filter
Filter disturbances using univariate ARIMA or ARIMAX model
Description
returns the numeric array of one or more response series Y
= filter(Mdl
,Z
)Y
resulting
from filtering the numeric array of one or more underlying disturbance series
Z
through the fully specified, univariate ARIMA model
Mdl
. Z
is associated with the model innovations
process that drives the specified ARIMA model.
returns the table or timetable Tbl2
= filter(Mdl
,Tbl1
)Tbl2
containing the results from
filtering the paths of disturbances in the input table or timetable
Tbl1
through Mdl
. The disturbance variable in
Tbl1
is associated with the model innovations process through
Mdl
. (since R2023b)
filter
selects the variable
Mdl.SeriesName
, or the sole variable in Tbl1
, as
the disturbance variable to filter through the model. To select a different variable in
Tbl1
to filter through the model, use the
DisturbanceVariable
name-value argument.
[___] = filter(___,
specifies options using one or more name-value arguments in
addition to any of the input argument combinations in previous syntaxes.
Name,Value
)filter
returns the output argument combination for the
corresponding input arguments. For example, filter(Mdl,Z,Z0=PS,X=Pred)
filters the
numeric vector of disturbances Z
through the ARIMAX
Mdl
, and specifies the numeric vector of presample disturbance data
PS
to initialize the model and the exogenous predictor data
X
for the regression component.
Examples
Filter Vector of Disturbances Through Model
Compute the impulse response function (IRF) of an ARMA model by filtering a vector of zeros, representing disturbances, through the model.
Specify a mean zero ARMA(2,0,1) model.
Mdl = arima(Constant=0,AR={0.5 -0.8},MA=-0.5, ...
Variance=0.1);
Simulate the first 20 responses of the IRF. Generate a disturbance series with a one-time, unit impulse, and then filter it.
z = [1; zeros(19,1)]; y = filter(Mdl,z);
y
is a 20-by-1 response path resulting from filtering the disturbance path z
through the model. y represents the IRF. The filter
function requires one presample observation to initialize the model. By default, filter
uses the unconditional mean of the process, which is 0
.
y = y/y(1);
Normalize the IRF such that the first element is 1.
Plot the impulse response function.
figure stem((0:numel(y)-1)',y,"filled"); title("Impulse Response")
The impulse response assesses the dynamic behavior of a system to a one-time, unit impulse.
Alternatively, you can use the impulse
function to plot the IRF for an ARIMA process.
Simulate and Filter Multiple Paths
Filter a matrix of disturbance paths. Return the paths of responses and innovations, which drive the data-generating processes.
Create a mean zero ARIMA(2,0,1) model.
Mdl = arima(Constant=0,AR={0.5,-0.8},MA=-0.5, ...
Variance=0.1);
Generate 20 random, length 100 paths from the model.
rng(1,"twister"); % For reproducibility [ySim,eSim,vSim] = simulate(Mdl,100,NumPaths=20);
ySim
, eSim
, and vSim
are 100-by-20 matrices of 20 simulated response, innovation, and conditional variance paths of length 100, respectively. Because Mdl does not have a conditional variance model, vSim
is a matrix completely composed of the value of Mdl.Variance
.
Obtain disturbance paths by standardizing the simulated innovations.
zSim = eSim./sqrt(vSim);
Filter the disturbance paths through the model.
[yFil,eFil] = filter(Mdl,zSim);
yFil
and eFil
are 100-by-20 matrices. The columns are independent paths generated from filtering corresponding disturbance paths in zSim
through the model Mdl
.
Confirm that the outputs of simulate
and filter
are identical.
sameE = norm(eSim - eFil) < eps
sameE = logical
1
sameY = norm(ySim - yFil) < eps
sameY = logical
1
The logical values 1
confirm the outputs are effectively identical.
Filter Disturbance Path in Timetable
Since R2023b
Fit an ARIMA(1,1,1) model to the weekly average NYSE closing prices. Supply a timetable of data and specify the series for the fit. Then, filter randomly generated Gaussian noise paths through the estimated model to simulate responses and innovations.
Load Data
Load the US equity index data set Data_EquityIdx
.
load Data_EquityIdx
T = height(DataTimeTable)
T = 3028
The timetable DataTimeTable
includes the time series variable NYSE
, which contains daily NYSE composite closing prices from January 1990 through December 2001.
