Response variable, specified as a vector of length n, where n is the number of observations. Each entry in y is the response for the corresponding row of X.

Missing values (NaN's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.

Data Types: single| double

Matrix of explanatory variables (also called 'regressors') of dimension n x (p-1) where p denotes the number of explanatory variables including the intercept. Rows of X represent observations, and columns represent variables. By default, there is a constant term in the model, unless you explicitly remove it using input option intercept, so do not include a column of 1s in X. Missing values (NaN's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.

Data Types: single| double

n x r matrix or vector of length r. If Z is a n x r matrix it contains the r variables which form the scedastic function.

If Z is a vector of length r it contains the indexes of the columns of matrix X which form the scedastic function.

Therefore, if for example the explanatory variables responsible for heteroscedasticity are columns 3 and 5 of matrix X, it is possible to use both the syntax regressH(y,X,X(:,[3 5])) or the syntax regressH(y,X,[3 5])

Data Types: single| double

If bsb=[] (default) then all units are used to produce parameter estimates, else, just the units forming bsb are used

Example: 'bsb',20:50

Data Types: double

A number between 0 and 1 which defines the confidence level which is used to produce the bands. The default value of conflev is 0.99.

Example: 'conflev',0.999

Data Types: double

Indicator for the constant term (intercept) in the fit, specified as the comma-separated pair consisting of 'Intercept' and either true to include or false to remove the constant term from the model.

Example: 'intercept',false

Data Types: boolean

it is possible to supply the output produced by functions, regressH or regressHart or regressHhar or FSRHeda.

Note that if input optional argument outH is supplied the model is not fitted and the parameter estimates are taken from outH.

Example: out=regress(y,X,Z); 'outH',out

Data Types: struct

If originalScale is true, plot is shown in the original scale (default). If originalScale is false forecasts are shown on the transformed scale.

Example: 'originalScale',false

Data Types: boolean

Scalar which identifies the column of X to put in x axis of the plot. Default value of selcolX is 1.

Example: 'selcolX',2

Data Types: double

If typeH is 'art' (default) than the skedastic function is modelled as follows $$\sigma^2_i = \sigma^2 (1 + \exp(\gamma_0 + \gamma_1 Z(i,1) + \cdots + \gamma_{r} Z(i,r)))$$ on the other hand, if typeH is 'har' then traditional formulation due to Harvey is used as follows $$\sigma^2_i = \exp(\gamma_0 + \gamma_1 Z(i,1) + \cdots + \gamma_{r} Z(i,r)) =\sigma^2 (\exp(\gamma_1 Z(i,1) + \cdots + \gamma_{r} Z(i,r))$$

Remark. Missing values (NaN's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.

Example: 'typeH','har'

Data Types: character or string