Re: time based moving average (and other newbie mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg92847] Re: time based moving average (and other newbie mathematica*From*: Mark Fisher <particlefilter at gmail.com>*Date*: Wed, 15 Oct 2008 05:36:25 -0400 (EDT)*References*: <gcn496$751$1@smc.vnet.net> <gcv7m8$e6i$1@smc.vnet.net>

On Oct 13, 6:25 am, Mark Fisher <particlefil... at gmail.com> wrote: > On Oct 10, 4:37 am, falcon <shahb... at gmail.com> wrote: > > > > > Hi, > > I see that Mathematica provides a couple of moving average functions. > > As far as I can tell, they are based on the number of elements in an > > array. Is there a function for doing moving average based on time? > > In other words, if I pass in intra-day data containing prices, times > > (up to a millisecond) and some other fields, can I get Mathematica to > > to give me a 5 minute moving average rather than moving average of the > > last 100 trades? Obviously this five minute window may contain any > > number of elements. > > > Secondly, along the same idea, I have a file with a large number of > > stocks. They are all mixed in (the file is in chronological order). > > Is there an sql type 'group by' command that lets me see moving > > averages for each stock? > > > Third, if I'm able to get moving average for each stock in the list, > > can I plot all of them in one command (I guess this technique is > > called "small multiples" in charting vernacular). Obviously I will > > only have 20 or 30 stocks. > > > Thanks > > Following up on my previous post, this version is faster: > > MovingTimeAverage = > Compile[{{data, _Real, 2}, {lag, _Real, 0}}, > Module[{j = 1}, > Table[ > While[data[[i, 1]] - data[[j, 1]] > lag, = j++]; > {data[[i, 1]], Mean[data[[j ;; i, 2]]]}, > {i, Length[data]}] > ]] > > It didn't occur to me right away to put the two pieces together. > > --Mark In a private communication, Daniel Lichtblau sent me a yet faster version. It uses of Accumulate[] as part of a faster way to compute the mean, by differencing the accumulated values and avoiding the repeated calls to Mean[]. MovingTimeAverage = Compile[{{data, _Real, 2}, {lag, _Real, 0}}, Module[{ j = 1, d2 = Prepend[Accumulate[data[[All, 2]]], 0] }, Table[ While[data[[i, 1]] - data[[j, 1]] > lag, j++]; {data[[i, 1]], (d2[[i + 1]] - d2[[j]])/(i + 1 - j)}, {i, Length[data]}] ]] --Mark