По поводу Flexible Least Squares

`fls` <-
function (A, b, mu=1, ncap=length(b), smoothed=TRUE)
{
  m <- nrow (A)
  n <- ncol (A)
  M <- array (0,c(n,n,ncap))
  E <- array (0,c(n,ncap))
  X <- array (0,c(n,ncap))
  R <- matrix(0,n,n)
  diag(R) <- diag(R) + mu
  for (j in 1:ncap) {
    Z <- solve(qr(R + tcrossprod(A[j,]),LAPACK=TRUE),diag(1.0,n));
    M[,,j] <- mu*Z             # (5.7b)
    v <- b[j]*A[j,]
    if(j==1) p <- rep(0,n)
    else p <- mu*E[,j-1]
    w <- p + v
    E[,j] <- Z %*% w           # (5.7c)
    R <- -mu*mu*Z
    diag(R) <- diag(R) + 2*mu
  }
# Calculate eqn (5.15) FLS estimate at ncap
  Q <- -mu*M[,,ncap-1]
  diag(Q) <- diag(Q) + mu
  Ancap <- A[ncap,,drop=FALSE]
  C <- Q + t(Ancap) %*% Ancap
  d <- mu*E[,ncap-1,drop=FALSE] + b[ncap]*t(Ancap)
  X[,ncap] <- C %*% d
  X[,ncap] <- solve(qr(C,LAPACK=TRUE),d)
  if (smoothed) {
# Use eqn (5.16) to obtain smoothed FLS estimates for 
# X[,1], X[,2], ..., X[,ncap-1]
    for (j in 1:(ncap-1)) {
      l <- ncap - j
      X[,l] <- E[,l] + M[,,l] %*% X[,l+1]
    }
  }
  else {
    X <- X[,ncap]
  }
  X
}

function [ frc, parRet ] = algFlexibleLeastSquares( inputTS, idxHist, idxFrc, par )
% ALGFLEXIBLELEASTSQUARES
% forecast time series using FLS algorithm
%
% [ frc, parRet ] = algFlexibleLeastSquares( inputTS, idxHist, idxFrc, par )
%
% Arguments
% inputTS [struct] input data in format "ts"

%Arguments
% ts - structure:
%   ts.s[T,N] - matrix of time series; forecasting time series is in the
%                 first column; other columns - additional time series
%   ts.t[T,1] - time in format datenum
%   ts.period[K,N] - periods of the time series ts.s
%   ts.legend[1,N] - description of the time series
%   ts.readme[string] - information about time series

[frc, parRet] = algFlexibleLeastSquares(tsMSFT_INTC, (1:100)', (101:200)', struct('train', true, 'U', diag(repmat(1,1,1)), 'V', eye(1)));
frc.s

load('tsMSFT_INTC.mat')
[frc, parRet] = algFlexibleLeastSquares(tsMSFT_INTC, (1:100)', (101:200)', struct('train', true, 'U', diag(repmat(1,1,1)), 'V', eye(1)));
frc.s

ss=frc.s;
tt=frc.t;
t=tt-min(tt);
figure, plot(1:100,ss,1:100,t);
corr(ss,t)

load('tsMSFT_INTC.mat')
[frc, parRet] = forecastRetrospective(tsMSFT_INTC, (1:100)', (101:200)', struct('train', true, 'U', diag(repmat(1,1,1)), 'V', eye(1)));
frc.s

Error using  \
Matrix dimensions must agree.
 
Error in evaluateLOO (line 65)
        Q2(iTime) = {inv(H{iTime} * ((V \ Q2{iTime + 1}) \ (inv(V))') * H{iTime}' +
        inv(Q1{iTime} + lambda * V' * U * V) )};
 
Error in estimateLambda (line 44)
        currentLOO = evaluateLOO(currentLambda, y, C, U, V);
 
Error in forecastRetrospective (line 71)
        lambda = estimateLambda(y(1:T), C(:, 1:T), U, V);

[frc, parRet] = forecastRetrospective(tsMSFT_INTC, (1:100)', (101:200)');

struct('train', true, 'U', diag(repmat(1,1,1)), 'V', eye(1))