基于李雅普诺夫指数的噪声时间序列混沌动力学测试matlab代码.rar

function [H, pValue, Lambda, Orders, CI, allLambda] = chaostest(X, ActiveFN, maxOrders, alpha, flag) %CHAOSTEST performs the test for Chaos to test the positivity of the % dominant Lyapunov Exponent LAMBDA. % % The test hypothesis are: % Null hypothesis: LAMBDA >= 0 which indicates the presence of chaos. % Alternative hypothesis: LAMBDA < 0 indicates no chaos. % This is a one tailed test. % % [H, pValue, LAMBDA, Orders, CI, AllLambda] = ... % CHAOSTEST(Series, ActiveFN, maxOrders, ALPHA, FLAG) % % Inputs: % Series - a vector of observation to test. % % Optional inputs: % ActiveFN - String containing the activation function to use in the % neural net estimation. ActiveFN can be the 'LOGISTIC' function % f(u) = 1 / (1 + exp(- u)), domain = [0, 1], or 'TANH' function % f(u) = tanh(u), domain = [-1, 1], or 'SIGMOID' function % f(u) = u * (1 + |u/2|) / (2 + |u| + u^2 / 2), domain = [-1, 1]. % Default = 'TANH'. % % maxOrders - the maximum orders that the chaos function defined % in CHAOSFN can take. This must be a vector containing 3 elements. % maxOrders = [L, m, q]. % Increasing the model's orders can slow down calculations. % Default = [5, 6, 5]. % % ALPHA - The significance level for the test (default = 0.05) % % FLAG - String specifying the method to carry out the test, by % varying the triplet (L, m, q) {'VARY' or anything else} or by % fixing them {'FIX'}. Default = {'VARY'}. % % Outputs: % H = 0 => Do not reject the null hypothesis of Chaos at significance % level ALPHA. % H = 1 => Reject the null hypothesis of Chaos at significance level % ALPHA. % % pValue - is the p-value, or the probability of observing the given % result by chance given that the null hypothesis is true. Small % values of pValue cast doubt on the validity of the null hypothesis % of Chaos. % % LAMBDA - The dominant Lyapunov Exponent. % If LAMBDA is positive, this indicates the presence of Chaos. % If LAMBDA is negative, this indicates the absence of Chaos. % % Orders - gives the triplet (L, m, q) that maximizes the Lyapunov % exponent computed from all L*m*q estimations. % % CI - Confidence interval for LAMBDA at level ALPHA. % % allLambda - all the computed Lyapunov exponents for all L-by-m-by-q % estimations. % % The algorithm uses the Jacobian method in contrast to the direct % method, it needs the optimazition and the statistics toolboxes. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Copyright (c) 17 March 2009 by Ahmed BenSa�da % % Department of Finance, IHEC Sousse - Tunisia % % Email: ahmedbensaida@yahoo.com % % $ Revision 5.1 $ Date: 2 April 2016 $ % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % References: % BenSa�da, A. and Litimi, H. (2013), "High level chaos in the % exchange and index markets", Chaos, Solitons & Fractals 54: % 90-95. % BenSa�da, A. (2014), "Noisy chaos in intraday financial % data: Evidence from the American index", Applied % Mathematics and Computation 226: 258-265. % BenSa�da, A. (2015), "A practical test for noisy chaotic % dynamics", SoftwareX 3-4:1-5. % % Check if the Optimization and Statistics toolboxes are installed. % 1 if installed, 0 if not. existToolbox = license('test','optimization_toolbox') && ... license('test','statistics_toolbox'); if ~existToolbox error('The ''CHAOSTEST'' function needs both Optimization and Statistics toolboxes.') end % Set initial conditions. if (nargin >= 1) && (~isempty(X)) if istable(X) % Convert Table to an array. X = table2array(X); end if numel(X) == length(X) % Check for a vector. X = X(:); % Convert to a column vector. else error(' Observation ''Series'' must be a vector.'); end % Remove any NaN (i.e. missing values) observation from 'Series'. X(isnan(X)) = []; else error(' Must enter at least observation vector ''Series''.'); end % % Specify the activation function to use in CHAOSFN and ensure it to be a % string. Set default if necessary. % if nargin >= 2 && ~isempty(ActiveFN) if ~ischar(ActiveFN) error(' Activation function ''ActiveFN'' must be a string.') end % Specify the activation function to use: % ActiveFN = {'logistic', 'tanh', 'funfit'}. if ~any(strcmpi(ActiveFN , {'tanh' , 'logistic' , 'sigmoid'})) error('Activaton function ''ActiveFN'' must be TANH, LOGISTIC, or SIGMOID'); end else ActiveFN = 'tanh'; end % % Ensure the maximum orders maxL, maxM and maxQ are positive integers, and % set default if necessary. % if (nargin >= 3) && ~isempty(maxOrders) if numel(maxOrders) ~= 3 || any((maxOrders - round(maxOrders) ~= 0)) || ... any((maxOrders <= 0)) error(' Maximum orders ''maxOrders'' must a vector of 3 positive integers.'); end else maxOrders = [5, 6, 5]; end maxL = maxOrders(1); maxM = maxOrders(2); maxQ = maxOrders(3); % Check for a minimum size of vector X. if length(X) <= maxL * maxM error(' Observation ''Series'' must have at least %d obeservations.',maxL*maxM+1) end % % Ensure the significance level, ALPHA, is a % scalar, and set default if necessary. % if (nargin >= 4) && ~isempty(alpha) if numel(alpha) > 1 error(' Significance level ''Alpha'' must be a scalar.'); end if (alpha <= 0 || alpha >= 1) error(' Significance level ''Alpha'' must be between 0 and 1.'); end else alpha = 0.05; end % % Check the method to carry out the test, by varying (L, m, q) or by fixing % them, and set default if necessary. The method must be a string. % if nargin >= 5 && ~isempty(flag) if ~ischar(flag) error(' Regressions type ''FLAG'' must be a string.') end else flag = 'VARY'; end if strcmpi(flag, 'FIX') StartL = maxL; StartM = maxM; StartQ = maxQ; else StartL = 1; StartM = 1; StartQ = 1; end % Initialize the Lyapunov Exponent to a small number. Lambda = - Inf; Orders = [maxL, maxM, maxQ]; % Initialized all value of Lambdas. allLambda = -Inf(maxL, maxM, maxQ); % % Create the structure OPTIONS to use for nonlinear least square function % LSQNONLIN (included in the optimization toolbox). % Options = optimset('lsqnonlin'); Options = optimset(Options, 'Display', 'off'); % Use the user supplied analytical Jacobian in CHAOSFN. Options = optimset(Options, 'Jacobian', 'on'); % Initialize the starting value for the coefficient THETA. StartValue = 0.5; for L = StartL:maxL for m = StartM:maxM for q = StartQ:maxQ A = StartValue * ones(q, m); % Contains the coefficients gamma(i,j). B = StartValue * ones(q, 1); % Contains the coefficients gamma(0,j). C = StartValue * ones(1, q); % Contains the coefficients beta(j). D = StartValue; % Constant. %E = StartValue * ones(1, m); % Linear coefficients for lagged X. Theta0 = [reshape(A', 1, q*m), B', C, D]; %Theta0 = [reshape(A', 1, q*m), B', C, D, E]; Theta = lsqnonlin(@chaosfn, Theta0, [], [], Options, X, L, m, q, ActiveFN); T = length(X) - m*L; % New sample size. % % Use an inner function JACOBMATX to compute the Jacobian needed % to compute the Lyapunov Exponent LAMBDA. This jacobian is relative % to X and not to parameter THETA. N.B: the jacobian gi