL, fill = NA, logdiff = FALSE,
        scale = 100, power = 1, stubs = length(n) + length(diff) > 2L,
        keep.ids = TRUE, ...)
# S3 method for grouped_df
G(x, n = 1, diff = 1, t = NULL, fill = NA, logdiff = FALSE,
  scale = 100, power = 1, stubs = TRUE, 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 taking growth rates, e.g. diff = 2 means computing the growth rate of the growth rate.

g

a factor, GRP object, or atomic vector / list of vectors (internally grouped with group) 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

a time vector or list of vectors. See flag.

cols

data.frame method: Select columns to compute growth rates 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.

logdiff

logical. Compute log-difference growth rates instead of exact growth rates. See Details.

scale

logical. Scale factor post-applied to growth rates, default is 100 which gives growth rates in percentage terms. See Details.

power

numeric. Apply a power to annualize or compound growth rates e.g. fgrowth(AirPassengers, 12, power = 1/12) is equivalent to ((AirPassengers/flag(AirPassengers, 12))^(1/12)-1)*100.

stubs

logical. TRUE will rename all computed columns by adding a prefix "LnGdiff." / "FnGdiff.", or "LnDlogdiff." / "FnDlogdiff." if logdiff = TRUE.

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). 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

fgrowth/G by default computes exact growth rates using repeat(diff) ((x[i]/x[i-n])^power - 1)*scale, so for diff > 1 it computes growth rate of growth rates. If logdiff = TRUE, approximate growth rates are computed using log(x[i]/x[i-n])*scale for diff = 1 and repeat(diff-1) x[i] - x[i-n] thereafter (usually diff = 1 for log-differencing). For further details see the help pages of fdiff and flag.

Value

x where the growth rate was taken diff times using lags n of itself, scaled by scale. Computations can be grouped by g/by and/or ordered by t. See Details and Examples.

Examples

## Simple Time Series: AirPassengers
G(AirPassengers)                      # Growth rate, same as fgrowth(AirPassengers)
#>              Jan         Feb         Mar         Apr         May         Jun
#> 1949          NA   5.3571429  11.8644068  -2.2727273  -6.2015504  11.5702479
#> 1950  -2.5423729   9.5652174  11.9047619  -4.2553191  -7.4074074  19.2000000
#> 1951   3.5714286   3.4482759  18.6666667  -8.4269663   5.5214724   3.4883721
#> 1952   3.0120482   5.2631579   7.2222222  -6.2176166   1.1049724  19.1256831
#> 1953   1.0309278   0.0000000  20.4081633  -0.4237288  -2.5531915   6.1135371
#>              Jul         Aug         Sep         Oct         Nov         Dec
#> 1949   9.6296296   0.0000000  -8.1081081 -12.5000000 -12.6050420  13.4615385
#> 1950  14.0939597   0.0000000  -7.0588235 -15.8227848 -14.2857143  22.8070175
#> 1951  11.7977528   0.0000000  -7.5376884 -11.9565217  -9.8765432  13.6986301
#> 1952   5.5045872   5.2173913 -13.6363636  -8.6124402  -9.9476440  12.7906977
#> 1953   8.6419753   3.0303030 -12.8676471 -10.9704641 -14.6919431  11.6666667
#>  [ reached getOption("max.print") -- omitted 7 rows ]
G(AirPassengers, logdiff = TRUE)      # Log-difference
#>              Jan         Feb         Mar         Apr         May         Jun
#> 1949          NA   5.2185753  11.2117298  -2.2989518  -6.4021859  10.9484233
#> 1950  -2.5752496   9.1349779  11.2477983  -4.3485112  -7.6961041  17.5632569
#> 1951   3.5091320   3.3901552  17.1148256  -8.8033349   5.3744276   3.4289073
#> 1952   2.9675768   5.1293294   6.9733338  -6.4193158   1.0989122  17.5008910
#> 1953   1.0256500   0.0000000  18.5717146  -0.4246291  -2.5863511   5.9339440
#>              Jul         Aug         Sep         Oct         Nov         Dec
#> 1949   9.1937495   0.0000000  -8.4557388 -13.3531393 -13.4732594  12.6293725
#> 1950  13.1852131   0.0000000  -7.3203404 -17.2245905 -15.4150680  20.5443974
#> 1951  11.1521274   0.0000000  -7.8369067 -12.7339422 -10.3989714  12.8381167
#> 1952   5.3584246   5.0858417 -14.6603474  -9.0060824 -10.4778951  12.0363682
#> 1953   8.2887660   2.9852963 -13.7741925 -11.6202008 -15.8901283  11.0348057
#>  [ reached getOption("max.print") -- omitted 7 rows ]
G(AirPassengers, 1, 2)                # Growth rate of growth rate
#>                Jan           Feb           Mar           Apr           May
#> 1949            NA            NA   121.4689266  -119.1558442   172.8682171
#> 1950  -118.8861985  -476.2318841    24.4588745  -135.7446809    74.0740741
#> 1951   -84.3406593    -3.4482759   441.3333333  -145.1444623  -165.5214724
#> 1952   -78.0120482    74.7368421    37.2222222  -186.0900757  -117.7716390
#> 1953   -91.9400187  -100.0000000           Inf  -102.0762712   502.5531915
#>                Jun           Jul           Aug           Sep           Oct
#> 1949  -286.5702479   -16.7724868  -100.0000000          -Inf    54.1666667
#> 1950  -359.2000000   -26.5939597  -100.0000000          -Inf   124.1561181
#> 1951   -36.8217054   238.2022472  -100.0000000          -Inf    58.6231884
#> 1952  1630.8743169   -71.2188729    -5.2173913  -361.3636364   -36.8421053
#> 1953  -339.4468705    41.3580247   -64.9350649  -524.6323529   -14.7438216
#>                Nov           Dec
#> 1949     0.8403361  -206.7948718
#> 1950    -9.7142857  -259.6491228
#> 1951   -17.3961841  -238.6986301
#> 1952    15.5031995  -228.5801714
#> 1953    33.9227124  -179.4086022
#>  [ reached getOption("max.print") -- omitted 7 rows ]
G(AirPassengers, 12)                  # Seasonal growth rate (data is monthly)
#>             Jan        Feb        Mar        Apr        May        Jun
#> 1949         NA         NA         NA         NA         NA         NA
#> 1950  2.6785714  6.7796610  6.8181818  4.6511628  3.3057851 10.3703704
#> 1951 26.0869565 19.0476190 26.2411348 20.7407407 37.6000000 19.4630872
#> 1952 17.9310345 20.0000000  8.4269663 11.0429448  6.3953488 22.4719101
#> 1953 14.6198830  8.8888889 22.2797927 29.8342541 25.1366120 11.4678899
#>             Jul        Aug        Sep        Oct        Nov        Dec
#> 1949         NA         NA         NA         NA         NA         NA
#> 1950 14.8648649 14.8648649 16.1764706 11.7647059  9.6153846 18.6440678
#> 1951 17.0588235 17.0588235 16.4556962 21.8045113 28.0701754 18.5714286
#> 1952 15.5778894 21.6080402 13.5869565 17.9012346 17.8082192 16.8674699
#> 1953 14.7826087 12.3966942 13.3971292 10.4712042  4.6511628  3.6082474
#>  [ reached getOption("max.print") -- omitted 7 rows ]

