fit_ACF

Fits one or more theoretical autocorrelation functions to the sample ACF of an xts series. Three parametric models are available: the Cauchy-type autocorrelation structure (CAS, a two-parameter model with algebraic decay), the Hurst-Kolmogorov process (HK, a one-parameter fractional Gaussian noise model), and the short-range dependence model (SRD, a one-parameter exponential decay). Parameters are estimated by minimising the root-mean-square error between the theoretical and sample ACFs up to lag_max, using the L-BFGS-B optimiser with positivity constraints on all parameters. The function returns fitted parameter vectors for each model type, a data frame of theoretical ACF values at each lag, and a ggplot overlay of the fitted curves on the empirical autocorrelation.

Usage

fit_ACF(
  ts,
  lag_max,
  type = list("CAS", "HK", "SRD"),
  ignore_zeros = FALSE,
  zero_threshold = 0.01
)

Arguments

ts

An xts object containing the time series data.

lag_max

Integer. Maximum lag to use in fitting.

type

Character vector of ACF model types. Options are "CAS", "HK", and "SRD". Default all three.

ignore_zeros

Logical. If TRUE, values below zero_threshold are excluded. Default FALSE.

zero_threshold

Numeric. Threshold below which values are treated as zero. Default 0.01.

Value

A list with elements ACF_params (named list of fitted parameter vectors per model), ACF_fitted (data frame of theoretical ACF values with a lag column), and ACF_plot (ggplot of sample ACF with fitted curves overlaid).

Examples

ts <- xts::xts(rnorm(365), order.by = as.Date("2020-01-01") + 0:364)
acfs <- fit_ACF(ts, lag_max = 10, type = c("CAS", "HK", "SRD"))
acfs$ACF_plot