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.

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 indexed data / compatibility with plm:

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

# S3 method for 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 pdata.frame
D(x, n = 1, diff = 1, cols = is.numeric, fill = NA, rho = 1, stubs = TRUE,
  shift = "time", keep.ids = TRUE, ...)
# S3 method for pdata.frame
Dlog(x, n = 1, diff = 1, cols = is.numeric, fill = NA, rho = 1, stubs = TRUE,
     shift = "time", 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, ...)

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.

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 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). 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.

Examples

## Simple Time Series: AirPassengers
D(AirPassengers)                      # 1st difference, same as fdiff(AirPassengers)
#>       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
#> 1949   NA    6   14   -3   -8   14   13    0  -12  -17  -15   14
#> 1950   -3   11   15   -6  -10   24   21    0  -12  -25  -19   26
#> 1951    5    5   28  -15    9    6   21    0  -15  -22  -16   20
#> 1952    5    9   13  -12    2   35   12   12  -33  -18  -19   22
#> 1953    2    0   40   -1   -6   14   21    8  -35  -26  -31   21
#>  [ reached getOption("max.print") -- omitted 7 rows ]
D(AirPassengers, -1)                  # Forward difference
#>      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
#> 1949  -6 -14   3   8 -14 -13   0  12  17  15 -14   3
#> 1950 -11 -15   6  10 -24 -21   0  12  25  19 -26  -5
#> 1951  -5 -28  15  -9  -6 -21   0  15  22  16 -20  -5
#> 1952  -9 -13  12  -2 -35 -12 -12  33  18  19 -22  -2
#> 1953   0 -40   1   6 -14 -21  -8  35  26  31 -21  -3
#>  [ reached getOption("max.print") -- omitted 7 rows ]
Dlog(AirPassengers)                   # Log-difference
#>               Jan          Feb          Mar          Apr          May
#> 1949           NA  0.052185753  0.112117298 -0.022989518 -0.064021859
#> 1950 -0.025752496  0.091349779  0.112477983 -0.043485112 -0.076961041
#> 1951  0.035091320  0.033901552  0.171148256 -0.088033349  0.053744276
#> 1952  0.029675768  0.051293294  0.069733338 -0.064193158  0.010989122
#> 1953  0.010256500  0.000000000  0.185717146 -0.004246291 -0.025863511
#>               Jun          Jul          Aug          Sep          Oct
#> 1949  0.109484233  0.091937495  0.000000000 -0.084557388 -0.133531393
#> 1950  0.175632569  0.131852131  0.000000000 -0.073203404 -0.172245905
#> 1951  0.034289073  0.111521274  0.000000000 -0.078369067 -0.127339422
#> 1952  0.175008910  0.053584246  0.050858417 -0.146603474 -0.090060824
#> 1953  0.059339440  0.082887660  0.029852963 -0.137741925 -0.116202008
#>               Nov          Dec
#> 1949 -0.134732594  0.126293725
#> 1950 -0.154150680  0.205443974
#> 1951 -0.103989714  0.128381167
#> 1952 -0.104778951  0.120363682
#> 1953 -0.158901283  0.110348057
#>  [ reached getOption("max.print") -- omitted 7 rows ]
D(AirPassengers, 1, 2)                # Second difference
#>       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
#> 1949   NA   NA    8  -17   -5   22   -1  -13  -12   -5    2   29
