Name

BNG_ur1 — Bai and Ng Panel Unit Root Test

CALLING SEQUENCE

res = BNG_ur1(Y,t_order,typeoflag,pmax,kmax,criteria,signif)

PARAMETERS

Input

• 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)

Output

• 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):

  **************************************

  - 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):

  ************************************************

  - 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:

  ****************

  - 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)

DESCRIPTION

Bai and Ng (2004) test of unit root (ref: "A PANIC attack on unit root and cointegration", Econometrica, vol. 72, n.4, p.1127-1177).

EXAMPLE

res=BNG_ur1(Y,0,'common',4,5,'BIC3',0.05)
 
Example provides the BNG_ur test for all 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). 

               

AUTHOR

Christophe Hurlin 2004 / Eric Dubois 2008