Class: regARIMA
Filter disturbances through regression model with ARIMA errors
[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 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: 
NaN
s in Z
, U0
, X
,
and Z0
indicate missing values and filter
removes
them. The software merges the presample data sets (U0
and Z0
),
then uses listwise deletion to remove any NaN
s. filter
similarly
removes NaN
s from the effective sample data (Z
and X
).
Removing NaN
s in the data reduces the sample size.
Such removal can also create irregular time series.
Removing NaN
s in the main data
reduces the effective sample size. Such removal can also create irregular
time series.
filter
assumes that you synchronize
presample data such that the latest observation of each presample
series occurs simultaneously.
All predictor series (i.e. columns) in X
are
associated with each error series in Z
to produce numPaths
response
series Y
.

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.