Does Pandas calculate ewm wrong?

问题:

When trying to calculate the exponential moving average (EMA) from financial data in a dataframe it seems that Pandas' ewm approach is incorrect.

The basics are well explained in the following link: http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averages

When going to Pandas explanation, the approach taken is as follows (using the "adjust" parameter as False):

   weighted_average[0] = arg[0];    weighted_average[i] = (1-alpha) * weighted_average[i-1] + alpha * arg[i] 

This in my view is incorrect. The "arg" should be (for example) the closing values, however, arg[0] is the first average (i.e. the simple average of the first series of data of the length of the period selected), but NOT the first closing value. arg[0] and arg[i] can therefore never be from the same data. Using the "min_periods" parameter does not seem to resolve this.

Can anyone explain me how (or if) Pandas can be used to properly calculate the EMA of data?

回答1:

There are several ways to initialize an exponential moving average, so I wouldn't say pandas is doing it wrong, just different.

Here would be a way to calculate it like you want:

In [20]: s.head() Out[20]:  0    22.27 1    22.19 2    22.08 3    22.17 4    22.18 Name: Price, dtype: float64  In [21]: span = 10  In [22]: sma = s.rolling(window=span, min_periods=span).mean()[:span]  In [24]: rest = s[span:]  In [25]: pd.concat([sma, rest]).ewm(span=span, adjust=False).mean() Out[25]:  0           NaN 1           NaN 2           NaN 3           NaN 4           NaN 5           NaN 6           NaN 7           NaN 8           NaN 9     22.221000 10    22.208091 11    22.241165 12    22.266408 13    22.328879 14    22.516356 15    22.795200 16    22.968800 17    23.125382 18    23.275312 19    23.339801 20    23.427110 21    23.507635 22    23.533520 23    23.471062 24    23.403596 25    23.390215 26    23.261085 27    23.231797 28    23.080561 29    22.915004 Name: Price, dtype: float64 

回答2:

You can compute EWMA using alpha or coefficient (span) in Pandas ewm function.

Formula for using alpha: (1 - alpha) * previous_val + alpha * current_val where alpha = 1 / period

Formula for using coeff: ((current_val - previous_val) * coeff) + previous_val where coeff = 2 / (period + 1)

Here is how you can use Pandas for computing above formulas:

con = pd.concat([df[:period][base].rolling(window=period).mean(), df[period:][base]])  if (alpha == True):     df[target] = con.ewm(alpha=1 / period, adjust=False).mean() else:     df[target] = con.ewm(span=period, adjust=False).mean() 

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