Differencing with Log Transformation to Make Time Series Stationary

This function attempts to make a non-stationary time series stationary by applying differencing with a logarithmic transformation. It iteratively increases the differencing order until stationarity is achieved or informs the user if the transformation is not possible.

Usage

util_difflog_ts(.time_series)

Arguments

.time_series

A time series object to be made stationary.

Value

If the time series is already stationary or the differencing with a logarithmic transformation is successful,

Details

The function calculates the frequency of the input time series using the stats::frequency function and checks if the minimum value of the time series is greater than 0. It then applies differencing with a logarithmic transformation incrementally until the Augmented Dickey-Fuller test indicates stationarity (p-value < 0.05) or until the differencing order reaches the frequency of the data.

If differencing with a logarithmic transformation successfully makes the time series stationary, it returns the stationary time series and related information as a list with the following elements:

• stationary_ts: The stationary time series after the transformation.

• ndiffs: The order of differencing applied to make it stationary.

• adf_stats: Augmented Dickey-Fuller test statistics on the stationary time series.

• trans_type: Transformation type, which is "diff_log" in this case.

• ret: TRUE to indicate a successful transformation.

If the data either had a minimum value less than or equal to 0 or requires more differencing than its frequency allows, it informs the user and suggests trying double differencing with a logarithmic transformation.

See also

Other Utility: auto_stationarize(), calibrate_and_plot(), internal_ts_backward_event_tbl(), internal_ts_both_event_tbl(), internal_ts_forward_event_tbl(), model_extraction_helper(), ts_get_date_columns(), ts_info_tbl(), ts_is_date_class(), ts_lag_correlation(), ts_model_auto_tune(), ts_model_compare(), ts_model_rank_tbl(), ts_model_spec_tune_template(), ts_qq_plot(), ts_scedacity_scatter_plot(), ts_to_tbl(), util_doublediff_ts(), util_doubledifflog_ts(), util_log_ts(), util_singlediff_ts()

Author

Steven P. Sanderson II, MPH

Examples

# Example 1: Using a time series dataset
util_difflog_ts(AirPassengers)
#> Differencing of order 1 made the time series stationary
#> $stationary_ts
#>               Jan          Feb          Mar          Apr          May
#> 1949               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
#> 1954  0.014815086 -0.081678031  0.223143551 -0.034635497  0.030371098
#> 1955  0.055215723 -0.037899273  0.136210205  0.007462721  0.003710579
#> 1956  0.021353124 -0.024956732  0.134884268 -0.012698583  0.015848192
#> 1957  0.028987537 -0.045462374  0.167820466 -0.022728251  0.019915310
#> 1958  0.011834458 -0.066894235  0.129592829 -0.039441732  0.042200354
#> 1959  0.066021101 -0.051293294  0.171542423 -0.024938948  0.058840500
#> 1960  0.029199155 -0.064378662  0.069163360  0.095527123  0.023580943
#>               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
#> 1954  0.120627988  0.134477914 -0.030254408 -0.123344547 -0.123106058
#> 1955  0.154150680  0.144581229 -0.047829088 -0.106321592 -0.129875081
#> 1956  0.162204415  0.099191796 -0.019560526 -0.131769278 -0.148532688
#> 1957  0.172887525  0.097032092  0.004291852 -0.144914380 -0.152090098
#> 1958  0.180943197  0.121098097  0.028114301 -0.223143551 -0.118092489
#> 1959  0.116724274  0.149296301  0.019874186 -0.188422419 -0.128913869
#> 1960  0.125287761  0.150673346 -0.026060107 -0.176398538 -0.097083405
#>               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
#> 1954 -0.120516025  0.120516025
#> 1955 -0.145067965  0.159560973
#> 1956 -0.121466281  0.121466281
#> 1957 -0.129013003  0.096799383
#> 1958 -0.146750091  0.083510633
#> 1959 -0.117168974  0.112242855
#> 1960 -0.167251304  0.102278849
#> 
#> $ndiffs
#> [1] 1
#> 
#> $adf_stats
#> $adf_stats$test_stat
#> [1] -6.431315
#> 
#> $adf_stats$p_value
#> [1] 0.01
#> 
#> 
#> $trans_type
#> [1] "diff_log"
#> 
#> $ret
#> [1] TRUE
#> 

# Example 2: Using a different time series dataset
util_difflog_ts(BJsales)$ret
#> Data either had a minimum value less than or equal to 0, or requires more than
#> differencing than its frequency, trying double differencing log.
#> [1] FALSE