Matlab程序命令

1、 Matlab程序命令（三）：使用Matlab进行回归%A矩阵为36×217的矩阵，即用1978-2013年31个省（直辖市、自治区）国内生产总值、人口、财政收入、财政支出、固定资产投资、全社会消费品零售总额、进出口数据组成的矩阵。y=A(:,1); %提取A矩阵中的第1列x1=A(:,2); %提取A矩阵中的第2列x2=A(:,4); %提取A矩阵中的第4列x=horzcat(x1,x2); %把x1,x2横排vnames=strvcat('y','x1','x2'); %命名变量result=ols(y,x); %用ols回归prt

2、(result,vnames) %对回归结果进行格式化并命名Ordinary Least-squares Estimates Dependent Variable = y R-squared = 0.9929 Rbar-squared = 0.9927 sigma2 = 226704.9623 Durbin-Watson = 0.2427 Nobs, Nvars = 36, 2 *Variable Coefficient t-statistic t-probability x1 0.512321 5.737780 0.000002 x2 4.703050 53.340145 0.000000p

3、lt(result) %显示回归结果拟合值与实际值，残差的图形关于ols回归函数，可以使用help ols命令查看function results=ols(y,x)% PURPOSE: least-squares regression%-% USAGE: results = ols(y,x)% where: y = dependent variable vector (nobs x 1)% x = independent variables matrix (nobs x nvar)%-% RETURNS: a structure% results.meth = 'ols'% r

4、esults.beta = bhat% results.tstat = t-stats% results.yhat = yhat% results.resid = residuals% results.sige = e'*e/(n-k)% results.rsqr = rsquared% results.rbar = rbar-squared% results.dw = Durbin-Watson Statistic% results.nobs = nobs% results.nvar = nvars% results.y = y data vector% -% SEE ALSO: p

5、rt(results), plt(results)%-help olsContents of ols:FDELW2 - wswdel,wwsdel,wmatdel=fdelw2(xcoord,ycoord)FOLS2 - bmax, srds, prhigher, emax, maxlik=fols2(x, y)fmess_car2 - bmax, srds, prhighers, emax, logliks=fmess_car2(x, y, d)mprint - PURPOSE: print an (nobs x nvar) matrix in formatted formx_ols2_ga

6、1 - This example script estimates some election data via ols and MESS-AR. ols is both a directory and a function. PURPOSE: least-squares regression - USAGE: results = ols(y,x) where: y = dependent variable vector (nobs x 1) x = independent variables matrix (nobs x nvar) - RETURNS: a structure result

7、s.meth = 'ols' results.beta = bhat (nvar x 1) results.tstat = t-stats (nvar x 1) results.bstd = std deviations for bhat (nvar x 1) results.yhat = yhat (nobs x 1) results.resid = residuals (nobs x 1) results.sige = e'*e/(n-k) scalar results.rsqr = rsquared scalar results.rbar = rbar-squar

8、ed scalar results.dw = Durbin-Watson Statistic results.nobs = nobs results.nvar = nvars results.y = y data vector (nobs x 1) results.bint = (nvar x2 ) vector with 95% confidence intervals on beta - SEE ALSO: prt(results), plt(results) -result = ols(y,x); %最小二乘法bhat = result.beta; % 估计结果disp(The R-sq

9、uared is:'); %显示拟合优度R2result.rsqr %拟合优度R2disp(The 2nd t-statistic is:'); %显示第二个t统计量result.tstat(2,1) %第二个t统计量result.tstat(1,1) %第一个t统计量result.resid %显示残差result.y %显示y变量result.x %显示x变量prt(result) %对回归结果进行格式化Ordinary Least-squares Estimates R-squared = 0.9929 Rbar-squared = 0.9927 sigma2 = 226

10、704.9623 Durbin-Watson = 0.2427 Nobs, Nvars = 36, 2 *Variable Coefficient t-statistic t-probability variable 1 0.512321 5.737780 0.000002 variable 2 4.703050 53.340145 0.000000result = ols(y,x); %使用最小二乘法回归prt(result) %对回归结果进行格式化;bill_clinton = ols(y,x); %关于左边字母的使用，可以使用其他字母result2 = ols(y,x); %关于左边字母

11、的使用，可以使用其他字母restricted = ols(y,x); %关于左边字母的使用，可以使用其他字母unrestricted = ols(y,x); %关于左边字母的使用，可以使用其他字母The regression function library is in a subdirectory regress.（回归函数库在子目录中）regression function library（回归函数库）ar_g %Gibbs sampling Bayesian autoregressive model（pjlv7中有此函数）查看ar_g函数。help ar_g PURPOSE: MCMC

12、estimates Bayesian heteroscedastic AR(k) model imposing stability restrictions using Gibbs sampling y = b0 + y(t-1) b1 + y(t-2) b2 +,.,y(t-k) bk + E, E = N(0,sige*V), sige = gamma(nu,d0), b = N(c,T), V = diag(v1,v2,.vn), r/vi = ID chi(r)/r, r = Gamma(m,k) - USAGE: results = ar_g(y,nlag,ndraw,nomit,p

