Can I compute the logarithmic return from a time series without any intermediate calculations?

Yes, you definitely can do so. To illustrate, Let's assume the price time series (i.e. textrm{P_{t}}) are stored in A1:A300 range.

To compute logarithmic price

$$p_{t}= ln(P_{t})$$  
  • In Excel, in cell B1, type +LN(A1:A300) and hit return. This will compute the log of first data cell.
  • select cell B1:B300, hit F2 to edit the formula, and ctrl+Alt+Enter together. This will populate the B1:B300 and format the fomula as {=LOG($ A $1:$ A $300)}

 

To compute logarithmic returns

$$r_{t}= ln(frac{P_{t}}{P_{t-1}})= ln(P_{t})-ln(P_{t-1}) = (1-B)ln(P_{t})$$  
  • In Excel, in cell B1, type +DIFF(LN($ A $1:$ A $300),1,1) and hit return. This will compute the log price and difference it next (i.e. log return).
  • select cell B1:B300, hit F2 to edit the formula, and ctrl+Alt+Enter together. This will populate the B1:B300 and format the fomula as {=DIFF(LN($ A $1:$ A $300),1,1)}

 

To compute the ACF(k=3) of a logarithmic return directly

 

  • In Excel, in cell B1, type +ACF(DIFF(LN($ A $1:$ A $300),1,1),1,3) and hit return. This will compute the log return time series and the ACF on the derived series.
  • select cell B1:B300, hit F2 to edit the formula, and ctrl+Alt+Enter together. This will populate the B1:B300 and format the fomula as {=ACF(DIFF(LN($ A $1:$ A $300),1,1),1,3)}
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