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Is it possible to pull history on non-price/volume fields such as TR.EPSActValue? get_timeseries API only seems to cater for price/volume data and the get_data API doesn't accept start and end dates.

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Yes, it is possible. E.g.

ek.get_data('IBM.N', ['TR.EPSActValue.date', 'TR.EPSActValue'], {'SDate':0, 'EDate':-7, 'Frq':'FQ', 'Period':'FI0'})

retrieves quarterly actual EPS for IBM for the last 8 quarters. I strongly recommend using Eikon Excel for data retrieval modeling where you can take advantage of Formula Builder wizard that helps you figure out what parameters you need to use in get_data method. Alternatively you can use Data Item Browser. The following tutorial talks about this at length.
https://developers.thomsonreuters.com/eikon-apis/eikon-web-and-scripting-apis/learning?content=14707&type=learning_material_item

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