single differencing

[spsanderson]

Function:

util_singlediff_ts <- function(.time_series){
  
  time_series <- .time_series
  f <- stats::frequency(time_series)
  
  # Single Differencing
  diff_order <- 1
  while ((ts_adf_test(diff(time_series, diff_order))$p_value >= 0.05) & 
         (diff_order <= f)){
    diff_order <- diff_order + 1
  }
  
  if (diff_order <= f){
    rlang::inform(
      message = paste0("Differencing of order "
                       , diff_order
                       , " made the time series stationary"),
      use_cli_format = TRUE
    )
    # Return
    stationary_ts <- diff(time_series, diff_order)
    return(
      list(
        stationary_ts = stationary_ts,
        ndiffs = diff_order,
        adf_stats = ts_adf_test(stationary_ts),
        trans_type = "diff",
        ret = TRUE
      )
    )
  } else {
    rlang::inform(
      message = "Data requires more single differencing than its frequency, 
      trying double differencing",
      use_cli_format = TRUE
    )
    return(list(ret = FALSE))
  }
}

Examples:

> util_singlediff_ts(x)
Differencing of order 1 made the time series stationary
$stationary_ts
      Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
1949         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
1954    3  -16   47   -8    7   30   38   -9  -34  -30  -26   26
1955   13   -9   34    2    1   45   49  -17  -35  -38  -37   41
1956    6   -7   40   -4    5   56   39   -8  -50  -49  -35   35
1957    9  -14   55   -8    7   67   43    2  -63  -57  -42   31
1958    4  -22   44  -14   15   72   56   14 -101  -45  -49   27
1959   23  -18   64  -10   24   52   76   11  -96  -56  -45   43
1960   12  -26   28   42   11   63   87  -16  -98  -47  -71   42

$ndiffs
[1] 1

$adf_stats
$adf_stats$test_stat
[1] -7.318571

$adf_stats$p_value
[1] 0.01


$trans_type
[1] "diff"

> util_singlediff_ts(BJsales)
Data requires more single differencing than it's frequency, trying double differencing
[1] FALSE
> util_singlediff_ts(runif(150)*-1)
Differencing of order 1 made the time series stationary
$stationary_ts
  [1] -0.199334020 -0.405116486  0.590357560  0.166843754 -0.163220006 -0.533997485  0.095366330
  [8] -0.167604990  0.269771407  0.043851176 -0.238503639  0.545457803 -0.703349104  0.485737021
 [15]  0.424492740 -0.720034091  0.247324778  0.464171128 -0.968713508  0.720220389 -0.550252271
 [22]  0.255699790  0.362067311 -0.280077365 -0.377524094  0.735850255 -0.809971313  0.121800410
 [29]  0.444487421  0.150259752 -0.607661907  0.257703898  0.016731712 -0.157938169 -0.237527736
 [36]  0.768846860 -0.059804210 -0.259113024 -0.292553812  0.487359701  0.163451193 -0.516499517
 [43] -0.312687791  0.860701943 -0.250419705  0.062004191  0.124676413 -0.212882027 -0.391927560
 [50]  0.064205276 -0.280662073  0.758255146 -0.634289159  0.065316930  0.034516889  0.263628801
 [57] -0.464274600  0.456768314 -0.041977592  0.035204496  0.247522469  0.012192849 -0.488957954
 [64]  0.615057614 -0.642823332  0.286549293 -0.305455529  0.457831864  0.283263163 -0.781747269
 [71]  0.100599769 -0.109366291  0.714104377 -0.637413358  0.362123290  0.057238544 -0.471831386
 [78]  0.742285622 -0.815847773  0.259446705 -0.171638282  0.703008331 -0.527874797  0.619769761
 [85] -0.809977247  0.285991152 -0.299418453  0.247889457  0.158268320  0.213583108 -0.073844956
 [92] -0.184198547  0.272371987  0.094834895  0.057669017 -0.786592620  0.080256307 -0.214912091
 [99]  0.548541406 -0.050912870  0.177355615  0.008136612  0.157661706  0.073309486 -0.931609492
[106]  0.454148983 -0.307877811  0.406538821 -0.538995945  0.674232300 -0.580408069  0.009849190
[113]  0.271019108  0.452756844 -0.413571892 -0.137050760  0.166092831  0.068262939  0.051889502
[120] -0.424266676  0.265518842  0.186085937  0.362844683 -0.911294385 -0.042765180  0.370250624
[127] -0.285321412  0.357269767 -0.220633768  0.596657596 -0.533908903 -0.245580622  0.081047537
[134]  0.689387710 -0.587924560  0.443573975  0.086234805  0.013907032  0.026974607 -0.628625843
[141] -0.005484627  0.732938970  0.029198175 -0.742391955  0.488160006  0.050056203 -0.580750523
[148]  0.641111367 -0.313284928

$ndiffs
[1] 1

$adf_stats
$adf_stats$test_stat
[1] -5.76895

$adf_stats$p_value
[1] 0.01


$trans_type
[1] "diff"