I(0) and I(1) Factors

[CharlieEVIEWS]

Dear all,

Here's a subroutine I wrote to recursively (!j) estimate Stock and Watson (2002) I(0) factors and Bai (2004) I(1) factors based on a Gauss code by Igor Masten where N>T.

Note: X is our matrix of time series created from g1_standstat1 - a group of standardized stationary variables.

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'Stock and Watson Code: %start = "1980q1" %endminusone = "2002q4-1" !noiterations = 20 for !j = 1 to !noiterations smpl {%start} {%endminusone}+!j stom(g1_standstat1,X) scalar T = @rows(X) scalar N = @columns(X) 'maximum number of factors: scalar k_max = 4 'Because N>T: sym XX = X*@transpose(X) scalar il = T-1-k_max+1 scalar iu = T-1 'Note: VA corresponds to VEctors, VE corresponds to VAlues matrix va = @eigenvectors(XX) vector ve = @eigenvalues(XX) for !i = il to iu vector factor!i = ((T-1)^(0.5))*@columnextract(va,!i) matrix(T,k_max) factors colplace(factors,factor!i,!i-il+1) next matrix loadings = @transpose(factors)*X/(T-1) 'For a normalization, multiply/divide by the element [kmax,1] of the loadings matrix. scalar norm = loadings(k_max,1) factors = factors*norm loadings = loadings/norm 'Re-extract normalized factors from this matrix as series for future subroutines, in reverse order: 'i.e. the factor associated with the largest eigenvalue is F_1, second is F_2,...,F_k_max mtos(factors,factorgroup1) for !i = 1 to k_max scalar temp = k_max-!i+1 rename ser0{temp} f_1_!i_!j next delete temp delete factorgroup1

This is our subroutine for estimating I(1) factors, where g1_standnonstat1 is our group of nonstationary standardized variables and the subscript denotes the I(1) property.

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'Bai (2004) Code stom(g1_standnonstat1,i_X) scalar i_T = @rows(i_X) scalar i_N = @columns(i_X) scalar i_k_max = 4 sym i_XX = i_X*@transpose(i_X) 'Note the difference with the stationary routine here: scalar i_il = T-k_max+1 scalar i_iu = T matrix i_va = @eigenvectors(i_XX) vector i_ve = @eigenvalues(i_XX) for !i = i_il to i_iu 'Again, note the difference with the stationary routine here: vector i_factor!i = (T)*@columnextract(i_va,!i) matrix(i_T,i_k_max) i_factors colplace(i_factors,i_factor!i,!i-i_il+1) next matrix i_loadings = @transpose(i_factors)*X/(i_T^2) 'normalize scalar i_norm = i_loadings(i_k_max,1) i_factors = i_factors*i_norm i_loadings = i_loadings/i_norm 'Re-extract normalized factors from this matrix, in reverse order: i.e. the factor associated with the largest eigenvalue is if1, second is i_F_2,...,i_F_km_max mtos(i_factors,i_factorsgroup1) for !i = 1 to i_k_max scalar temp = i_k_max-!i+1 rename ser0{temp} if1_!i_!j next delete temp delete i_factorsgroup1

Best wishes

[CharlieEVIEWS]

Where T>N:

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%start = "1960q1" %endminusone = "2002q4-1" !noiterations = 20 for !j = 1 to !noiterations smpl {%start}+1 {%endminusone}+!j 'Stock and Watson (2002) - I(0) factors where T>N stom(g1_standstat1,X) scalar T = @rows(X) scalar N = @columns(X) 'maximum number of factors: scalar k_max = 4 sym XX = @transpose(X)*X scalar il = N-k_max+1 scalar iu = N matrix va = @eigenvectors(XX) vector ve = @eigenvalues(XX) for !i = il to iu vector loadings!i = (N)^(0.5)*@rowextract(@transpose(va),!i) matrix(k_max,N) loadings rowplace(loadings,loadings!i,!i-il+1) next matrix factors = ((X*@transpose(loadings))/N) 'For a normalization, multiply/divide by the element [kmax,1] of the loadings matrix. scalar norm = loadings(k_max,1) factors = factors*norm loadings = loadings/norm 'Re-extract normalized factors from this matrix as series for future subroutines, in reverse order: 'i.e. the factor associated with the largest eigenvalue is F_1, second is F_2,...,F_km_max mtos(factors,factorgroup1) for !i = 1 to k_max scalar temp = k_max-!i+1 rename ser0{temp} f_1_!i_!j next delete temp delete factorgroup1 for !i = il to iu delete loadings!i next

And again, for the case where we want to extract I(1) factors:

