基于bootstrap的格兰杰检验

function [h,pValue,stat,cValue,reg] = adftest(y,varargin) %ADFTEST Augmented Dickey-Fuller test for a unit root % % Syntax: % % [h,pValue,stat,cValue,reg] = adftest(y) % [h,pValue,stat,cValue,reg] = adftest(y,param1,val1,param2,val2,...) % % Description: % % Dickey-Fuller tests assess the null hypothesis of a unit root in a % univariate time series y. All tests use the model % % y(t) = c + d*t + a*y(t-1) + b1*(1-L)y(t-1) % + b2*(1-L)y(t-2) % + ... % + bp*(1-L)y(t-p) % + e(t), % % where L is the lag operator Ly(t) = y(t-1). The null hypothesis % restricts a = 1. Variants of the test, appropriate for series with % different growth characteristics, restrict the drift and deterministic % trend coefficients, c and d, respectively, to be 0. Lagged differences % bk*(1-L)y(t-k), k = 1, ..., p, "augment" the test to account for serial % correlations in the innovations process e(t). % % Input Arguments: % % y - Vector of time-series data. The last element is the most recent % observation. NaNs indicating missing values are removed. % % Optional Input Parameter Name/Value Pairs: % % NAME VALUE % % 'lags' Scalar or vector of nonnegative integers indicating the % number p of lagged changes of y to include in the model. % The default value is 0. % % 'model' String or cell vector of strings indicating the model % variant. Values are 'AR' (autoregressive), 'ARD' % (autoregressive with drift), or 'TS' (trend stationary). % The default value is 'AR'. % % o When the value is 'AR', the null model % % y(t) = y(t-1) + b1*(1-L)y(t-1) % + b2*(1-L)y(t-2) % + ... % + bp*(1-L)y(t-p) % + e(t) % % is tested against the alternative model % % y(t) = a*y(t-1) + b1*(1-L)y(t-1) % + b2*(1-L)y(t-2) % + ... % + bp*(1-L)y(t-p) % + e(t) % % with AR(1) coefficient a < 1. % % o When the value is 'ARD', the null model % % y(t) = y(t-1) + b1*(1-L)y(t-1) % + b2*(1-L)y(t-2) % + ... % + bp*(1-L)y(t-p) % + e(t) % % is tested against the alternative model % % y(t) = c + a*y(t-1) + b1*(1-L)y(t-1) % + b2*(1-L)y(t-2) % + ... % + bp*(1-L)y(t-p) % + e(t) % % with drift coefficient c and AR(1) coefficient a < 1. % % o When the value is 'TS', the null model % % y(t) = c + y(t-1) + b1*(1-L)y(t-1) % + b2*(1-L)y(t-2) % + ... % + bp*(1-L)y(t-p) % + e(t) % % is tested against the alternative model % % y(t) = c + d*t + a*y(t-1) + b1*(1-L)y(t-1) % + b2*(1-L)y(t-2) % + ... % + bp*(1-L)y(t-p) % + e(t) % % with drift coefficient c, deterministic trend coefficient % d, and AR(1) coefficient a < 1. % % 'test' String or cell vector of strings indicating the type of % test statistic. Values are 't1', 't2', or 'F'. The default % value is 't1'. % % o When the value is 't1', a standard t statistic % % t1 = (a-l)/se % % is computed from OLS estimates of the AR(1) coefficient a % and its standard error se in the alternative model. The % test assesses the significance of the restriction a = 1. % % o When the value is 't2', a lag-adjusted, "unstudentized" t % statistic % % t2 = T*(a-1)/(1-b1-...-bp) % % is computed from OLS estimates of the AR(1) coefficient a % and the stationary coefficients b1, ..., bp in the % alternative model. T is the effective sample size, % adjusted for lags and missing values. The test assesses % the significance of the restriction a = 1. % % o When the value is 'F', an F statistic is computed to % assess the significance of a joint restriction on the % alternative model. If the value of 'model' is 'ARD', the % restriction is a = 1 and c = 0. If the value of 'model' % is 'TS', the restriction is a = 1 and d = 0. An F test is % invalid when the value of 'model' is 'AR'. % % 'alpha' Scalar or vector of nominal significance levels for the % tests. Values must be between 0.001 and 0.999. The default % value is 0.05. % % Scalar or single string parameter values are expanded to the length of % any vector value (the number of tests). Vector values must have equal % length. If any value is a row vector, all outputs are row vectors. % % Output Arguments: % % h - Vector of Boolean decisions for the tests, with length equal to the % number of tests. Values of h equal to 1 indicate rejection of the % unit-root null in favor of the alternative model. Values of h equal % to 0 indicate a failure to reject the unit-root null. % % pValue - Vector of p-values of the test statistics, with length equal % to the number of tests. When the value of 'test' is 't1' or 't2', % p-values are left-tail probabilities. When the value of 'test' is % 'F', p-values are right-tail probabilities. % % stat - Vector of test statistics, with length equal to the number of % tests. Statistics are computed using OLS estimates of the % coefficients in the alternative model. % % cValue - Vector of critical values for the tests, with length equal to % the number of tests. When the value of 'test' is 't1' or 't2', % critical values are for left-tail probabilities. When the value of % 'test' is 'F', critical values are for right-tail probabilities. % % reg - Structure of regression statistics from the OLS estimation of % coefficients in the alternative model. The number of records is % equal to the number of tests. Each record has the following fields: % % num Length of the input series y, with NaNs removed % size Effective sample size, adjusted for lags, difference* % names Regression coefficient names % coeff Estimated coefficient values % se Estimated coefficient standard errors % Cov Estimated coefficient covariance matrix % tStats t statistics of coefficients and p-values % FStat F statistic and p-value % yMu Mean of y, adjusted for lags, difference* % ySigma Standard deviation of y, adjusted for lags, difference* % yHat Fitted values of y, adjusted for lags, difference* % res Regression residuals % DWStat Durbin-Watson statistic % SSR Regression sum of squares % SSE Error sum of squares % SST Total sum of squares % MSE Mean squared error %