Moving Average with Variable Window Size

Say I have a time series with time t and data x. Both are column vectors of length n (where n can be very big).

t is sorted, but not monotonic. The step size between successive times in t is variable (and can be 0).

I'd like to calculate the simple moving average of x, but using a window size based on time, not on the number of elements.

For example, a moving average based on a 10 second window. For every t, it will take an average of the last 10s of x. But since the timestep sizes are variable, this could mean that the number of previous elements of x being averaged also varies.

I know how to do this using a loop through t, but that would be very slow considering n can be hundreds of thousands to millions of points.

Is there a clever way to do this without a loop?

Answer 1

[Steven Lord]

See the "Sample Points for Moving Average" example in the documentation page for movmean. While that example has uniformly spaced sample points, you could use non-uniformly spaced sample points.

[ET]

Nice, this worked. Thank you!

t = 0 + cumsum(rand(10,1));

x = 3*t;

t = seconds(t);

% Loop method

xm = NaN(size(t));

windowSize = seconds(1.1); % arbitrary size

for k = 1:length(t)

id = find(t(1:k) >= (t(k)-windowSize));

if isempty(id)

continue

end

xm(k) = mean(x(id));

clear id

end

% movmean method

xm2 = movmean(x,[windowSize,0],'SamplePoints',t)

[seconds(t),x,xm,xm2]