114 lines
2.6 KiB
Mathematica
114 lines
2.6 KiB
Mathematica
|
%% This function was automatically generated. When modifying its signature, take care to apply
|
||
|
|
%% modifications also to the descriptor files in the repository.
|
||
|
|
%% function out = my_app(Time Series File, Number of lags , Number of standard deviations)
|
||
|
|
|
||
|
|
function [acf,lags,bounds,numLags,numMA,numSTD] = ...
|
||
|
|
autocorr(time_series,numLags,numMA,numSTD)
|
||
|
|
|
||
|
|
[rows,columns] = size(time_series);
|
||
|
|
|
||
|
|
if (rows ~= 1) && (columns ~= 1)
|
||
|
|
|
||
|
|
error('Input file must be a vector');
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
time_series = time_series(:); % Ensure a column vector
|
||
|
|
N = length(time_series); % Sample size
|
||
|
|
defaultLags = 20; % Recommendation of [1]
|
||
|
|
|
||
|
|
% Ensure numLags is a positive integer or set default:
|
||
|
|
|
||
|
|
if (nargin >= 2) && ~isempty(numLags)
|
||
|
|
|
||
|
|
if numel(numLags) > 1
|
||
|
|
|
||
|
|
error('Number of lags must be a scalar value');
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
if (round(numLags) ~= numLags) || (numLags <= 0)
|
||
|
|
|
||
|
|
error('Number of lags must be a positive integer');
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
if numLags > (N-1)
|
||
|
|
|
||
|
|
error('Number of ACF lags must not exceed the number of observations minus one');
|
||
|
|
% numLags = min(defaultLags,N-1)
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
else
|
||
|
|
|
||
|
|
numLags = min(defaultLags,N-1); % Default
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
% Ensure numMA is a nonnegative integer or set default:
|
||
|
|
|
||
|
|
if (nargin >= 3) && ~isempty(numMA)
|
||
|
|
|
||
|
|
if numel(numMA) > 1
|
||
|
|
|
||
|
|
error('Number of moving average must be a scalar value');
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
if (round(numMA) ~= numMA) || (numMA < 0)
|
||
|
|
|
||
|
|
error('Number of moving average must be a positive integer');
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
if numMA >= numLags
|
||
|
|
|
||
|
|
error('Number of moving average must be lower than number of lags');
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
else
|
||
|
|
|
||
|
|
numMA = 0; % Default
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
% Ensure numSTD is a positive scalar or set default:
|
||
|
|
|
||
|
|
if (nargin >= 4) && ~isempty(numSTD)
|
||
|
|
|
||
|
|
if numel(numSTD) > 1
|
||
|
|
|
||
|
|
error('Number of standard deviations must be a scalar value');
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
if numSTD < 0
|
||
|
|
|
||
|
|
error('Number of standard deviations cannot be negative');
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
else
|
||
|
|
|
||
|
|
numSTD = 2; % Default
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
nFFT = 2^(nextpow2(length(time_series))+1);
|
||
|
|
F = fft(time_series-mean(time_series),nFFT);
|
||
|
|
F = F.*conj(F);
|
||
|
|
acf = ifft(F);
|
||
|
|
acf = acf(1:(numLags+1)); % Retain non-negative lags
|
||
|
|
acf = acf./acf(1); % Normalize
|
||
|
|
acf = real(acf);
|
||
|
|
|
||
|
|
% Compute approximate confidence bounds using the approach in [1],
|
||
|
|
% equations 2.1.13 and 6.2.2, pp. 33 and 188, respectively:
|
||
|
|
|
||
|
|
sigmaNMA = sqrt((1+2*(acf(2:numMA+1)'*acf(2:numMA+1)))/N);
|
||
|
|
bounds = sigmaNMA*[numSTD;-numSTD];
|
||
|
|
lags = (0:numLags)';
|
||
|
|
|
||
|
|
end
|