conditional_acf: Computing conditional autocorrelations at given lags

In PuwasalaG/conduits: CONDitional UI for Time Series normalisation

Computing conditional autocorrelations at given lags

Description

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

Usage

conditional_acf(data, formula, lag_max, fit_mean, fit_var, df_correlation)

Arguments

data	a tibble containing all the time series including $ystar*ystar_t-k$ which are uniquely identified by the corresponding Timestamp.
formula	A GAM formula. See formula.gam.
lag_max	Maximum lag at which to calculate the conditional acf
fit_mean	Model object of class "conditional_moment" returned from conditional_mean
fit_var	Model object of class "conditional_moment" returned from conditional_var
df_correlation	a vector specifying the degrees of freedom to be considered for each numerical predictor when fitting additive models for conditional auto-correlations. Each component of the vector should corresponds to each predictor specified in "z_numeric".

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.

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

fit_var <- 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
  )
fit_c_acf <- old_ts |>
  tidyr::drop_na() |>
  conditional_acf(
    turbidity_upstream ~ splines::ns(level_upstream, df = 5) +
      splines::ns(conductance_upstream, df = 5),
    lag_max = 10, fit_mean = fit_mean, fit_var = fit_var,
    df_correlation = c(5, 5)
  )

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