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My question relates to calculation total debt as percent of GDP (quarterly). Since debt is a stock and GDP is a flow, I can understand calculation it on an annual basis but not quarterly.

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Even if the measure calculated is total debt at a point in time as a percentage of annual GDP, the frequency with which it is calculated could be quarterly. Taking quarter 1 2018 as an example, debt would be the total at end of that quarter. GDP might relate to the last available full year, ie 2017, or to the year ending in that quarter, ie from quarter 2 2017 to quarter 1 2018.

A chart of such quarterly data for the US may be viewed here.

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