[Y,E,U]
= filter(Mdl,Z)
[Y,E,U]
= filter(Mdl,Z,Name,Value)
[
filters
errors to produce responses, innovations, and unconditional disturbances
of a univariate regression model with ARIMA time series errors.Y
,E
,U
]
= filter(Mdl
,Z
)
[
filters
errors using additional options specified by one or more Y
,E
,U
]
= filter(Mdl
,Z
,Name,Value
)Name,Value
pair
arguments.

Regression model with ARIMA errors, specified as a model returned
by The parameters of 

Errors that drive the innovation process, specified as a As a column vector, 
Specify optional commaseparated 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 unconditional disturbances that provide initial values
for the ARIMA error model, specified as the commaseparated pair consisting
of
Default: 

Predictor data in the regression model, specified as the commaseparated
pair consisting of The columns of Default: 

Presample errors providing initial values for the input error
series,
Default: 
Notes


Simulated responses, returned as a 

Simulated, mean 0 innovations of the ARIMA error model, returned
as a 

Simulated unconditional disturbances, returned as a 
filter
generalizes simulate
.
Both filter a series of errors to produce responses (Y
),
innovations (E
), and unconditional disturbances
(U
). However, simulate
autogenerates
a series of mean zero, unit variance, independent and identically
distributed (iid) errors according to the distribution in Mdl
.
In contrast, filter
requires that you specify your
own errors, which can come from any distribution.
[1] Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.
[2] Davidson, R., and J. G. MacKinnon. Econometric Theory and Methods. Oxford, UK: Oxford University Press, 2004.
[3] Enders, W. Applied Econometric Time Series. Hoboken, NJ: John Wiley & Sons, Inc., 1995.
[4] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[5] Pankratz, A. Forecasting with Dynamic Regression Models. John Wiley & Sons, Inc., 1991.
[6] Tsay, R. S. Analysis of Financial Time Series. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005.