Perform an estimation of the noise given a list of $t_0$.

This function performs an estimation of the standard deviation of the noise at different times.

estimate_sigma_list(data, t0_list, k0_list)

Arguments

data	A list, where each element represents a curve. Each curve have to be defined as list with two entries: $t The sampling points $x The observed points
t0_list	A vector of numeric, the sampling points at which we estimate \(H0\). We will consider the \(8k0 - 7\) nearest points of \(t_0\) for the estimation of \(H_0\) when \(\sigma\) is unknown.
k0_list	A vector of numeric, the number of neighbors of \(t_0\) to consider. Should be set as $$k0 = M * exp(-(log(log(M))**2))$$. We can set a different \(k_0\), but in order to use the same for each \(t_0\), just put a unique numeric.

data

A list, where each element represents a curve. Each curve have to be defined as list with two entries:

$t The sampling points
$x The observed points

t0_list

A vector of numeric, the sampling points at which we estimate $H0$. We will consider the $8k0 - 7$ nearest points of $t_0$ for the estimation of $H_0$ when $\sigma$ is unknown.

k0_list

A vector of numeric, the number of neighbors of $t_0$ to consider. Should be set as $$k0 = M * exp(-(log(log(M))**2))$$. We can set a different $k_0$, but in order to use the same for each $t_0$, just put a unique numeric.

Value

A list, an estimation of sigma at different $t_0$.

Examples

df <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
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estimate_sigma_list(df, t0_list = c(0.25, 0.5, 0.75), k0 = 14)
#> [1] 0.06458909 0.06458778 0.06472795

Perform an estimation of the noise given a list of \(t_0\).

Arguments

Value

Examples