If I have a (financial) time series, and I sample it with two different periods, at 5 and at 60 minute intervals, can I create an exponential moving average on the 5 minute sampled data which is the same as an exponential moving average on the 60 minute sampled data?
Something like this:
e1 = EMA(a1) applied on sampled_data(60 min)
e2 = EMA(a2) applied on sampled_data(5 min)
a1 and a2 are the smoothing factors of the exponential moving average (the period)
Can I compute the a2 value for any a1 value, such that e1 = e2?
When I say that e1 = e2 I mean that if I graph the values of the EMA computed from 5 min data on top of the 60 min data chart and EMA, the two EMAs should be superposed. This means that in between two data points for EMA(60 min) there will be 60/5=12 data points for EMA(5 min).