This is an interesting question because I think the optimal solution is different for the mean than it is for the other sample statistics.
I've provided a simulation example below that you can work through.
First, choose some arbitrary parameters and simulate some data:
%#Set some arbitrary parameters
T = 100; N = 5;
WindowLength = 10;
%#Simulate some data
X = randn(T, N);
For the mean, use filter
to obtain a moving average:
MeanMA = filter(ones(1, WindowLength) / WindowLength, 1, X);
MeanMA(1:WindowLength-1, :) = nan;
I had originally thought to solve this problem using conv
as follows:
MeanMA = nan(T, N);
for n = 1:N
MeanMA(WindowLength:T, n) = conv(X(:, n), ones(WindowLength, 1), 'valid');
end
MeanMA = (1/WindowLength) * MeanMA;
But as @PhilGoddard pointed out in the comments, the filter
approach avoids the need for the loop.
Also note that I've chosen to make the dates in the output matrix correspond to the dates in X
so in later work you can use the same subscripts for both. Thus, the first WindowLength-1
observations in MeanMA
will be nan
.
For the variance, I can't see how to use either filter
or conv
or even a running sum to make things more efficient, so instead I perform the calculation manually at each iteration:
VarianceMA = nan(T, N);
for t = WindowLength:T
VarianceMA(t, :) = var(X(t-WindowLength+1:t, :));
end
We could speed things up slightly by exploiting the fact that we have already calculated the mean moving average. Simply replace the within loop line in the above with:
VarianceMA(t, :) = (1/(WindowLength-1)) * sum((bsxfun(@minus, X(t-WindowLength+1:t, :), MeanMA(t, :))).^2);
However, I doubt this will make much difference.
If anyone else can see a clever way to use filter
or conv
to get the moving window variance I'd be very interested to see it.
I leave the case of skewness and kurtosis to the OP, since they are essentially just the same as the variance example, but with the appropriate function.
A final point: if you were converting the above into a general function, you could pass in an anonymous function as one of the arguments, then you would have a moving average routine that works for arbitrary choice of transformations.
Final, final point: For a sequence of window lengths, simply loop over the entire code block for each window length.