#> 1950  -17   14    4  -21   -4   34   -3  -21  -12  -13    6   45
#> 1951  -21    0   23  -43   24   -3   15  -21  -15   -7    6   36
#> 1952  -15    4    4  -25   14   33  -23    0  -45   15   -1   41
#> 1953  -20   -2   40  -41   -5   20    7  -13  -43    9   -5   52
#>  [ reached getOption("max.print") -- omitted 7 rows ]
Dlog(AirPassengers, 1, 2)             # Second log-difference
#>                Jan           Feb           Mar           Apr           May
#> 1949            NA            NA  0.0599315450 -0.1351068163 -0.0410323405
#> 1950 -0.1520462214  0.1171022747  0.0211282048 -0.1559630954 -0.0334759292
#> 1951 -0.1703526544 -0.0011897681  0.1372467045 -0.2591816057  0.1417776255
#> 1952 -0.0987053985  0.0216175262  0.0184400436 -0.1339264957  0.0751822792
#> 1953 -0.1101071821 -0.0102565002  0.1857171458 -0.1899634367 -0.0216172197
#>                Jun           Jul           Aug           Sep           Oct
#> 1949  0.1735060916 -0.0175467375 -0.0919374953 -0.0845573880 -0.0489740046
#> 1950  0.2525936098 -0.0437804375 -0.1318521311 -0.0732034040 -0.0990425008
#> 1951 -0.0194552025  0.0772322010 -0.1115212744 -0.0783690671 -0.0489703553
#> 1952  0.1640197884 -0.1214246638 -0.0027258289 -0.1974618914  0.0565426503
#> 1953  0.0852029504  0.0235482200 -0.0530346967 -0.1675948883  0.0215399175
#>                Nov           Dec
#> 1949 -0.0012012013  0.2610263193
#> 1950  0.0180952250  0.3595946540
#> 1951  0.0233497089  0.2323708802
#> 1952 -0.0147181273  0.2251426335
#> 1953 -0.0426992749  0.2692493398
#>  [ reached getOption("max.print") -- omitted 7 rows ]
D(AirPassengers, 12)                  # Seasonal difference (data is monthly)
#>      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
#> 1949  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
#> 1950   3   8   9   6   4  14  22  22  22  14  10  22
#> 1951  30  24  37  28  47  29  29  29  26  29  32  26
#> 1952  26  30  15  18  11  40  31  43  25  29  26  28
#> 1953  25  16  43  54  46  25  34  30  28  20   8   7
#>  [ reached getOption("max.print") -- omitted 7 rows ]
D(AirPassengers,                      # Quasi-difference, see a better example below
  rho = pwcor(AirPassengers, L(AirPassengers)))
#>              Jan         Feb         Mar         Apr         May         Jun
#> 1949          NA  10.4581994  18.6970315   2.2543065  -2.8651096  18.8164476
#> 1950   1.6970315  15.5776155  20.0154743  -0.3874454  -4.6262775  28.9756690
#> 1951  10.5727493  10.7717760  33.9708028  -7.9146474  15.4882724  12.8465205
#> 1952  11.6076884  15.8067152  20.1649634  -4.3175671   9.2047687  42.2843794
#> 1953   9.7222383   7.8018490  47.8018490   8.3940631   3.3542577  23.1154256
#>              Jul         Aug         Sep         Oct         Nov         Dec
#> 1949  18.3737225   5.8911921  -6.1088079 -11.5864721 -10.2631631  18.1397566
#> 1950  26.9309974   6.7669098  -5.2330902 -18.7107544 -13.7058882  30.5378101
#> 1951  28.0853526   7.9212650  -7.0787350 -14.6758152  -9.5515330  25.8115814
#> 1952  20.6775667  21.1552309 -23.3671048  -9.6806814 -11.3971778  28.8465205
#> 1953  30.6727005  18.5086129 -24.1729443 -16.5661316 -22.6010707  28.1649634
#>  [ reached getOption("max.print") -- omitted 7 rows ]

