acf

Builtin index · Signal processing

result = acf(x, [max_lag=])

Input: x, max_lag · Output: result

What it is

x: a length-N real vector. max_lag (optional number, default min(40, N-1), R's own acf() default): highest lag to compute.

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = acf(x, [max_lag=])`	`x` vector`x`: a length-N real vector. `max_lag` number, optional`max_lag` (optional number, default `min(40, N-1)`, R's own `acf()` default): highest lag to compute.	`max_lag+1` —lag 0 through `max_lag`	Returns a vector of length `max_lag+1` (lag 0 through `max_lag`), the autocorrelation function. The first lag at which it falls below `1/e` is the usual correlation-time estimate.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

fs = 1000
n = 0:1:511
t = n / fs
x = sin(2*pi*20*t) + 0.2*randn(512, seed=4)

r = acf(x, max_lag=50)
below = find_peaks(-abs(r - 1/e))
print("acf[0] = {r[0]}, acf drops below 1/e near lag {below[0]}")

h_tone = hurst_exponent(x)
h_walk = hurst_exponent(cumsum(randn(512, seed=5)))
print("hurst (periodic+noise) = {h_tone}, hurst (random walk) = {h_walk}")

output

acf[0] = 1, acf drops below 1/e near lag 9
hurst (periodic+noise) = 0.71599, hurst (random walk) = 0.998318

from signal-processing

How it works

acf(x, [max_lag=]) — see the free function's own doc comment. max_lag defaults to min(40, length(x)-1) — R's own acf() default, a reasonable "show the interesting part" cutoff for a series of any real length.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.