head(G(AirPassengers, -2:2, 1:3))     # Sequence of leaded/lagged and iterated growth rates
#>            F2G1       F2G2       F2G3        FG1        FG2         FG3  --
#> [1,] -15.151515 -266.66667   77.97753  -5.084746  -52.05811   -90.63805 112
#> [2,]  -8.527132   91.86047 -285.94592 -10.606061 -556.06061   757.77959 118
#> [3,]   9.090909 -149.83165  -51.15620   2.325581  -64.82558   -60.41293 132
#> [4,]  -4.444444  -49.40171  -63.68691   6.611570 -163.75443 -1006.58997 129
#> [5,] -18.243243 -306.75676  330.09195 -10.370370   18.06268         NaN 121
#>             G1        G2        G3      L2G1       L2G2 L2G3
#> [1,]        NA        NA        NA        NA         NA   NA
#> [2,]  5.357143        NA        NA        NA         NA   NA
#> [3,] 11.864407  121.4689        NA 17.857143         NA   NA
#> [4,] -2.272727 -119.1558 -198.0957  9.322034         NA   NA
#> [5,] -6.201550  172.8682 -245.0774 -8.333333 -146.66667   NA
#>  [ reached getOption("max.print") -- omitted 1 row ]

# let's do some visual analysis
plot(G(AirPassengers, c(0, 1, 12)))

plot(stl(window(G(AirPassengers, 12), # Taking seasonal growth rate removes most seasonal variation
                1950), "periodic"))



## Time Series Matrix of 4 EU Stock Market Indicators, recorded 260 days per year
plot(G(EuStockMarkets,c(0,260)))                    # Plot series and annual growth rates

summary(lm(L260G1.DAX ~., G(EuStockMarkets,260)))   # Annual growth rate of DAX regressed on the
#> 
#> Call:
#> lm(formula = L260G1.DAX ~ ., data = G(EuStockMarkets, 260))
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -19.5094  -4.7763   0.4586   5.0337  18.2316 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  4.48795    0.38357   11.70  < 2e-16 ***
#> L260G1.SMI   0.37048    0.02635   14.06  < 2e-16 ***
#> L260G1.CAC   0.82319    0.02092   39.34  < 2e-16 ***
#> L260G1.FTSE -0.25008    0.03883   -6.44 1.58e-10 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 7.817 on 1596 degrees of freedom
#>   (260 observations deleted due to missingness)
#> Multiple R-squared:  0.8585,	Adjusted R-squared:  0.8582 
#> F-statistic:  3226 on 3 and 1596 DF,  p-value: < 2.2e-16
#> 
                                                    # growth rates of the other indicators

