Try this:
UPDATE h SET Avg1WkVol = d.Avg1WkVol
FROM Test_HistoricalData h
INNER JOIN (SELECT a.RowID, Avg1WkVol = (SELECT AVG(Volume)
FROM Test_HistoricalData b
WHERE b.Symbol = a.Symbol
AND b.MarketDate < a.MarketDate
AND b.MarketDate > a.MarketDate-8)
FROM Test_HistoricalData a
) d ON d.RowID = h.RowID
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden