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I would like to create a composite indicator and to do prediction on this one. Probably I will use ARIMA or another model for this prediction.

I need to create this composite index combining 6 variables and I would like to use PCA and factor analysis in order to create the weights of each variable.

I’ve got time series of 6 variables (for 400 records) and I would like to create a composite indicator.

I know how to create this composite index using a particular point in time of my time series (with PCA and FA) but my question is: how can I create my composite index using PCA and FA taking into account that I have time series of my 6 variables?

iliasfl
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Paola
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  • I'm referring to something like http://www.cup.ualberta.ca/wp-content/uploads/2013/04/SEICUPWebsite_10April13.pdf. In one point in time I've got 6 columns (variables) and 400 records (rows). I think I can use PCA and FA with these data. What I would like to know is to how to use the time series of my variables. – Paola Nov 05 '15 at 14:16
  • sorry, yes for each variable (indicator) and each time point I have 400 records (entities). The time points are 70 for each variable. – Paola Nov 05 '15 at 14:30
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    400 entities are 400 cities and the variables are 6 financial variables, the time series of each variable has 70 months. I want to combine these 6 variables into one combined financial indicator and after that I want to do prediction on this one. – Paola Nov 05 '15 at 14:38
  • Thanks, now I understand. Well, it seems that you can simply pool the data across time points, i.e. combine your 400 cities at 70 months into 400*70=28000 data points and then do PCA or FA on all these data, i.e. your data matrix will have 28000 rows and 6 columns. – amoeba Nov 05 '15 at 14:43
  • In terms of the literature I'm aware of, the groundwork for longitudinal PCA was done by Pieter Kroonenberg in the 80s with papers like this https://openaccess.leidenuniv.nl/bitstream/handle/1887/11649/7_702_043.pdf?sequence=1 (see page 105 of the doc for a visualization of the 3 mode data matrix). More recently, Hyndman's papers on time series and *functional data analysis* using PCA will have more relevance for you. – Mike Hunter Nov 06 '15 at 14:06
  • To amoeba's point about creating a single, large matrix, Hyndman also wrote a paper about leveraging the moments of the distributions of the features in this matrix as input to a *global* analysis of time series information. Regrettably, while I have a link to this paper *somewhere* I can't find it now and an online search for it failed to turn it up. *It does exist*! Maybe ask Hyndman for it... – Mike Hunter Nov 06 '15 at 14:12

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