Running-Optimal-Average

The running optimal average is a smooth/flexible model that can describe time series data. This uses a Gaussian window function that moves through the data giving stronger weights to points close to the centre of the Gaussian. Therefore the width of the window function, delta, controls the flexibility of the model, with a small delta providing a very flexible model.

The function also calculates the effective no. of parameters as a very flexible model will correspond to large no. of parameters while a rigid model (low delta) has a low effective no. of parameters.

An error envelope is also calculated for the model.

Usage:

t, model, errs, P = RunningOptimalAverage(t_data, Flux, Flux_err, delta)

Calculate running optimal average on a fine grid of 1000 equally spaced points over the range of data. Also returns errors and effective number of parameters.

Import using:

from ROA import RunningOptimalAverage

Parameters

t_data : float array : Time values of the data points

Flux : float array : Flux data values

Flux_err : float array : Errors for the flux data points

delta : float : Window width of the Gaussian memory function - controls how flexible the model is

Returns

t : float array : Time values of the grid used to calculate ROA

model : float array : Running optimal average's calculated for each time t

errs : float array : Errors of the running optimal average

P : float : Effective number of parameters for the model