Plot the daily NYSE price series.
figure
plot(DataTimeTable.Time,DataTimeTable.NYSE)
title("NYSE Daily Closing Prices: 1990 - 2001")
Prepare Timetable for Estimation
When you plan to supply a timetable, you must ensure it has all the following characteristics:
The selected response variable is numeric and does not contain any missing values.
The timestamps in the
Time
variable are regular, and they are ascending or descending.
Remove all missing values from the timetable, relative to the NYSE price series.
DTT = rmmissing(DataTimeTable,DataVariables="NYSE");
T_DTT = height(DTT)
T_DTT = 3028
Because all sample times have observed NYSE prices, rmmissing
does not remove any observations.
Determine whether the sampling timestamps have a regular frequency and are sorted.
areTimestampsRegular = isregular(DTT,"days")
areTimestampsRegular = logical
0
areTimestampsSorted = issorted(DTT.Time)
areTimestampsSorted = logical
1
areTimestampsRegular = 0
indicates that the timestamps of DTT
are irregular. areTimestampsSorted = 1
indicates that the timestamps are sorted. Business day rules make daily macroeconomic measurements irregular.
Remedy the time irregularity by computing the weekly average closing price series of all timetable variables.
DTTW = convert2weekly(DTT,Aggregation="mean"); areTimestampsRegular = isregular(DTTW,"weeks")
areTimestampsRegular = logical
1
T_DTTW = height(DTTW)
T_DTTW = 627
DTTW
is regular.
figure
plot(DTTW.Time,DTTW.NYSE)
title("NYSE Daily Closing Prices: 1990 - 2001")
Create Model Template for Estimation
Suppose that an ARIMA(1,1,1) model is appropriate to model NYSE composite series during the sample period.
Create an ARIMA(1,1,1) model template for estimation. Set the response series name to NYSE
.
Mdl = arima(1,1,1);
Mdl.SeriesName = "NYSE";
Mdl
is a partially specified arima
model object.
Fit Model to Data
Fit an ARIMA(1,1,1) model to weekly average NYSE closing prices. Specify the entire series.
EstMdl = estimate(Mdl,DTTW);
ARIMA(1,1,1) Model (Gaussian Distribution): Value StandardError TStatistic PValue ________ _____________ __________ ___________ Constant 0.86386 0.46496 1.8579 0.06318 AR{1} -0.37582 0.22719 -1.6542 0.09809 MA{1} 0.47221 0.21741 2.172 0.029858 Variance 55.89 1.832 30.507 2.1199e-204
EstMdl
is a fully specified, estimated arima
model object. By default, estimate
backcasts for the required Mdl.P = 2
presample responses.
Filter Random Gaussian Disturbance Paths
Generate 2 random, independent series of length T_DTTW
from the standard Gaussian distribution. Store the matrix of series as one variable in DTTW
.
rng(1,"twister") % For reproducibility DTTW.Z = randn(T_DTTW,2);
DTTW contains a new variable called Z containing a T_DTTW
-by-2 matrix of two disturbance paths.
Filter the paths of disturbances through the estimated ARIMA model. Specify the table variable name containing the disturbance paths.
Tbl2 = filter(EstMdl,DTTW,DisturbanceVariable="Z");
tail(Tbl2)
Time NYSE NASDAQ Z NYSE_Response NYSE_Innovation NYSE_Variance ___________ ______ ______ _____________________ ________________ ___________________ ______________ 16-Nov-2001 577.11 1886.9 -1.8948 0.41292 358.78 433.57 -14.166 3.087 55.89 55.89 23-Nov-2001 583 1898.3 1.3583 0.27051 367.95 436.63 10.155 2.0223 55.89 55.89 30-Nov-2001 581.41 1925.8 -0.9118 1.1119 363.35 445.61 -6.8165 8.3125 55.89 55.89 07-Dec-2001 584.96 1998.1 -0.14964 -2.418 361.61 428.95 -1.1187 -18.077 55.89 55.89 14-Dec-2001 574.03 1981 -0.40114 0.98498 359.6 434.9 -2.9989 7.3636 55.89 55.89 21-Dec-2001 582.1 1967.9 -0.57758 0.0039243 355.48 437.04 -4.318 0.029338 55.89 55.89 28-Dec-2001 590.28 1967.2 2.0039 -0.92415 370.84 430.2 14.981 -6.9089 55.89 55.89 04-Jan-2002 589.8 1950.4 -0.50964 -0.43856 369.19 427.09 -3.8101 -3.2787 55.89 55.89
size(Tbl2)
ans = 1×2
627 6
Tbl2
is a 627-by-6 timetable containing all variables in DTTW
, and the two filtered response paths NYSE_Response
, innovation paths NYSE_Innovation
, and constant variance paths NYSE_Variance
(Mdl.Variance = 55.89
).
