How to extend a stock index backwards using another related index

I have two stock market indices covering different time periods with different scales that I want to combine into one longer series. The two indexes differ in terms of how they were calculated, one as more stock components than the other hence the scales of the indices differ significantly.

Index 1) Old index - starts in 1962 until 1990.
Index 2) New index - starts in 1984 till now.

I want to extend the new index (index 2) backwards based on the values of the old index so that I have a new single index starting in 1960 up till now. From 1984 I want to use the actual values for index 2, for all previous values use the old index as a basis to extroplate backwards the balues for index 1). What is right way to do this? I’m guessing it requires some kind of rebasing. Do I need to normalise the data in order to do this (e.g. convert to between 1 and o and then reconvert back)

Thanks,

Lucas

Unless you have a constant correlation I can't see how you can do this.

If you do have a constant correlation, apply it to all the index1 data prior to 1984.

Even if you have that I'm not sure you can calculate the index2 data prior to the start of the index1 data by 2 years unless you make some fairly extreme assumptions.

edit: if you want to find the correlation simply divide one by the other. If it's constant, it'll be a straight line. Even if it's a regular curve you can still use it but you'll need to determine the differential. If it's squiggly and outside the bounds you're prepared to work with - then consider it non-correlated. If it is squiggly and within the bounds you're prepared to work with, do so, but factor your variance.