I understand that Principal Component Analysis (PCA) can be applied basically for cross sectional data. Can PCA be used for time series data effectively by specifying year as time series variable and running PCA normally? I have found that dynamic PCA works for panel data and the coding in Stata is designed for panel data and not time series. Is there any specific type of PCA which works on time series data?
Update. Let me explain in detail.
I am presently constructing an index for Infrastructure in India with variables like road length, rail route length, electricity generation capacity, number of telephone subscribers etc. I have 12 variables through 22 years for 1 country. Though I have reviewed papers that apply PCA on time series and even panel data, PCA is designed for cross sectional data which assumes i.i.d assumption. Panel and cross sectional data violates it and PCA does not take into account the time series dimension in it. I have seen dynamic PCA being applied only on panel data. I want to know if there is a specific PCA that is applied on time series or running static PCA with year defined as time series variable will do the job?