Re: vectorized moving average?

[James Sherman Jr.]

I can't double-check right now, but I think it is that filter is setup
so that it does (in this simplified case), let b be the coefficients
and has length m,

y(n) = b(1)*x(n) + b(2)*x(n-1) ... + b(m)*x(n-m+1)

So, the first value of your coefficient vector (sweep as you call it)
should be the value you want to weigh the "current" value of x (what
you call a).  Thus, long story short, I believe that your sweep value
should be:

sweep = (ma_days:-1:1).^alpha;
norm_sweep = sweep/sum(sweep);

Just reversed of what you put in.  Also, as a side note, the reason
why there wasn't much difference between movavg and filter for what
you put in, is because you just gave it uniform noise, so any average
function is really just approximating the average of the noise.

On Tue, May 11, 2010 at 1:41 PM, Tim Rueth <address@hidden> wrote:
>
> Thanks for showing how to use filter() to do a simple moving average.  I 
> implemented your code, and it agrees with movavg(x,10,10,0), which calculates 
> a 10-day simple moving average.  There's only a difference in the first 9 
> numbers due to assumed values of negative time (movavg calculates a "run-in" 
> period).  As you might recall, I'm trying to use filter() to avoid movavg()'s 
> for-loop.
>
> Now, what I'm trying to do is a weighted moving average, identical to the 
> "alpha" parameter of movavg().  When alpha=0, it's a simple moving average, 
> and agrees with filter().  If I change alpha to 1, I'm suppose to get a 
> linear MA.  Here's the code in movavg.m that does the weighting (lead is the 
> number of days to average, equal to 10 in the above case):
>
>   lead = (1:lead).^alpha;
>   ## Adjust the weights to equal 1
>   lead = lead / sum (lead);
>
>  So, for a 10-day linearly-weighted moving average (lead = 10, alpha = 1), 
> the previous 9 days and current day should be weighted as follows: 1/55, 
> 2/55, 3/55...10/55, with the greatest weight (10/55) applied to the current 
> day.  So, I tried a simple test case with just a 2-day MA on a 6-element 
> vector:
>
> ma_days = 2;
> alpha = 1;
> len = 6;
> a = rand(1,len);
>
> # Calculate MA using movavg()
> ma = movavg(a,ma_days,ma_days,alpha);
>
> # Calculate MA using filter()
> sweep = (1:ma_days).^alpha;
> norm_sweep = sweep/sum(sweep);
> f = filter(norm_sweep,1,a);
>
> disp(ma);
> disp(f);
>
> The movavg() and filter() results are similar, but not equal.  I'm guessing I 
> don't have the arguments for filter() correct, but I can't figure out what I 
> did wrong.  Particularly, I'm not sure what the second argument of filter() 
> is supposed to do.  Help?
>
> ________________________________
> From: address@hidden [mailto:address@hidden On Behalf Of James Sherman Jr.
> Sent: Friday, May 07, 2010 12:58 PM
> To: address@hidden
> Cc: Octave-ML
> Subject: Re: vectorized moving average?
>
> I'm not sure what you mean by weighting of 0.5, but to do a simple 10-day 
> average, it'd be
> x = rand(1, 100);
> y = filter(1/10*ones(1, 10), 1, x)
> This assumes that the values at negative time (x(0), x(-1), etc) are all 
> zero.  So, for example, the first value of y would be x(1)/10.
> On Fri, May 7, 2010 at 3:33 PM, Tim Rueth <address@hidden> wrote:
>>
>> I looked at both conv() and filter(), but can't figure out how to do a
>> moving average with them.  Perhaps I'm not understanding the functions of
>> the input vars correctly.
>>
>> Let's say I have an array, a = rand(1,100).  Can you tell me how I'd use
>> conv() and filter() to take, say the 10-day moving average of it, with a
>> weighting of 0.5?
>>
>> Thanks!
>>
>>
>> > -----Original Message-----
>> > From: Andy Buckle [mailto:address@hidden
>> > Sent: Thursday, May 06, 2010 12:06 AM
>> > To: address@hidden
>> > Cc: address@hidden
>> > Subject: Re: vectorized moving average?
>> >
>> > conv is also an m file, but it only has a few ifs in. then it
>> > calls filter to get the job done. which is an oct file.
>> >
>> > Andy
>> >
>> > On Thu, May 6, 2010 at 6:28 AM, Tim Rueth <address@hidden> wrote:
>> > > Does anyone know how to take an n-day weighted moving average of a
>> > > vector without using a for-loop?  I looked at the M code
>> > for movavg()
>> > > and it uses a for-loop, so I'm guessing there probably isn't a way,
>> > > but I thought I'd check.  Thanks.
>> > >
>> > > --Tim
>> > > _______________________________________________
>> > > Help-octave mailing list
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>> > >
>> > >
>> >
>> >
>> >
>> > --
>> > /* andy buckle */
>> >
>>
>>
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