Hi Bill,
I think I've got it!

Private Sub Worksheet_Calculate()
Application.EnableEvents = False
Dim iRowOffset As Integer
Range("A1").Offset(3, 0).Value = Range("A1").Offset(2, 0).Value 'A4
takes on A3 value
Range("A1").Offset(2, 0).Value = Range("A1").Offset(1, 0).Value 'A3
takes on A2 value
Range("A1").Offset(1, 0).Value = Range("A1").Offset(0, 0).Value 'A2
takes on A1 value
If Range("A4") < "" Then
For iRowOffset = Application.Count(Range("B:B")) To 1 Step -1
'Shift old averages down 1 row
Let Cells(iRowOffset + 1, 2).Value = Cells(iRowOffset, 2).Value
'Shift old time values down 1 row
Let Cells(iRowOffset + 1, 3).Value = Cells(iRowOffset, 3).Value
Next iRowOffset
Let Range("B1") = Application.Average(Range("A2:A4"))
'Put time when average was calculated into C1
Let Range("C1") = Now
Range("A5").Clear
End If
Application.EnableEvents = True
End Sub

It wouldn't work till I got rid of the first loop, which was pretty
unnecessary and down right confusing.
Now, as soon as a new price comes in it is fed into A2 after all the
values below it are shifted down one row. If A2, A3 and A4 all have
values then the average is calculated and fed into B1, after all older
averages are shifted down one row, and similarly with the time that the
average was calculated.

There could still be a problem though Bill. The code is triggered by
anything that causes automatic calculation to occur, and that's just
about everything, even just typing then entering text on any sheet.
Switching to manual calc won't do cause then nothing happens. So, it
looks like the whole workbook has to be devoted to this one purpose, at
least during the period of time that you are receiving downloaded data.

Ken Johnson