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I want to know whether my data are trending, co-integrated, have unit roots, have autocorrelation, or have heteroskedasticity. I want to do all this using Stata, so please suggest material or direct me a book on these topics

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You want to start with an introductory econometrics book. Stock and Watson's Introduction to Econometrics covers these topics with stata replication files.

Here is a link to the replication files

http://wps.aw.com/aw_stock_ie_3/178/45691/11696965.cw/index.html

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