## how does eviews compute pca scores; pc1= index?

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rel123
Posts: 4
Joined: Sun Oct 07, 2018 2:40 am

### how does eviews compute pca scores; pc1= index?

Hi there. I am writing a thesis that involves developing an index using PCA. I have 5 variables with quarterly data spanning 30 years. I standardized the variables in excel and performed PCA on the standardized variables. I did the Proc/Make Principal Components ... process to save the first principal component scores. (i) How is this output computed? I want to replicate the process in excel so i know exactly what is going on under the hood, in case my thesis adviser asks about it. (ii) for those who have developed an index using PCA before, is the output produced in this process the index or are there other steps I still need to do? Thanks.

EViews Mirza
Posts: 46
Joined: Sat Apr 22, 2017 8:23 pm

### Re: how does eviews compute pca scores; pc1= index?

In broad strokes, EViews performs the following steps:

1. Compute correlation/covariance matrix (depending on specification chosen), and the default scaling is 1/n as opposed to 1/(n-1). This makes no difference asymptotically, of course.
2. Compute eigenvectors and eigenvalues from the correlation/covariance matrix.
3. Compute scores as follows:
a) Normalize each of the original series used in computing the covariance matrix -- that is, demean and divide by standard deviation. Note, the default scaling is again 1/n -- and put the normalized variables into a matrix, say M.
b) Do a cross product of each row of M with the j^th principal component. This will yield the j^th score vector.

I hope this clarifies things.
Last edited by EViews Mirza on Sat Oct 20, 2018 10:39 am, edited 1 time in total.

rel123
Posts: 4
Joined: Sun Oct 07, 2018 2:40 am