You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: CO_trev.m
    path of file: ./repos/hctsa/Operations
    
    the code of the file until where you have to start completion: function out = CO_trev(y,tau)
% CO_trev   Normalized nonlinear autocorrelation, trev function of a time series
%
% Calculates the trev function, a normalized nonlinear autocorrelation,
% mentioned in the documentation of the TSTOOL nonlinear time-series analysis
% package (available here: http://www.physik3.gwdg.de/tstool/).
%
% The quantity is often used as a nonlinearity statistic in surrogate data
% analysis, cf. "Surrogate time series", T. Schreiber and A. Schmitz, Physica D,
% 142(3-4) 346 (2000).
%
%---INPUTS:
%
% y, time series
%
% tau, time lag (can be 'ac' or 'mi' to set as the first zero-crossing of the
%       autocorrelation function, or the first minimum of the automutual
%       information function, respectively)
%
%---OUTPUTS:
% The raw trev expression, its magnitude, the numerator and its magnitude, and
% the denominator.

% ------------------------------------------------------------------------------
% Copyright (C) 2020, Ben D. Fulcher <ben.d.fulcher@gmail.com>,
% <http://www.benfulcher.com>
%
% If you use this code for your research, please cite the following two papers:
%
% (1) B.D. Fulcher and N.S. Jones, "hctsa: A Computational Framework for Automated
% Time-Series Phenotyping Using Massive Feature Extraction, Cell Systems 5: 527 (2017).
% DOI: 10.1016/j.cels.2017.10.001
%
% (2) B.D. Fulcher, M.A. Little, N.S. Jones, "Highly comparative time-series
% analysis: the empirical structure of time series and their methods",
% J. Roy. Soc. Interface 10(83) 20130048 (2013).
% DOI: 10.1098/rsif.2013.0048
%
% This function is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free Software
% Foundation, either version 3 of the License, or (at your option) any later
% version.
%
% This program is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
% FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
% details.
%
% You should have received a copy of the GNU General Public License along with
% this program. If not, see <http://www.gnu.org/licenses/>.

    
function out = CO_trev(y,tau)
% CO_trev   Normalized nonlinear autocorrelation, trev function of a time series
%
% Calculates the trev function, a normalized nonlinear autocorrelation,
% mentioned in the documentation of the TSTOOL nonlinear time-series analysis
% package (available here: http://www.physik3.gwdg.de/tstool/).
%
% The quantity is often used as a nonlinearity statistic in surrogate data
% analysis, cf. "Surrogate time series", T. Schreiber and A. Schmitz, Physica D,
% 142(3-4) 346 (2000).
%
%---INPUTS:
%
% y, time series
%
% tau, time lag (can be 'ac' or 'mi' to set as the first zero-crossing of the
%       autocorrelation function, or the first minimum of the automutual
%       information function, respectively)
%
%---OUTPUTS:
% The raw trev expression, its magnitude, the numerator and its magnitude, and
% the denominator.

% ------------------------------------------------------------------------------
% Copyright (C) 2020, Ben D. Fulcher <ben.d.fulcher@gmail.com>,
% <http://www.benfulcher.com>
%
% If you use this code for your research, please cite the following two papers:
%
% (1) B.D. Fulcher and N.S. Jones, "hctsa: A Computational Framework for Automated
% Time-Series Phenotyping Using Massive Feature Extraction, Cell Systems 5: 527 (2017).
% DOI: 10.1016/j.cels.2017.10.001
%
% (2) B.D. Fulcher, M.A. Little, N.S. Jones, "Highly comparative time-series
% analysis: the empirical structure of time series and their methods",
% J. Roy. Soc. Interface 10(83) 20130048 (2013).
% DOI: 10.1098/rsif.2013.0048
%
% This function is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free Software
% Foundation, either version 3 of the License, or (at your option) any later
% version.
%
% This program is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
% FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
% details.
%
% You should have received a copy of the GNU General Public License along with
% this program. If not, see <http://www.gnu.org/licenses/>.
% ------------------------------------------------------------------------------

%-------------------------------------------------------------------------------
%% Set defaults:
if nargin < 2 || isempty(tau)
    tau = 'ac';
end