Estimation of noise variance for time series.

Given a time series signal, potentially with missing/unobserved values, this function estimates the level of noise under the assumption of local continuity/smoothness.

Usage

estimateNoise(probs, read_pos, k, min_diffs)

Arguments

probs

Numeric vector of (observed) time series measurements.

read_pos

Integer vector of measurement positions in the time series (same length as probs).

k

Integer, maximum gap size tolerated when computing \(\Delta x\).

min_diffs

Integer, minimum number of lag-1 differences required to produce an estimate (default -1 = auto).

Value

A vector with the following items:

1. Mean signal

2. Total variance

3. Noise variance estimate

4. Number of adjacent positions used for the estimate

Details

\(\mathrm{Noise variance} \approx 0.5\,\mathrm{Var}(\Delta x)\) where \(\Delta x\) are lag-1 differences that may skip up to k missing values. This follows from error propagation and the assumption of low varying x in adjacent measurements.

Examples

estimateNoise(
    c(0.1, 0.25, 0.3, 0.45, 0.5, 0.7, 0.7),
    c(1L, 2L, 3L ,4L, 6L, 8L, 11L),
    2L, 1)
#>       mean      total  noise_raw     ndiffs 
#> 0.42857143 0.05154762 0.00300000 6.00000000