Estimate lag-1 temporal autocorrelation — estimate_temporal

Estimate the lag-1 autocorrelation rho_t of a leaf-wax record's residuals after a flat-mean detrend, ordering by age. This is the quantity that enters the within-record detection threshold from manuscript Section 4.5.3 (Var(X1 - X2) = 2 sigma^2 (1 - rho_t)).

Usage

estimate_temporal_autocorrelation(
  d2h_wax,
  age,
  method = c("ar1", "lomb_scargle")
)

Arguments

d2h_wax: Numeric vector of leaf-wax delta-2-H measurements (per mil).
age: Numeric vector of sample ages, same length as d2h_wax.
method: One of "ar1" or "lomb_scargle".

Value

Numeric scalar in [-1, 1], or NA_real_ when the residuals are constant (e.g., n < 3 finite samples).

Details

Two methods are supported:

"ar1" (default): Pearson correlation of resid[-n] with resid[-1] after age-ordering. For irregularly sampled series this is an approximation; see "lomb_scargle" for an alternative.
"lomb_scargle": not yet implemented. Returns an error pointing the user at "ar1" until the spectral implementation lands. The plan is to estimate rho_t from the dominant timescale of a Lomb-Scargle periodogram on the irregularly sampled series.

Examples

# \donttest{
set.seed(1)
n <- 200
rho <- 0.7
e  <- numeric(n); e[1] <- rnorm(1, 0, 5)
for (k in 2:n) e[k] <- rho * e[k-1] + rnorm(1, 0, 5 * sqrt(1 - rho^2))
ag <- seq(0, 10000, length.out = n)
estimate_temporal_autocorrelation(-150 + e, ag)
#> [1] 0.6923911
# }