head(D(AirPassengers, -2:2, 1:3))     # Sequence of leaded/lagged and iterated differences
#>      F2D1 F2D2 F2D3 FD1 FD2 FD3  -- D1  D2  D3 L2D1 L2D2 L2D3
#> [1,]  -20  -31  -69  -6   8  25 112 NA  NA  NA   NA   NA   NA
#> [2,]  -11   -5  -12 -14 -17 -12 118  6  NA  NA   NA   NA   NA
#> [3,]   11   38   77   3  -5 -27 132 14   8  NA   20   NA   NA
#> [4,]   -6    7   49   8  22  23 129 -3 -17 -25   11   NA   NA
#> [5,]  -27  -39  -19 -14  -1  12 121 -8  -5  12  -11  -31   NA
#>  [ reached getOption("max.print") -- omitted 1 row ]

# 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
#> 
#> Call:
#> lm(formula = DAX ~ ., data = L(EuStockMarkets, c(0, 260)))
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -224.33  -57.02  -12.40   51.51  359.96 
#> 
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -123.26123   59.74149  -2.063   0.0393 *  
#> L260.DAX      -0.02126    0.02151  -0.988   0.3232    
#> SMI            0.37415    0.01356  27.589   <2e-16 ***
#> L260.SMI       0.28186    0.01901  14.826   <2e-16 ***
#> CAC            0.52973    0.01544  34.305   <2e-16 ***
#> L260.CAC      -0.23401    0.02145 -10.911   <2e-16 ***
#> FTSE          -0.03944    0.01780  -2.215   0.0269 *  
#> L260.FTSE      0.02888    0.02182   1.324   0.1858    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 84.02 on 1592 degrees of freedom
#>   (260 observations deleted due to missingness)
#> Multiple R-squared:  0.9943,	Adjusted R-squared:  0.9942 
#> F-statistic: 3.94e+04 on 7 and 1592 DF,  p-value: < 2.2e-16
#> 
r <- residuals(mod)                                     # Obtain residuals
pwcor(r, L(r))                                          # Residual Autocorrelation
#> [1] .97
fFtest(r, L(r))                                         # F-test of residual autocorrelation
#>     R-Sq.       DF1       DF2   F-Stat.   P-value 
#>     0.937         1      1597 23690.699     0.000 
                                                        # (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)
#> 
#> Call:
#> lm(formula = QD1.DAX ~ ., data = D(L(EuStockMarkets, c(0, 260)), 
#>     rho = pwcor(r, L(r))))
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -87.131  -9.079  -0.439   9.228 119.993 
#> 
#> Coefficients:
#>                 Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)   -17.979391   2.094867  -8.583   <2e-16 ***
#> QD1.L260.DAX    0.048116   0.034403   1.399    0.162    
#> QD1.SMI         0.343808   0.013902  24.731   <2e-16 ***
#> QD1.L260.SMI    0.014331   0.022530   0.636    0.525    
#> QD1.CAC         0.459655   0.024406  18.834   <2e-16 ***
#> QD1.L260.CAC   -0.031068   0.030598  -1.015    0.310    
#> QD1.FTSE        0.220516   0.020682  10.662   <2e-16 ***
#> QD1.L260.FTSE   0.007577   0.025948   0.292    0.770    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 19.06 on 1591 degrees of freedom
#>   (261 observations deleted due to missingness)
#> Multiple R-squared:  0.8582,	Adjusted R-squared:  0.8576 
#> F-statistic:  1376 on 7 and 1591 DF,  p-value: < 2.2e-16
#> 
rCO <- residuals(modCO)
fFtest(rCO, L(rCO))                                     # No more autocorrelation
#>    R-Sq.      DF1      DF2  F-Stat.  P-value 
#>    0.001        1     1596    2.326    0.127 

