I've run into the following situation with regards to some time series data. My situation is that I have a series of daily portfolio excess returns, for a 10 year period. Let's say I calculate the annualized tracking error of this portfolio in two ways:1. STDEV(Daily Excess)*SQRT(252)2. STDEV(Monthly Excess)*SQRT(12)I would expect these two methods to give the same results, which is indeed the case for randomly generated data. However, the two tracking error numbers are coming out quite differently using the real data (on the order of 10% or so). This is the case both for the whole period, and in all 36 month windows. My question is, what property might this time series be exhibiting to produce this kind of result? I've noticed that the autocorrelation (1M Lag) of monthly excess returns is significantly higher than the autocorrelation of daily excess returns (.2 vs. 0). However, eliminating this autocorrelation via a very naive method has not eliminated the discrepancy at all. Thanks in advance for any thoughts you might have.

QuoteOriginally posted by: RrolackI've run into the following situation with regards to some time series data. My situation is that I have a series of daily portfolio excess returns, for a 10 year period. Let's say I calculate the annualized tracking error of this portfolio in two ways:1. STDEV(Daily Excess)*SQRT(252)2. STDEV(Monthly Excess)*SQRT(12)I would expect these two methods to give the same results, which is indeed the case for randomly generated data. However, the two tracking error numbers are coming out quite differently using the real data (on the order of 10% or so). This is the case both for the whole period, and in all 36 month windows. My question is, what property might this time series be exhibiting to produce this kind of result? return smoothing? QuoteI've noticed that the autocorrelation (1M Lag) of monthly excess returns is significantly higher than the autocorrelation of daily excess returns (.2 vs. 0). However, eliminating this autocorrelation via a very naive method has not eliminated the discrepancy at all. Thanks in advance for any thoughts you might have.Could you elaborate on what naive method you tried?Is it simillar to this paper where they correct the return series in the presence of serial correlation?.

QuoteCould you elaborate on what naive method you tried?The method I used is actually quite similar to the one in that paper. One thing I'm a bit confused by: the Ljung-Box stat they use is able to detect autocorrelation with multiple lags, while their method of adjusting for autocorrelation only handles one specific lag. Is anyone aware of a statistically reasonable way to correct for autocorrelation with multiple lags?