Time Shift Between Time Series

This function computes an approximation to the time-shift between pairs of time series as the absolute time difference between pairs of observations in the time series x and y connected by the dynamic time warping path.

If the time series are long enough, the extremes of the warping path are trimmed (5% of the total path length each) to avoid artifacts due to early misalignments.

It returns a data frame with the modal, mean, median, minimum, maximum, quantiles 0.25 and 0.75, and standard deviation. The modal and the median are the most generally accurate time-shift descriptors.

This function requires scaled and detrended time series. Still, it might yield non-sensical results in case of degenerate warping paths. Plotting dubious results with [distantia_dtw_plot())] is always a good approach to identify these cases.

[distantia_dtw_plot())]: R:distantia_dtw_plot())

Usage

distantia_time_delay(
  tsl = NULL,
  distance = "euclidean",
  bandwidth = 1,
  two_way = FALSE
)

Arguments

tsl

(required, time series list) list of zoo time series. Default: NULL

distance

(optional, character vector) name or abbreviation of the distance method. Valid values are in the columns "names" and "abbreviation" of the dataset distances. Default: "euclidean".

bandwidth

(optional, numeric) Proportion of space at each side of the cost matrix diagonal (aka Sakoe-Chiba band) defining a valid region for dynamic time warping, used to control the flexibility of the warping path. This method prevents degenerate alignments due to differences in magnitude between time series when the data is not properly scaled. If 1 (default), DTW is unconstrained. If 0, DTW is fully constrained and the warping path follows the matrix diagonal. Recommended values may vary depending on the nature of the data. Ignored if lock_step = TRUE. Default: 1.

two_way

(optional, logical) If TRUE, the time shift between the time series pairs y and x is added to the results

Value

data frame

See also

Other distantia_support: distantia_aggregate(), distantia_boxplot(), distantia_cluster_hclust(), distantia_cluster_kmeans(), distantia_matrix(), distantia_model_frame(), distantia_spatial(), distantia_stats(), utils_block_size(), utils_cluster_hclust_optimizer(), utils_cluster_kmeans_optimizer(), utils_cluster_silhouette()

Examples

#load two long-term temperature time series
#local scaling to focus in shape rather than values
#polynomial detrending to make them stationary
tsl <- tsl_init(
  x = cities_temperature[
    cities_temperature$name %in% c("London", "Kinshasa"),
    ],
  name = "name",
  time = "time"
) |>
  tsl_transform(
    f = f_scale_local
  ) |>
  tsl_transform(
    f = f_detrend_poly,
    degree = 35 #data years
  )


if(interactive()){
  tsl_plot(
    tsl = tsl,
    guide = FALSE
  )
}

#compute shifts
df_shift <- distantia_time_delay(
  tsl = tsl,
  two_way = TRUE
)

df_shift
#>          x        y  distance units  min   q1 median     mean modal   q3  max
#> 1 Kinshasa   London euclidean  days  150  181    212  203.607   212  215  304
#> 2   London Kinshasa euclidean  days -150 -181   -212 -203.607  -212 -215 -304
#>         sd
#> 1 34.49699
#> 2 34.49699
#positive shift values indicate
#that the samples in Kinshasa
#are aligned with older samples in London.