ARIMA or ARIMAX model, specified as an `arima`

model returned by `arima`

or `estimate`

.

The properties of `Mdl`

cannot contain `NaN`

s.

Response data, specified as a numeric column vector or numeric
matrix. If `Y`

is a matrix, then it has `numObs`

observations
and `numPaths`

rows.

`infer`

infers the residuals and variances of `Y`

. `Y`

represents
the time series characterized by `Mdl`

, and it is
the continuation of the presample series `Y0`

.

If `Y`

is a column vector, then it
represents one path of the underlying series.

If `Y`

is a matrix, then it represents `numObs`

observations
of `numPaths`

paths of an underlying time series.

`infer`

assumes that observations across any
row occur simultaneously. The last observation of any series is the
latest.

**Data Types: **`double`

Specify optional comma-separated pairs of `Name,Value`

arguments.
`Name`

is the argument
name and `Value`

is the corresponding
value. `Name`

must appear
inside single quotes (`' '`

).
You can specify several name and value pair
arguments in any order as `Name1,Value1,...,NameN,ValueN`

.

Presample innovations that have mean 0 and provide initial values
for the model, specified as the comma-separated pair consisting of `'E0'`

and
a numeric column vector or numeric matrix.

`E0`

must contain at least `numPaths`

columns
and enough rows to initialize the ARIMA model and any conditional
variance model. That is, `E0`

must contain at least `Mdl.Q`

innovations,
but can be greater if you use a conditional variance model. If the
number of rows in `E0`

exceeds the number necessary,
then `infer`

only uses the latest observations. The
last row contains the latest observation.

If the number of columns exceeds `numPaths`

,
then `infer`

only uses the first `numPaths`

columns.
If `E0`

is a column vector, then `infer`

applies
it to each inferred path.

**Data Types: **`double`

Presample conditional variances providing initial values for
any conditional variance model, specified as the comma-separated pair
consisting of `'V0'`

and a numeric column vector
or matrix with positive entries.

`V0`

must contain at least `numPaths`

columns
and enough rows to initialize the variance model. If the number of
rows in `V0`

exceeds the number necessary, then `infer`

only
uses the latest observations. The last row contains the latest observation.

If the number of columns exceeds `numPaths`

,
then `infer`

only uses the first `numPaths`

columns.
If `V0`

is a column vector, then `infer`

applies
it to each inferred path.

By default, `infer`

sets the necessary observations
to the unconditional variance of the conditional variance process.

**Data Types: **`double`

Exogenous predictors in the regression model, specified as the
comma-separated pair consisting of `'X'`

and a matrix.

The columns of `X`

are separate, synchronized
time series, with the last row containing the latest observations.

If you do not specify `Y0`

, then the number
of rows of `X`

must be at least ```
size(Y,2)
+ Mdl.P
```

. Otherwise, the number of rows of `X`

should
be at least `numel(Y,2)`

. In either case, if the
number of rows of `X`

exceeds the number necessary,
then `infer`

only uses the latest observations.

By default, the conditional mean model does not have a regression
coefficient.

**Data Types: **`double`

Presample response data that provides initial values for the
model, specified as the comma-separated pair consisting of `'Y'`

and
a numeric column vector or numeric matrix. `Y0`

must
contain at least `Mdl.P`

rows and `numPaths`

columns.
If the number of rows in `Y0`

exceeds `Mdl.P`

,
then `infer`

only uses the latest `Mdl.P`

observations.
The last row contains the latest observation. If the number of columns
exceeds `numPaths`

, then `infer`

only
uses the first `numPaths`

columns. If `Y0`

is
a column vector, then `infer`

applies it to each inferred
path.

By default, `infer`

backcasts to obtain the necessary
observations.

**Data Types: **`double`