# Principal Component Analysis on Time series data and panel data

I am trying to build an index on infrastructure and compare the index over the years and between nations. Since the variables are highly correlated with each other, review has suggested me to proceed with PCA for index construction. All tutorials show PCA reducing questions/variables like in cross sectional data. For time series data, I am having variables like road length, accidents, density, unsurfaced roads etc for 20 years on India. For panel data, same variables will be available for 20 years statewise. I need to reduce them into components using scores. Can I use PCA? Does it calculate factor loadings across time the same way it does for cross sections? Will the same hold for panel data. I propose to do the analysis in Stata.

• As far as I know, PCA requires i.i.d. observations; hence, it rarely can be applied to time series data. Nevertheless, there have been a number of academic papers where PCA is applied on time series data that is not i.i.d. For example, PCA is used to summarize information from a large number of macroeconomic variables in factor-augmented vector autoregressive models (unfortunately, I was not able to find an example of such an academic paper quickly). – Richard Hardy May 27 '15 at 18:41
• @Richard Hardy Thanks. That is exactly what I'm about to do; Summarizing variables is my prime objective. Can u explain me the significance of iid observations while doing PCA? However, this is an excerpt from a discussion on statalist. Please let me know how much u agree on this. – Nisha Simon May 29 '15 at 6:03
• Excerpt Part 1 - [When you refer to making an index, I take it that you are trying to create a single variable that in some reasonable way summarizes the three variables that are its constituents: you are trying to reduce financial development from 3 degrees of freedom down to 1. PCA is often a reasonable way to do this, and the fact that you have panel data doesn't really matter, if you are just going to use this index as a variable in later analysis. – Nisha Simon May 29 '15 at 6:13
• Excerpt Part 2 - If you want to use the index to predict some other outcome in a regression model, though, it might be better to just include the 3 variables of the index directly in the regression model as predictors instead. It isn't clear why combining the three variables into an index is better than that: presumably your data set is large enough that saving 2 degrees of freedom shouldn't be necessary. On the other hand, perhaps you are looking for some simple measure of financial development to use as an outcome. In that case forming an index makes sense. – Nisha Simon May 29 '15 at 6:13
• Excerpt Part 3 - To see how this outcome measure responds to other variables that operate in these countries over the time periods you have or to make comparisons of trends in this outcome over time in different countries, you definitely need the index to mean the same thing in each country at each time: so a single PCA would make sense; a separate PCA for each country would not. – Nisha Simon May 29 '15 at 6:15