## World Development Panel Data
head(fdiff(num_vars(wlddev), 1, 1,                      # Computes differences of numeric variables
             wlddev$country, wlddev$year))              # fdiff requires external inputs..
#>   year decade PCGDP LIFEEX GINI        ODA    POP
#> 1   NA     NA    NA     NA   NA         NA     NA
#> 2    1      0    NA  0.516   NA  115310005 172437
#> 3    1      0    NA  0.509   NA -119240005 182031
#> 4    1      0    NA  0.500   NA  124880005 191764
#> 5    1      0    NA  0.492   NA   58200012 201576
#> 6    1      0    NA  0.485   NA   45919983 211539
head(D(wlddev, 1, 1, ~country, ~year))                  # Differences of numeric variables
#>       country year D1.decade D1.PCGDP D1.LIFEEX D1.GINI     D1.ODA D1.POP
#> 1 Afghanistan 1960        NA       NA        NA      NA         NA     NA
#> 2 Afghanistan 1961         0       NA     0.516      NA  115310005 172437
#> 3 Afghanistan 1962         0       NA     0.509      NA -119240005 182031
#> 4 Afghanistan 1963         0       NA     0.500      NA  124880005 191764
#> 5 Afghanistan 1964         0       NA     0.492      NA   58200012 201576
#> 6 Afghanistan 1965         0       NA     0.485      NA   45919983 211539
head(D(wlddev, 1, 1, ~country))                         # Without t: Works because data is ordered
#>       country D1.year D1.decade D1.PCGDP D1.LIFEEX D1.GINI     D1.ODA D1.POP
#> 1 Afghanistan      NA        NA       NA        NA      NA         NA     NA
#> 2 Afghanistan       1         0       NA     0.516      NA  115310005 172437
#> 3 Afghanistan       1         0       NA     0.509      NA -119240005 182031
#> 4 Afghanistan       1         0       NA     0.500      NA  124880005 191764
#> 5 Afghanistan       1         0       NA     0.492      NA   58200012 201576
#> 6 Afghanistan       1         0       NA     0.485      NA   45919983 211539
head(D(wlddev, 1, 1, PCGDP + LIFEEX ~ country, ~year))  # Difference of GDP & Life Expectancy
#>       country year D1.PCGDP D1.LIFEEX
#> 1 Afghanistan 1960       NA        NA
#> 2 Afghanistan 1961       NA     0.516
#> 3 Afghanistan 1962       NA     0.509
#> 4 Afghanistan 1963       NA     0.500
#> 5 Afghanistan 1964       NA     0.492
#> 6 Afghanistan 1965       NA     0.485
head(D(wlddev, 0:1, 1, ~ country, ~year, cols = 9:10))  # Same, also retaining original series
#>       country year PCGDP D1.PCGDP LIFEEX D1.LIFEEX
#> 1 Afghanistan 1960    NA       NA 32.446        NA
#> 2 Afghanistan 1961    NA       NA 32.962     0.516
#> 3 Afghanistan 1962    NA       NA 33.471     0.509
#> 4 Afghanistan 1963    NA       NA 33.971     0.500
#> 5 Afghanistan 1964    NA       NA 34.463     0.492
#> 6 Afghanistan 1965    NA       NA 34.948     0.485
head(D(wlddev, 0:1, 1, ~ country, ~year, 9:10,          # Dropping id columns
       keep.ids = FALSE))
#>   PCGDP D1.PCGDP LIFEEX D1.LIFEEX
#> 1    NA       NA 32.446        NA
#> 2    NA       NA 32.962     0.516
#> 3    NA       NA 33.471     0.509
#> 4    NA       NA 33.971     0.500
#> 5    NA       NA 34.463     0.492
#> 6    NA       NA 34.948     0.485

