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There are N data sets in periods occurring weekly/monthly, across a 10-year historical timeline.

In each period, five dates are observed (labelled a to e), where a denotes the day the period starts/an event occurs (T=0), while b to e denotes subsequent days following the event (T = 2 to 4).

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An illustration is created to better understand how the components are structured and fed into the formulae for statistical inference. enter image description here

Question: Is there a method to elicit principal components from the N data sets, and also find correlation?

P.S. This model intends to observe events/numbers (e.g. in the economic calendar) occurring weekly and monthly that affects changes in market prices.

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Your question is more about "how to estimate correlations between variables sampled at different frequencies?" than about PCA. After all, PCA is just diagonalization of the covariance (or correlation) matrix, aiming to obtain principal vectors driving the joint dynamics of your variables in an $L^2$ sense.

Since data are by construction not synchronized at the high frequency rate (i.e. you never have simultaneous trades or quote updates on two different instruments), this issue is celebrated as the Epps effect in intra-day finance (one day I will create a "tag wiki page" to describe it in detail). But it apply to any other covariance computations.

The "simplest" way to counter the Epps effect has been proposed by Ayashi and Yoshida in "On Covariance Estimation of Non-synchronously Observed Diffusion Processes". Thus you should have a look at this paper. They propose adjustments to the following simple principle: "do computations on overlapping periods only". Of course it introduces bias, and they explain how to compensate them.

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