Bai and Ng Panel Unit Root Test
res = BNG_ur1(Y,t_order,typeoflag,pmax,kmax,criteria,signif)
* Y = matrix (T,N) of observations
The data matrix may be unbalanced.
Missing Values must be specified as %nan
* t_order = -1 : no individual effect
0 : individual effects (Default)
1 : individual effects and time trends
* typeoflag = the string:
- 'common' if the lag order is common to all variables (in that case, the lag order is determined as in Bai and Ng, 2004)
- 'individual' if the lag order is optimally chosen for each variable
* pmax = Maximum of the lag order authorized for the individual ADF tests
* kmax = The maximum number of common factors used to compute the criterion functions for the estimation of r, the number of common factors. It is not specified rmax = min(N,T)
* criteria = Criteria used to estimate the number of common factors
= 'IC1', 'IC2', 'IC3', 'PC1', 'PC2', 'PC3', 'AIC3', 'BIC3' (see Bai and Ng (2002))
* signif = significance level for the individual ADF tests (0.05, 0.01 or 0.1)
* res= a results tlist with:
- res('meth') = 'BNG panel ur test'
- res('y') = (T x k) matrix of data
- res('t_order') = the trend order (0 or 1)
- res('t_orderlit') = the trend order in plain english
- res('ratio1') = Variance of idiosyncratic component divised by the variance observed data (both in first differences)
- res('Rratio2') = Variance of residuals of common components divised by variance on idiosyncratic component
- res('ADFe') = Individual ADF statistics on idiosyncratic component : ADFe(i)
- res('ADFe_pvalue') = Individual ADF statistics on idiosyncratic component : ADFe(i)
- res('ADFe_pi') = Number of ADF terms in ADF tests on e(i,t)
- res('pmax') = Maximum Lag Order for individual ADF regressions on e(i,t)
- res('ADFe_Ti') = Adjusted time dimension for ADF tests on e(i,t)
- res('nbfactors') = Estimated number of common factors
- res('khat') = Estimated Numbers of Factor with IC1, IC2, IC3, PC1, PC2, PC3, AIC3 and BIC3
- res('criteria') = Criteria used to estimate the number of common factors. Default value = 1 (IC1)
- res('IC') = IC1, IC2 and IC3 Information criterions for r=1,...,kmax
- res('PC') = PC1, PC2 and PC3 Information criterions for r=1,...,kmax
- res('BIC3') = BIC3 Information criterion for k=1,...,kmax (only BIC criteria function of N and T)
- res('AIC3') = AIC3 Information criterion (only AIC criteria function of N and T) : it tends to overestimate r
- res('kmax') = Maximum number of common factors authorized
When there is one common factor (r = 1):
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- res('BNG.ADF_F') = ADF statistic on common factor: ADFf
- res('BNG.ADF_F_pvalue') = Pvalue associated to ADFf
- res('ADF_F_pi') = Number of ADF terms in ADF tests on e(i,t)
- res('ADF_F_Ti') = Adjusted time dimension for ADF tests on e(i,t)
When there is more than one common factor (r > 1):
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- res('MQc') = MQc(m) Statistics with critical values at 1%, 5% and 10% for m=r,...,1
- res('MQf') = MQf(m) Statistics with critical values at 1%, 5% and 10% for m=r,...,1
- res('MQc_r1') = Number of Common Stochastic Trends at 1%, 5% and 10% (MQc Test)
- res('MQf_r1') = Number of Common Stochastic Trends at 1%, 5% and 10% (MQf Test)
- res('MQf_p') = Optimal lag order for the VAR(p) on dYc (MQf test)
If t_order = 1:
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- res('PCe_Choi') = Pooled test standardized statistic (Choi 2001) on idiosyncratic components e: N(0,1) under H0
- res('PCe_Choi_critical') = Critical Values of the pooled test statistic (Choi, 2001) at 1%, 5% and 10%
- res('PCe_Choi_pvalue') = Pvalue Pooled test statistic (Choi 2001)
- res('PCe_MW') = Pooled test statistic (Maddala Wu 1999) on idiosyncratic components e : X(2N) under H0
- res('PCe_MW_critical') = Critical Values of the pooled test statistic (Maddala Wu 1999) at 1%, 5% and 10%
- res('PCe_MW_pvalue') = Pvalue Pooled test statistic (Maddala Wu 1999)
load(GROCERDIR+'/data/gdpan_oecd.dat'); Y=explone(dblist(GROCERDIR+'/data/gdpan_oecd.dat')); // extract matrix of data present in database res=BNG_ur1(log(Y),0,'common',4,5,'BIC3',0.05) // Example provides the BNG_ur test for all (logarithm of) Y columns, // with a constant but not trend (arg # 2 = 0), // the Lag order common to all variables (arg # 3 = 'common'), // the maximum number of lags in the ADF test set to 4 (arg # 4 = 4), // the maximum number of factors set to 5 (arg # 5 = 5), // the criteria to determine the number of factors set to the BIC criteria proposed by Bai and Ng (2002) (arg # 6 set to 'BIC3') // and the signficance level for the ADF tests set to 0.05 (arg # 7 = 0.05). | ![]() | ![]() |