Recently I got mix response on the difference between multivariate time series data and panel data. I completely understand the difference between cross sectional data, time series data and panel data. But sometimes it becomes difficult to distinguish between panel data and multivariate time series data.

For example, if we consider data on daily closing prices for last one year for 10 companies. Is it panel data or just multivariate time series data? I found such type of data categorised as multivariate time series in time series books, whereas some econometrics book categorised such type of data as panel data.

How can we statistically categorised data between multivariate time series and panel data?

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    $\begingroup$ In time series data, the serial or carry-over effect is always assumed for each series: x(t) is dependent on x(t-1). Time series thus is seen as a developmental process with intrinsic heritage in each subject (series) under the study. Panel data by default do not assume the serial effect; some analytical procedures of such data even state there must be no any carry-over. And if there should be one, it is modeled as an external, applied factor which is typically not subject-specific in parameters. $\endgroup$ – ttnphns Jun 11 at 6:07
  • $\begingroup$ The second difference pertains to the "multivariate", as you call it, situation. Say, you have two 2 companies (A,B) and 3 days of observation of their prices (t1,t2,t3). In panel (aka repeated measures) analysis the dataset is either 2 rows (companies) x 3 cols (times) - the wide format, or 6 x 1 - the long format. That means the two companies are (by default) are seen as two independent subjects. But in the two-series time series analysis the data will look as 3 rows (times, with carry over effect) x 2 cols (companies), and the companies are seen as potentially correlating variables. $\endgroup$ – ttnphns Jun 11 at 6:29
  • $\begingroup$ @ttnphns thank you for your response. It means it is correlation between the cross sectional units distinguish between panel data and multivariate time series. It means if there is no correlation between the two time series (as you mentioned) then it will become panel and if in panel data someone assume correlation between cross sectional units then panel will become multivariate time series data. Is it right? $\endgroup$ – Neeraj Jun 11 at 6:43
  • $\begingroup$ Well, I personally see it this way. If your two companies (A, B) are two processes so that the following influence is assumed true: A(t) depends on A(t-1) (and so for B) (autocorrelation), - I would call it "time series". Then, if additionally to assume: either A(t) depends on B(t) (correlation), or A(t) depends on B(t-1) (lagged correlation), - then I would call the time series "multivariate" (in the sense "two interrelated time series"). $\endgroup$ – ttnphns Jun 11 at 7:11
  • $\begingroup$ Nothing of these is assumed by default in panel data, where A and B are seen as two independent study units (usually randomly selected from their population or populations) each observed at different time follow-ups. $\endgroup$ – ttnphns Jun 11 at 7:11

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