13、rior,start) where: y = dependent variable vector nlag = # of lagged values ndraw = # of draws nomit = # of initial draws omitted for burn-in prior = a structure for prior information input: prior.beta, prior means for beta, c above priov.bcov, prior beta covariance , T above prior.rval, r prior hype

14、rparameter, default=4 prior.m, informative Gamma(m,k) prior on r prior.k, informative Gamma(m,k) prior on r prior.const, a switch for constant term, default = 1 (a constant included) prior.nu, a prior parameter for sige prior.d0, a prior parameter for sige (default = diffuse prior for sige) start =

15、(optional) structure containing starting values: defaults: OLS beta,sige, V= ones(n,1) start.b = beta starting values (nvar x 1) start.sig = sige starting value (scalar) start.V = V starting values (n x 1) - RETURNS: a structure: results.meth = 'ar_g' results.bdraw = bhat draws (ndraw-nomit

16、x nvar) results.sdraw = sige draws (ndraw-nomit x 1) results.vmean = mean of vi draws (nobs x 1) (if rval input) results.yhat = mean of posterior y-predicted values results.rdraw = r-value draws (ndraw-nomit x 1) results.pmean = b prior means, prior.beta from input results.pstd = b prior std deviati

17、ons sqrt(diag(T) results.r = value of hyperparameter r (if input) results.nobs = # of observations results.nadj = # of observations adjusted for feeding lags results.nvar = # of variables (including constant term) results.ndraw = # of draws results.nomit = # of initial draws omitted results.y = actu

18、al observations (nobs x 1) results.x = x-matrix of lagged values of y (nobs-nlag,nlag+const) results.nu = nu prior parameter results.d0 = d0 prior parameter results.m = m prior parameter (if input) results.k = k prior parameter (if input) results.time = time taken for sampling results.accept= accept

19、ance rate results.pflag = 'plevel' (default) or 'tstat' for bogus t-statistics - NOTES: a constant term is automatically included in the model unless you set prior.const = 0; - SEE ALSO: prt, prt_gibbs(results), coda - % REFERENCES: Chib (1993) Bayes regression with autoregressive er

20、rors: A gibbs sampling approach,' Journal of Econometrics, pp. 275-294. -boxcox %Box-Cox regression with 1 parameter（pjlv7中有此函数）help boxcox PURPOSE: box-cox regression using a single scalar transformation parameter for both y and (optionally) x - USAGE: results = boxcox1(y,x,lam_lo,lam_up,model,

21、foptions) where: y = dependent variable vector x = explanatory variables matrix (intercept vector in 1st column - if desired) lam_lo = scalar, lower limit for simplex search lam_up = scalar, upper limit for simplex search model = 0 for y-transform only = 1 for both y, and x-transform foptions = (opt

22、ional) structure OPTIONS, created with the OPTIMSET function. See OPTIMSET for details. - RETURNS: a structure: results.meth = 'boxcox' results.beta = bhat estimates results.lam = lamda estimate results.tstat = t-stats for bhat results.yhat = yhat (box-cox transformed) results.resid = residu

23、als results.sige = e'*e/(n-k) results.rsqr = rsquared results.rbar = rbar-squared results.nobs = nobs results.nvar = nvars results.y = y data vector (box-cox transformed) results.iter = # of iterations results.like = -log likelihood function value - NOTE: uses MATLAB simplex optimization functio

24、n fmin - SEE ALSO: prt(results), plt(results), boxcox2() - Overloaded methods: fints/boxcoxhwhite %Halbert White's heteroscedastic consistent estimates（pjlv7中有此函数）lad % least-absolute deviations regression（pjlv7中有此函数）logit %logit regression（pjlv7中有此函数）mlogit % multinomial logit regression（pjlv7中

25、有此函数）nwest % Newey-West hetero/serial consistent estimates（pjlv7中有此函数）ols %ordinary least-squares（pjlv7中有此函数）ols_g % Gibbs sampling Bayesian linear model（pjlv7中有此函数）olsar1 %Maximum Likelihood for AR(1) errors ols model（pjlv7中有此函数）olsc % Cochrane-Orcutt AR(1) errors ols model（pjlv7中有此函数）olst %regress

26、ion with t-distributed errors（pjlv7中有此函数）probit % probit regression（pjlv7中有此函数）probit_g % Gibbs sampling Bayesian probit model（pjlv7中有此函数）ridge % ridge regression（pjlv7中有此函数）robust % iteratively reweighted least-squares（pjlv7中有此函数）rtrace %ridge estimates vs parameters (plot) （pjlv7中有此函数）sur %seeming

27、ly unrelated regressions（pjlv7中有此函数）switch_em %switching regime regression using EM-algorithm（pjlv7中有此函数）theil %Theil-Goldberger mixed estimation（pjlv7中有此函数）thsls % three-stage least-squares（pjlv7中有此函数）tobit % tobit regression（pjlv7中有此函数）tobit_g % Gibbs sampling Bayesian tobit model（pjlv7中有此函数）tsls %two-stage least-squares（pjlv7中有此函数）waldf %Wald F-test（p