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'Factors extracted as per Bai (2004): with a subscript i_ denoting integrated variables. stom(g1_standnonstat1,i_X) scalar i_T = @rows(i_X) scalar i_N = @columns(i_X) scalar i_k_max = 4 sym i_XX = @transpose(i_X)*i_X scalar i_il = N-i_k_max+1 scalar i_iu = N matrix i_va = @eigenvectors(i_XX) vector i_ve = @eigenvalues(i_XX) for !i = i_il to i_iu vector i_loadings!i = (i_N)^(0.5)*@rowextract(@transpose(i_va),!i) matrix(i_k_max,i_N) i_loadings rowplace(i_loadings,i_loadings!i,!i-il+1) next matrix i_factors = ((i_X*@transpose(i_loadings))/N) 'Normalize scalar i_norm = i_loadings(i_k_max,1) i_factors = i_factors*i_norm i_loadings = i_loadings/i_norm 'Re-extract normalized factors from this matrix, in reverse order: i.e. the factor associated with the largest eigenvalue is if1, second is i_F_2,...,i_F_km_max mtos(i_factors,i_factorsgroup1) for !i = 1 to i_k_max scalar temp = i_k_max-!i+1 rename ser0{temp} if1_!i_!j next delete temp delete i_factorsgroup1 for !i = i_il to i_iu delete i_loadings!i next

Warmest regards,

Charlie

[hamidlalkhezri]

hi
im working favar model with Eviews and I thank you for your guidance.
I have a few questions
1- what do you mean from I(0),I(1) factors?You're talking about stability?
2-when I run program[ 'Stock and Watson (2002) - I(0) factors where T>N] "for statement unterminated in "for !J=1 to 20"
please guide me

[hamidlalkhezri]

hi
im working favar model with Eviews and I thank you for your guidance.
I have a few questions
1- what do you mean from I(0),I(1) factors?You're talking about stability?
2-when I run program[ 'Stock and Watson (2002) - I(0) factors where T>N] "for statement unterminated in "for !J=1 to 20"
please guide me

[hamidlalkhezri]

Where T>N:

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%start = "1960q1" %endminusone = "2002q4-1" !noiterations = 20 for !j = 1 to !noiterations smpl {%start}+1 {%endminusone}+!j 'Stock and Watson (2002) - I(0) factors where T>N stom(g1_standstat1,X) scalar T = @rows(X) scalar N = @columns(X) 'maximum number of factors: scalar k_max = 4 sym XX = @transpose(X)*X scalar il = N-k_max+1 scalar iu = N matrix va = @eigenvectors(XX) vector ve = @eigenvalues(XX) for !i = il to iu vector loadings!i = (N)^(0.5)*@rowextract(@transpose(va),!i) matrix(k_max,N) loadings rowplace(loadings,loadings!i,!i-il+1) next matrix factors = ((X*@transpose(loadings))/N) 'For a normalization, multiply/divide by the element [kmax,1] of the loadings matrix. scalar norm = loadings(k_max,1) factors = factors*norm loadings = loadings/norm 'Re-extract normalized factors from this matrix as series for future subroutines, in reverse order: 'i.e. the factor associated with the largest eigenvalue is F_1, second is F_2,...,F_km_max mtos(factors,factorgroup1) for !i = 1 to k_max scalar temp = k_max-!i+1 rename ser0{temp} f_1_!i_!j next delete temp delete factorgroup1 for !i = il to iu delete loadings!i next

And again, for the case where we want to extract I(1) factors:

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'Factors extracted as per Bai (2004): with a subscript i_ denoting integrated variables. stom(g1_standnonstat1,i_X) scalar i_T = @rows(i_X) scalar i_N = @columns(i_X) scalar i_k_max = 4 sym i_XX = @transpose(i_X)*i_X scalar i_il = N-i_k_max+1 scalar i_iu = N matrix i_va = @eigenvectors(i_XX) vector i_ve = @eigenvalues(i_XX) for !i = i_il to i_iu vector i_loadings!i = (i_N)^(0.5)*@rowextract(@transpose(i_va),!i) matrix(i_k_max,i_N) i_loadings rowplace(i_loadings,i_loadings!i,!i-il+1) next matrix i_factors = ((i_X*@transpose(i_loadings))/N) 'Normalize scalar i_norm = i_loadings(i_k_max,1) i_factors = i_factors*i_norm i_loadings = i_loadings/i_norm 'Re-extract normalized factors from this matrix, in reverse order: i.e. the factor associated with the largest eigenvalue is if1, second is i_F_2,...,i_F_km_max mtos(i_factors,i_factorsgroup1) for !i = 1 to i_k_max scalar temp = i_k_max-!i+1 rename ser0{temp} if1_!i_!j next delete temp delete i_factorsgroup1 for !i = i_il to i_iu delete i_loadings!i next

Warmest regards,

Charlie

hi
im working favar model with Eviews and I thank you for your guidance.
I have a few questions
1- what do you mean from I(0),I(1) factors?You're talking about stability?
2-when I run program[ 'Stock and Watson (2002) - I(0) factors where T>N] "for statement unterminated in "for !J=1 to 20"
please guide me