diff --git a/matlab/pac-tools/a2alpha.m b/matlab/pac-tools/a2alpha.m index 847bd46f53af59fa9f77941095a8ee0470b85002..2bb2b5171ef35f1f9cbca50b73387e20b0f02fd6 100644 --- a/matlab/pac-tools/a2alpha.m +++ b/matlab/pac-tools/a2alpha.m @@ -3,26 +3,26 @@ function alpha = a2alpha(a) % Computes the m alpha coefficients from the m a coefficients of the PAC model. % % INPUTS -% - a [double] m*1 vector of coefficients. +% - a [double] m×1 vector of coefficients. % % OUTPUTS -% - alpha [double] m*1 vector of coefficients. +% - alpha [double] m×1 vector of coefficients. % % NOTES % -% Given the current estimate of the PAC parameters a_0, a_1, ..., a_{m-1}, the routine does the following: +% Given the current estimate of the PAC parameters aâ‚€, aâ‚, ..., aₘ₋â‚, the routine does the following: % -% \alpha_{m} = a_{m-1} -% \alpha_{m-1} = a_{m-2}-a_{m-1} -% \alpha_{m-2} = a_{m-3}-a_{m-2} -% ... -% \alpha_3 = a_2-a_3 -% \alpha_2 = a_1-a_2 -% \alpha_1 = a_0-a_1-1 +% αₘ = aₘ₋₠+% αₘ₋₠= aₘ₋₂ - aₘ₋₠+% â‹® +% αᵢ = aᵢ₋₠- aáµ¢ ≡ - Δaáµ¢ +% â‹® +% α₂ = aâ‚ - aâ‚‚ +% α₠= aâ‚€ - aâ‚ - 1 % -% Note that the last elements of input a are (a_0, a_1, ..., a_{m-1}). +% Computed coefficients αᵢ define lag polynomial A(L) = 1 + αâ‚L + α₂L² + … + αₘ Láµ such that aâ‚€ = A(1). -% Copyright © 2018 Dynare Team +% Copyright © 2018-2024 Dynare Team % % This file is part of Dynare. % @@ -53,4 +53,4 @@ alpha = zeros(m, 1); % Compute the transformed parameters alpha(m) = a(m); alpha(2:m-1) = a(2:m-1)-a(3:m); -alpha(1) = a(1)-a(2)-1; \ No newline at end of file +alpha(1) = a(1)-a(2)-1;