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https://fred.stlouisfed.org/series/ND000334Q

From this not seasonally adjusted data, Q2 GDP merely dropped 1-4305/4674=8% QoQ? What makes this number to be so different from the 32.9% decline they published today supposedly calculated form the seasonally adjusted GDP data?

https://fred.stlouisfed.org/series/GDPC1

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  1. As Fred dataset clearly states the second series in quarterly series at an annual rate where the $32.9\%$ change is calculated just as the difference from preceding quarter. The annual rate change from preceding quarter is calculated differently than quarter-on-quarter rate. You can review the formulas fred uses here. Most of the discrepancy between the numbers can be attributed to that.

  2. the seasonal adjustment is done by Fed using algorithms not by calculating quarter-on-quarter value so a discrepancy might creep already just from different method of seasonally adjusting the data although that should not be excessive.

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Quarterly versus annualized values.

8x4 quarters is 36%.

The 32.6%-36% =3.6% error could be due to seasonality, a math error, a definitional difference or any number of factors that arent given. GDP fluctuating seasonally by 5% is my guess. Q2 is normally a high quarter, due to Christmas demand wiping out q1, so annual seasonal gdp should be lower.

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