How can I incrementally calculate a time series average?

Question

If I have a time series s, and if you'll pardon the pseudo code, such that

s = {t_i, v_i}

is there an easy way to calculate the series

{t_i, Mean[s[[t_0 ;; t_i]]}

As I say this is pseudo code. In reality s is a TimeSeries object

s = TimeSeries[v,{t}]

I can generate a new TimeSeries object using MovingAverage with ease, but that is not what I require. What I do require is to create a TimeSeries object which is at time t the mean of values in the initial time series having a timestamp less than or equal to t

I could code this up for a simple sequence, but given MovingAverage is supported I was hoping for something similar for this case.

Thanks in advance

Answer 1

You may use Accumulateand TimeSeriesThread.

With

s = TimeSeries[{a, b, c}];

then

t = TimeSeriesThread[Apply[Divide], {Accumulate[s], Range@s["PathLength"]}];
t["Values"]

{ a , (a+b)/2 , (a+b+c)/3 }

Hope this helps.

Answer 2

Perhaps you are looking for TimeSeriesWindow:

{#, Mean@TimeSeriesWindow[ts, {tmin, #}]} & /@ tvalues