Matrix containing estimated beta coefficients, (including the intercept when options.intercept=true) standard errors, t-stat and p-values The content of matrix B is as follows: 1st col = beta coefficients The order of the beta coefficients is as follows: 1) trend elements (if present). If the trend is of order two there are r+1 coefficients if the intercept is present otherwise there are just r components;

2) linear part of seasonal component 2, 4, 6, ..., s-2, s-1 coefficients (if present);

3) coefficients associated with the matrix of explanatory variables which have a potential effect on the time series under study (X);

4) non linear part of seasonal component, that is varying amplitude. If varying amplitude is of order k there are k coefficients (if present);

5) level shift component (if present). In this case there are two coefficients, the second (which is also the last element of vector beta) is an integer which specifies the time in which level shift takes place and the first (which is also the penultime element of vector beta) is a real number which identifies the magnitude of the upward (downward) level shift;

2nd col = standard errors;

3rd col = t-statistics;

4th col = p values.

vector of fitted values after final (NLS=non linear least squares) step.

$ (\hat \eta_1, \hat \eta_2, \ldots, \hat \eta_T)'$

Vector T-by-1 containing the raw residuals.

Vector T-by-1 containing the scaled residuals.

scale estimate of the residuals \[ \hat \sigma = cor \times \sum_{i \in S_m} [y_i- \eta(x_i,\hat \beta)]^2/(m-p) \] where $S_m$ is a set of cardinality $m$ which contains the units belonging to bsb and $p$ is the total number of estimated parameters and $cor$ is a correction factor to make the estimator consistent (see input options smallsamplecor and asymptcor).

$cov(\beta)/\hat \sigma^2$. p-by-p, square matrix.

If the model is linear out.invXX is equal to $(X'X)^{-1}$, else out.invXX is equal to $(A'A)^{-1}$ where $A$ is the matrix of partial derivatives. More precisely:

$cov(\beta)$. p-by-p, square matrix containing variance covariance matrix of estimated coefficients.

response vector y.

data matrix X containing trend, seasonal, expl and lshift, if the model is linear or linearized version of $\eta(x_i, \beta)$ if the model is non linear containing in the columns partial derivatives evaluated in correspondence of out.B(:,1) with respect to each parameter. In other words, the $i,j$-th element of out.X is \[ \frac{\partial \eta_i(x_i, \hat \beta)}{\partial \hat \beta_j} \]

$j=1, 2, \ldots, p$, $i \in S_m$.

The size of this matrix is: n-length(out.outliers)-by-p.

Reason nlinfit stopped. Integer.

If the model is non linear out.Exflag is equal to 1 if the maximization procedure did not produce warnings or the warning was different from "ILL Conditiioned Jacobian". For any other warning which is produced (for example, "Overparameterized", "IterationLimitExceeded", 'MATLAB:rankDeficientMatrix") out.Exflag is equal to -1;

Reason ALS routine stopped. Integer.

If in the iterations missing or NaN are found out.ExflagALS=-1.

Note that ALS routine is used just in case there was no convergence inside routine nlinfit in order to provide a better set of initial parameter estimates before retrying nlinfit.

If there was immediate convergence in nlinfit out.ExflagALS is empty.

Number of iterations in the ALS routine. Intger between 1 and 10000 (maximum number of iterations).

Note that ALS routine is used just in case there was no convergence inside routine nlinfit in order to provide a better set of initial parameter estimates before retrying nlinfit.

If there was immediate convergence in nlinfit out.iterALS is empty.