conditional_ccf: Computing conditional cross-correlations at given lags

In PuwasalaG/conduits: CONDitional UI for Time Series normalisation

Computing conditional cross-correlations at given lags

Description

This function computes cross correlation between $x_t$ and $y_t+k$ at $k = 1,2,...$ conditional on a set of time series $z_t$

Usage

conditional_ccf(
  data,
  formula,
  lag_max = 10,
  fit_mean_x,
  fit_var_x,
  fit_mean_y,
  fit_var_y,
  df_correlation
)

Arguments

data	a tibble containing all the time series including ystar*xstar which are uniquely identified by the corresponding Timestamp.
formula	A GAM formula. The response variable should be in the format of I(x*y) ~ . See formula.gam.
lag_max	Maximum lag at which to calculate the conditional ccf
fit_mean_x	Model object of class "conditional_moment" returned from conditional_mean for series x
fit_var_x	Model object of class "conditional_moment" returned from conditional_var for series x
fit_mean_y	Model object of class "conditional_moment" returned from conditional_mean for series y
fit_var_y	Model object of class "conditional_moment" returned from conditional_var for series y
df_correlation	a vector specifying the degrees of freedom to be considered for each numerical predictor when fitting additive models for conditional cross-correlations. Each component of the vector should corresponds to the degrees of freedom each predictor.

Details

Suppose $x_t$ and $y_t$ are conditionally normalised with respect to $z_t$ using conditional_mean and conditional_var. Then we can estimate the conditional cross-correlation between $x_t$ and $y_t$ at lag $k$, i.e. $r_k = E(x_ty_t+k|z_t)$ via generalised additive models (GAM). conditional_ccf uses natural splines implemented in splines package to estimate the conditional cross-correlations between two time series given a set of time series predictors. Users first need to normalise $x_t$ and $y_t$ at lag $k$ using conditional_mean and conditional_var

Value

The function returns a list of objects of class "glm" as described in glm. the length og the list is equal to lag_max

See Also

glm

Examples

old_ts <- NEON_PRIN_5min_cleaned |>
  dplyr::select(
    Timestamp, site, turbidity, level,
    conductance, temperature
  ) |>
  tidyr::pivot_wider(
    names_from = site,
    values_from = turbidity:temperature
  )

fit_mean_y <- old_ts |>
  conditional_mean(turbidity_downstream ~
    s(level_upstream, k = 8) +
    s(conductance_upstream, k = 8) +
    s(temperature_upstream, k = 8))

fit_var_y <- old_ts |>
  conditional_var(
    turbidity_downstream ~
      s(level_upstream, k = 7) +
      s(conductance_upstream, k = 7) +
      s(temperature_upstream, k = 7),
    family = "Gamma",
    fit_mean = fit_mean_y
  )

fit_mean_x <- old_ts |>
  conditional_mean(turbidity_upstream ~
    s(level_upstream, k = 8) +
    s(conductance_upstream, k = 8) +
    s(temperature_upstream, k = 8))

fit_var_x <- old_ts |>
  conditional_var(
    turbidity_upstream ~
      s(level_upstream, k = 7) +
      s(conductance_upstream, k = 7) +
      s(temperature_upstream, k = 7),
    family = "Gamma",
    fit_mean = fit_mean_x
  )

fit_c_ccf <- old_ts |>
  tidyr::drop_na() |>
  conditional_ccf(
    I(turbidity_upstream * turbidity_downstream) ~ splines::ns(
      level_upstream,
      df = 5
    ) +
      splines::ns(temperature_upstream, df = 5),
    lag_max = 10,
    fit_mean_x = fit_mean_x, fit_var_x = fit_var_x,
    fit_mean_y = fit_mean_y, fit_var_y = fit_var_y,
    df_correlation = c(5, 5)
  )

PuwasalaG/conduits documentation built on April 22, 2023, 3:40 p.m.