## World Development Panel Data
head(fgrowth(num_vars(wlddev), 1, 1,                    # Computes growth rates of numeric variables
             wlddev$country, wlddev$year))              # fgrowth requires external inputs..
#>         year decade PCGDP   LIFEEX GINI       ODA      POP
#> 1         NA     NA    NA       NA   NA        NA       NA
#> 2 0.05102041      0    NA 1.590335   NA  98.74969 1.916611
#> 3 0.05099439      0    NA 1.544202   NA -51.37884 1.985199
#> 4 0.05096840      0    NA 1.493830   NA 110.66998 2.050636
#> 5 0.05094244      0    NA 1.448294   NA  24.48259 2.112246
#> 6 0.05091650      0    NA 1.407306   NA  15.51770 2.170793
head(G(wlddev, 1, 1, ~country, ~year))                  # Growth of numeric variables, id's attached
#>       country year G1.decade G1.PCGDP G1.LIFEEX G1.GINI    G1.ODA   G1.POP
#> 1 Afghanistan 1960        NA       NA        NA      NA        NA       NA
#> 2 Afghanistan 1961         0       NA  1.590335      NA  98.74969 1.916611
#> 3 Afghanistan 1962         0       NA  1.544202      NA -51.37884 1.985199
#> 4 Afghanistan 1963         0       NA  1.493830      NA 110.66998 2.050636
#> 5 Afghanistan 1964         0       NA  1.448294      NA  24.48259 2.112246
#> 6 Afghanistan 1965         0       NA  1.407306      NA  15.51770 2.170793
head(G(wlddev, 1, 1, ~country))                         # Without t: Works because data is ordered
#>       country    G1.year G1.decade G1.PCGDP G1.LIFEEX G1.GINI    G1.ODA
#> 1 Afghanistan         NA        NA       NA        NA      NA        NA
#> 2 Afghanistan 0.05102041         0       NA  1.590335      NA  98.74969
#> 3 Afghanistan 0.05099439         0       NA  1.544202      NA -51.37884
#> 4 Afghanistan 0.05096840         0       NA  1.493830      NA 110.66998
#> 5 Afghanistan 0.05094244         0       NA  1.448294      NA  24.48259
#> 6 Afghanistan 0.05091650         0       NA  1.407306      NA  15.51770
#>     G1.POP
#> 1       NA
#> 2 1.916611
#> 3 1.985199
#> 4 2.050636
#> 5 2.112246
#> 6 2.170793
head(G(wlddev, 1, 1, PCGDP + LIFEEX ~ country, ~year))  # Growth of GDP per Capita & Life Expectancy
#>       country year G1.PCGDP G1.LIFEEX
#> 1 Afghanistan 1960       NA        NA
#> 2 Afghanistan 1961       NA  1.590335
#> 3 Afghanistan 1962       NA  1.544202
#> 4 Afghanistan 1963       NA  1.493830
#> 5 Afghanistan 1964       NA  1.448294
#> 6 Afghanistan 1965       NA  1.407306
head(G(wlddev, 0:1, 1, ~ country, ~year, cols = 9:10))  # Same, also retaining original series
#>       country year PCGDP G1.PCGDP LIFEEX G1.LIFEEX
#> 1 Afghanistan 1960    NA       NA 32.446        NA
#> 2 Afghanistan 1961    NA       NA 32.962  1.590335
#> 3 Afghanistan 1962    NA       NA 33.471  1.544202
#> 4 Afghanistan 1963    NA       NA 33.971  1.493830
#> 5 Afghanistan 1964    NA       NA 34.463  1.448294
#> 6 Afghanistan 1965    NA       NA 34.948  1.407306
head(G(wlddev, 0:1, 1, ~ country, ~year, 9:10,          # Dropping id columns
       keep.ids = FALSE))
#>   PCGDP G1.PCGDP LIFEEX G1.LIFEEX
#> 1    NA       NA 32.446        NA
#> 2    NA       NA 32.962  1.590335
#> 3    NA       NA 33.471  1.544202
#> 4    NA       NA 33.971  1.493830
#> 5    NA       NA 34.463  1.448294
#> 6    NA       NA 34.948  1.407306