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GLM_FORESD
Calculates the the standard deviation (sigma of the error terms (epsilon)) of the GLM^{i} model; given the values of explanatory variables.
Syntax
X
is the independent variables data matrix, such that each column represents one variable.
Betas
are the coefficients of the explanatory variables (a one dimensional array of cells (e.g. rows or columns)).
Phi
is the GLM dispersion paramter. Phi is only meaningful for Binomial (1/batch or trial size) and for Gaussian (variance).
Distribution  PHI 

Gaussian  Variance 
Poisson  1.0 
Binomial  Reciprocal of the batch/trial size) 
Lvk
is the link function that describes how the mean depends on the linear predictor (1=Identity (default), 2=Log, 3=Logit, 4=Probit, 5=LogLog).
Link  Description 

1  Identity (residuals ~ Normal distribution) 
2  Log (residuals ~ Poisson distribution) 
3  Logit (residuals ~ Binomial distribution) 
4  Probit(residuals ~ Binomial distribution) 
5  Complementary loglog (residuals ~ Binomial distribution) 
Remarks
 The underlying model is described here.
 GLM_FORESD returns an array of size equal to number of rows in the input response (Y) or explanatory variables (X).
 The number of rows in response variable (Y) must be equal to number of rows of the explanatory variables (X).
 The betas input is optional, but if the user provide one, the number of betas must equal to the number of explanatory variables (i.e. X) plus one (intercept).

For GLM with Poisson distribution,
 The values of response variable must be nonnegative integers.
 The value of the dispersion factor (Phi) must be either missing or equal to one.

For GLM with Binomial distribution,
 The values of the response variable must be nonnegative fraction between zero and one, inclusive.
 The value of the dispersion factor (Phi) must be a positive fraction (greater than zero, and less than one).
 For GLM with Guassian distribution, the dispersion factor (Phi) value must be positive.
 The GLM_FORESD is the same as GLM_VOL. It is introduced only for consistency with other models.
Files Examples
References
 Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0691042896
 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0471690740