get_est_Ar {rbbnp}

get the estimation of A and r

Description

This function estimates the parameters A and r by optimizing an objective function over a specified range of frequency values and r values.

Usage

get_est_Ar(Y = 1, X, xi_interval, r_stepsize = 150)

Arguments

Y

A numerical vector representing the sample data of variable Y.

X

A numerical vector representing the sample data of variable X.

xi_interval

A list with elements xi_lb and xi_ub representing the lower and upper bounds of the frequency interval.

r_stepsize

An integer value representing the number of steps in the r range. This controls the granularity of the estimation. Higher values lead to finer granularity but increase computation time.

Details

The function internally defines a range for the natural logarithm of frequency values (ln_xi_range) and a range for the parameter r (r_range). It then defines an optimization function optim_ln_A to minimize the integral of a given function over the ln_xi_range. The actual estimation is done by finding the r and A value that minimizes the the area of the line \ln A - r \ln \xi under the constraint that the line should not go below the Fourier transform curve.

Value

A named vector with elements est_A and est_r representing the estimated values of A and r, respectively.