Vectorize linear trend estimates

I have a few thousand time series of the same length, and for each I'd like to obtain its linear trend and the corresponding p-value. I use for loops and estimate the trend/p-value for each time series sequentially using the robustfit function.

The whole thing doesn't take much time. But still I wonder whether it is possible to vectorize the trend estimates. I understand I can get all linear trends at once using the backslash operator. But that doesn't give p-values.

Answer 1

[Matt J]

I understand I can get all linear trends at once using the backslash operator. But that doesn't give p-values.

First, it might not be a good idea to use backslash straightforwardly. Polynomial fitting has certain numerically sensitive properties. POLYFIT uses a QR decomposition:

    [Q,R] = qr(V,0);
    ws = warning('off','all'); 
    p = R\(Q'*y);    % Same as p = V\y;
    warning(ws);
    if size(R,2) > size(R,1)
       warning(message('MATLAB:polyfit:PolyNotUnique'))
    elseif warnIfLargeConditionNumber(R)
        if nargout > 2
            warning(message('MATLAB:polyfit:RepeatedPoints'));
        else
            warning(message('MATLAB:polyfit:RepeatedPointsOrRescale'));
        end
    end

But anyway, once you've found a solution to the system V*x=Y, it seems to me that you could vectorize the p-values by analyzing the residuals,

   R=V*x-Y; %residuals

    Rmean=mean(R,2);
     Rstd=std(R,0,2);

   R=bsxfun(@minus,R,Rmean); %Normalize the residuals
   R=bsxfun(@rdivide,R,Rstd);  

   pvalues=sum(R>=quantile,2);