# Can we model components in a set of multivariate multi-period time-series data?

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.

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.