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

# Dynamic Panel Data Models:
summary(lm(D(PCGDP) ~ L(PCGDP) + D(LIFEEX), data = wldi))            # Simple case
#> 
#> Call:
#> lm(formula = D(PCGDP) ~ L(PCGDP) + D(LIFEEX), data = wldi)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -16807.5   -107.5    -51.7    109.4  12574.6 
#> 
#> Indexed by:  iso3c [5] | year [4 (61)] 
#> 
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  9.179e+01  1.340e+01   6.852 7.76e-12 ***
#> L(PCGDP)     8.893e-03  5.577e-04  15.945  < 2e-16 ***
#> D(LIFEEX)   -2.928e+01  2.393e+01  -1.224    0.221    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 828.2 on 8803 degrees of freedom
#>   (4370 observations deleted due to missingness)
#> Multiple R-squared:  0.02932,	Adjusted R-squared:  0.0291 
#> F-statistic: 132.9 on 2 and 8803 DF,  p-value: < 2.2e-16
#> 
summary(lm(Dlog(PCGDP) ~ L(log(PCGDP)) + Dlog(LIFEEX), data = wldi)) # In log-differneces
#> 
#> Call:
#> lm(formula = Dlog(PCGDP) ~ L(log(PCGDP)) + Dlog(LIFEEX), data = wldi)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -1.07097 -0.02055  0.00291  0.02570  0.85699 
#> 
#> Indexed by:  iso3c [5] | year [5 (61)] 
#> 
#> Coefficients:
#>                Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)   0.0095557  0.0037921   2.520   0.0118 *  
#> L(log(PCGDP)) 0.0007847  0.0004352   1.803   0.0714 .  
#> Dlog(LIFEEX)  0.5462310  0.0883588   6.182 6.61e-10 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.059 on 8803 degrees of freedom
#>   (4370 observations deleted due to missingness)
#> Multiple R-squared:  0.004326,	Adjusted R-squared:  0.0041 
#> F-statistic: 19.12 on 2 and 8803 DF,  p-value: 5.158e-09
#> 
# Adding a lagged difference...
summary(lm(D(PCGDP) ~ L(D(PCGDP, 0:1)) + L(D(LIFEEX), 0:1), data = wldi))
#> 
#> Call:
#> lm(formula = D(PCGDP) ~ L(D(PCGDP, 0:1)) + L(D(LIFEEX), 0:1), 
#>     data = wldi)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -17019.6    -92.5    -41.8     93.5  12148.9 
#> 
#> Indexed by:  iso3c [4] | year [5 (61)] 
#> 
#> Coefficients:
#>                         Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)            76.347493  13.265922   5.755 8.95e-09 ***
#> L(D(PCGDP, 0:1))L1.--   0.004958   0.000550   9.014  < 2e-16 ***
#> L(D(PCGDP, 0:1))L1.D1   0.320853   0.010302  31.144  < 2e-16 ***
#> L(D(LIFEEX), 0:1)--   -46.694289  35.322935  -1.322    0.186    
#> L(D(LIFEEX), 0:1)L1    19.980467  35.083154   0.570    0.569    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 789.4 on 8610 degrees of freedom
#>   (4561 observations deleted due to missingness)
#> Multiple R-squared:  0.1266,	Adjusted R-squared:  0.1262 
#> F-statistic:   312 on 4 and 8610 DF,  p-value: < 2.2e-16
#> 
summary(lm(Dlog(PCGDP) ~ L(Dlog(PCGDP, 0:1)) + L(Dlog(LIFEEX), 0:1), data = wldi))
#> 
#> Call:
#> lm(formula = Dlog(PCGDP) ~ L(Dlog(PCGDP, 0:1)) + L(Dlog(LIFEEX), 
#>     0:1), data = wldi)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -1.18359 -0.01869  0.00317  0.02277  1.04980 
#> 
#> Indexed by:  iso3c [5] | year [5 (61)] 
#> 
#> Coefficients:
#>                               Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)                  1.085e-02  3.656e-03   2.969 0.002998 ** 
#> L(Dlog(PCGDP, 0:1))L1.--     7.837e-05  4.190e-04   0.187 0.851614    
#> L(Dlog(PCGDP, 0:1))L1.Dlog1  2.703e-01  1.017e-02  26.570  < 2e-16 ***
#> L(Dlog(LIFEEX), 0:1)--      -9.415e-02  1.626e-01  -0.579 0.562630    
#> L(Dlog(LIFEEX), 0:1)L1       5.539e-01  1.616e-01   3.428 0.000611 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.05602 on 8610 degrees of freedom
#>   (4561 observations deleted due to missingness)
#> Multiple R-squared:  0.08161,	Adjusted R-squared:  0.08118 
#> F-statistic: 191.3 on 4 and 8610 DF,  p-value: < 2.2e-16
#> 
# Same thing:
summary(lm(D1.PCGDP ~., data = L(D(wldi,0:1,1,9:10),0:1,keep.ids = FALSE)[,-1]))
#> 
#> Call:
#> lm(formula = D1.PCGDP ~ ., data = L(D(wldi, 0:1, 1, 9:10), 0:1, 
#>     keep.ids = FALSE)[, -1])
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -16776.5   -102.2    -17.2     91.5  12277.1 
#> 
#> Indexed by:  iso3c [4] | year [5 (61)] 
#> 
#> Coefficients: (1 not defined because of singularities)
#>                Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  -3.339e+02  6.105e+01  -5.470 4.62e-08 ***
#> L1.PCGDP      2.522e-03  6.527e-04   3.864 0.000112 ***
#> L1.D1.PCGDP   3.171e-01  1.029e-02  30.815  < 2e-16 ***
#> LIFEEX       -1.777e+01  3.548e+01  -0.501 0.616397    
#> L1.LIFEEX     2.433e+01  3.538e+01   0.688 0.491595    
#> D1.LIFEEX            NA         NA      NA       NA    
#> L1.D1.LIFEEX  2.143e+01  3.499e+01   0.612 0.540244    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 787.3 on 8609 degrees of freedom
#>   (4561 observations deleted due to missingness)
#> Multiple R-squared:  0.1314,	Adjusted R-squared:  0.1309 
#> F-statistic: 260.4 on 5 and 8609 DF,  p-value: < 2.2e-16
#> 
 
