Calculate cross-correlation coefficients for prewhitened time series

prewhitened_ccf() prewhitens time series, calculates cross-correlation coefficients, and returns statistically significant values.

Usage

prewhitened_ccf(
  input,
  output,
  input_col,
  output_col,
  keep_input = "both",
  keep_ccf = "both",
  max.order
)

Arguments

input

tsibble; The influential or "predictor-like" time series

output

tsibble; The affected or "response-like" time series

input_col

string; Name of the numeric column of the input tsibble

output_col

string; Name of the numeric column of the output tsibble

keep_input

string; values: "input_lags", "input_leads" or "both"; Default is "both".

keep_ccf

string; values: "positive", "negative", or "both; Default is "both"

max.order

integer; The maximum lag used in the CCF calculation.

Value

A tibble with the following columns:

• input_type: "lag" or "lead"

• input_series: lag or lead number

• signif_type: "Statistically Significant" or "Not Statistically Significant"

• signif_threshold: Threashold CCF value for statistical significance at the 95% level

• ccf: Calculated ccf value

Details

In a cross-correlation in which the direction of influence between two time-series is hypothesized or known,

• the influential time-series is called the "input" time-series

• the affected time-series is called the "output" time-series

The cross-correlation function calculates correlation values between lags and leads of the input series and the output series. Sometimes only correlations between the leads or lags of the input series and the output series make theoretical sense, or only positive or negative correlations make theoretical sense.

• The "keep_input" argument specifies whether you want to keep only output CCF values involving leads or lags of the input series or both.

• The "keep_ccf" argument specifies whether you want to keep only output positive, negative, or both CCF values.

prewhitened_ccf differences the series if it's needed, prewhitens, and outputs either statistically significant values of the CCF or the top non-statistically significant value if no statistically significant values are found. The prewhitening method that is used is from Cryer and Chan (2008, Chapter 11).

References

Cryer, D., Chan, K. (2008) Time Series Analysis, Springer Science+Business Media, LLC

Examples

oh_cases <- ohio_covid %>%
   dplyr::select(date, cases) %>%
   tsibble::as_tsibble(index = date)

oh_deaths <- ohio_covid %>%
   dplyr::select(date, deaths_lead0) %>%
   tsibble::as_tsibble(index = date)

oh_ccf_tbl <- prewhitened_ccf(input = oh_cases,
                              output = oh_deaths,
                              input_col = "cases",
                              output_col = "deaths_lead0",
                              max.order = 40,
                              keep_input = "input_lag",
                              keep_ccf = "positive")

oh_ccf_tbl
#> # A tibble: 1 × 5
#>   input_type input_series signif_type                   signif_thresh    ccf
#>   <chr>             <dbl> <chr>                                 <dbl>  <dbl>
#> 1 lag                   6 Not Statistically Significant         0.123 0.0772


library(dplyr, warn.conflicts = FALSE)

reg_cases_tsb <- us_regional_cases %>%
  tsibble::as_tsibble(index = date, key = region) %>%
  tsibble::group_by_key() %>%
  tidyr::nest() %>%
  arrange(region) %>%
  ungroup() %>%
  mutate(id = as.character(row_number()))

reg_deaths_tsb <- us_regional_deaths %>%
  tsibble::as_tsibble(index = date, key = region) %>%
  tsibble::group_by_key() %>%
  tidyr::nest() %>%
  arrange(region) %>%
  ungroup() %>%
  mutate(id = as.character(row_number()))

reg_ccf_vals <- purrr::map2_dfr(reg_cases_tsb$data,
                                reg_deaths_tsb$data,
                                prewhitened_ccf,
                                input_col = "reg_sev_day_cases",
                                output_col = "reg_sev_day_deaths",
                                max.order = 40,
                                .id = "id") %>%
  left_join(reg_cases_tsb %>%
             select(id, region), by = "id")

head(reg_ccf_vals)
#> # A tibble: 6 × 7
#>   id    input_type input_series signif_type          signif_thresh    ccf region
#>   <chr> <chr>             <dbl> <chr>                        <dbl>  <dbl> <chr> 
#> 1 1     lag                  28 Statistically Signi…         0.110  0.132 midwe…
#> 2 1     lag                  21 Statistically Signi…        -0.110 -0.137 midwe…
#> 3 1     lag                  19 Statistically Signi…         0.110  0.110 midwe…
#> 4 1     lag                  18 Statistically Signi…         0.110  0.125 midwe…
#> 5 1     lag                  14 Statistically Signi…        -0.110 -0.110 midwe…
#> 6 1     lag                   0 Statistically Signi…         0.110  0.222 midwe…