BGM function

Separate $R$ From $X$

$X$ may include some information related with $R$. The function extract factors from X which is not related with R by iteration based on Boivin et al. (2009).

BGM(X, R, K = 2, tolerance = 0.001, nmax = 100)

Arguments

• X: a large matrix from which principle components are extracted.
• R: a numeric vector which we are interesting in, for example interest rates.
• K: the number of extracted principle components.
• tolerance: the difference between factors when iterating.
• nmax: the max iterations, see details.

Returns

the first K principle components, i.e. $F_t^{(n)}$, not containing the information R.

Details

The algorithm is as follows:

1. Extract the first K principal components noted $F_t^{(0)}$ from X.
2. Regress X on $F_t^{(0)}$ and $R_t$, and get regression coefficients $\beta_R^{(0)}$ of $R_t$.
3. compute $X_0^{(0)} = X_t- R_t \beta_R$.
4. Extract the first K principal components noted $F_t^{(1)}$ from X_t^{(0)}.
5. repeat step 2 - step 4 until precision you want.

Examples

data('regdata')
BGM(X = regdata[,1:115],R = regdata[,ncol(regdata)], K = 2)

References

Boivin, J., M.P. Giannoni and I. Mihov, Sticky Prices and Monetary Policy: Evidence from Disaggregated US Data. American Economic Review, 2009. 99(1): p. 350-384.