## Grouped data
library(magrittr)
wlddev %>% fgroup_by(country) %>%
             fselect(PCGDP,LIFEEX) %>% fdiff(0:1,1:2)       # Adding a first and second difference
#>    PCGDP D1.PCGDP D2.PCGDP LIFEEX D1.LIFEEX D2.LIFEEX
#> 1     NA       NA       NA 32.446        NA        NA
#> 2     NA       NA       NA 32.962     0.516        NA
#> 3     NA       NA       NA 33.471     0.509    -0.007
#> 4     NA       NA       NA 33.971     0.500    -0.009
#> 5     NA       NA       NA 34.463     0.492    -0.008
#> 6     NA       NA       NA 34.948     0.485    -0.007
#> 7     NA       NA       NA 35.430     0.482    -0.003
#> 8     NA       NA       NA 35.914     0.484     0.002
#> 9     NA       NA       NA 36.403     0.489     0.005
#> 10    NA       NA       NA 36.900     0.497     0.008
#> 11    NA       NA       NA 37.409     0.509     0.012
#>  [ reached 'max' / getOption("max.print") -- omitted 13165 rows ]
#> 
#> Grouped by:  country  [216 | 61 (0)] 
wlddev %>% fgroup_by(country) %>%
             fselect(year,PCGDP,LIFEEX) %>% D(0:1,1:2,year) # Also using t (safer)
#>    year PCGDP D1.PCGDP D2.PCGDP LIFEEX D1.LIFEEX D2.LIFEEX
#> 1  1960    NA       NA       NA 32.446        NA        NA
#> 2  1961    NA       NA       NA 32.962     0.516        NA
#> 3  1962    NA       NA       NA 33.471     0.509    -0.007
#> 4  1963    NA       NA       NA 33.971     0.500    -0.009
#> 5  1964    NA       NA       NA 34.463     0.492    -0.008
#> 6  1965    NA       NA       NA 34.948     0.485    -0.007
#> 7  1966    NA       NA       NA 35.430     0.482    -0.003
#> 8  1967    NA       NA       NA 35.914     0.484     0.002
#> 9  1968    NA       NA       NA 36.403     0.489     0.005
#> 10 1969    NA       NA       NA 36.900     0.497     0.008
#>  [ reached 'max' / getOption("max.print") -- omitted 13166 rows ]
#> 
#> Grouped by:  country  [216 | 61 (0)] 
wlddev %>% fgroup_by(country) %>%                           # Dropping id's
             fselect(year,PCGDP,LIFEEX) %>% D(0:1,1:2,year, keep.ids = FALSE)
#>    PCGDP D1.PCGDP D2.PCGDP LIFEEX D1.LIFEEX D2.LIFEEX
#> 1     NA       NA       NA 32.446        NA        NA
#> 2     NA       NA       NA 32.962     0.516        NA
#> 3     NA       NA       NA 33.471     0.509    -0.007
#> 4     NA       NA       NA 33.971     0.500    -0.009
#> 5     NA       NA       NA 34.463     0.492    -0.008
#> 6     NA       NA       NA 34.948     0.485    -0.007
#> 7     NA       NA       NA 35.430     0.482    -0.003
#> 8     NA       NA       NA 35.914     0.484     0.002
#> 9     NA       NA       NA 36.403     0.489     0.005
#> 10    NA       NA       NA 36.900     0.497     0.008
#> 11    NA       NA       NA 37.409     0.509     0.012
#>  [ reached 'max' / getOption("max.print") -- omitted 13165 rows ]
#> 
#> Grouped by:  country  [216 | 61 (0)]