Supply Presample Responses
Assess the dynamic behavior of a system to a persistent change in a variable by plotting a step response. Supply presample responses to initialize the model.
Specify a mean zero ARIMA(2,0,1) process.
Mdl = arima(Constant=0,AR={0.5 -0.8},MA=-0.5, ...
Variance=0.1);
Simulate the first 20 responses to a sequence of unit disturbances. Generate a disturbance series of ones, and then filter it. Set all presample observations equal to zero.
Z = ones(20,1); Y = filter(Mdl,Z,Y0=zeros(Mdl.P,1)); Y = Y/Y(1);
The last step normalizes the step response function to ensure that the first element is 1.
Plot the step response function.
figure stem((0:numel(Y)-1)',Y,"filled"); title("Step Response")
Simulate Responses from ARIMAX Model
Create models for the response and predictor series. Set an ARIMAX(2,1,3) model to the response MdlY
, and an AR(1) model to the MdlX
.
MdlY = arima(AR={0.1 0.2},D=1,MA={-0.1 0.1 0.05}, ...
Constant=1,Variance=0.5,Beta=2);
MdlX = arima(AR=0.5,Constant=0,Variance=0.1);
Simulate a length 100 predictor series x
and a series of iid normal disturbances z
having mean zero and variance 1.
rng(1,"twister")
z = randn(100,1);
x = simulate(MdlX,100);
Filter the disturbances z
using MdlY
to produce the response series y
. Plot y
.
y = filter(MdlY,z,X=x); figure plot(y); xlabel("Time") ylabel("Response")
Filter Disturbances Through Composite Conditional Mean and Variance Model
Create the composite AR(1)/GARCH(1,1) model
Create the composite model.
CVMdl = garch(Constant=0.2,GARCH=0.1,ARCH=0.05); Mdl = arima(Constant=1,AR=0.5,Variance=CVMdl)
Mdl = arima with properties: Description: "ARIMA(1,0,0) Model (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" P: 1 D: 0 Q: 0 Constant: 1 AR: {0.5} at lag [1] SAR: {} MA: {} SMA: {} Seasonality: 0 Beta: [1×0] Variance: [GARCH(1,1) Model]
Mdl
is an arima
object. The property Mdl.Variance
contains a garch
object that represents the conditional variance model.
Generate a random series of 100 standard Gaussian of disturbances.
rng(1,"twister") % For reproducibility z = randn(100,1);
Filter the disturbances through the model. Return and plot the simulated conditional variances.
[y,e,v] = filter(Mdl,z); plot(z)
Input Arguments
Z
— Disturbance series paths zt
numeric column vector | numeric matrix
Underlying disturbance paths zt, specified
as a numobs
-by-1 numeric column vector or
numobs
-by-numpaths
numeric matrix.
numObs
is the length of the time series (sample size).
numpaths
is the number of separate, independent disturbance
paths.
zt drives the innovation process εt. For a variance process σt2, the innovation process is
Each row corresponds to a sampling time. The last row contains the latest set of disturbances.
Each column corresponds to a separate, independent path of disturbances.
filter
assumes that disturbances across any row occur
simultaneously.
Z
is the continuation of the presample disturbances
Z0
.
Data Types: double
Tbl1
— Time series data
table | timetable
Since R2023b
Time series data containing the observed disturbance variable
zt, associated with the model innovations
process εt, and, optionally, predictor
variables xt, specified as a table or
timetable with numvars
variables and numobs
rows.
You can optionally select the disturbance variable or numpreds
predictor variables by using the DisturbanceVariable
or
PredictorVariables
name-value arguments, respectively.
For a variance process σt2, the innovation process is
Each row is an observation, and measurements in each row occur simultaneously. The
selected disturbance variable is a single path (numobs
-by-1 vector)
or multiple paths (numobs
-by-numpaths
matrix) of
numobs
observations of disturbance data.
Each path (column) of the selected disturbance variable is independent of the other
paths, but path
of all presample and
in-sample variables correspond, for j
=
1,…,j
numpaths
. Each selected predictor variable is a
numobs
-by-1 numeric vector representing one path. The
filter
function includes all predictor variables in the
model when it filters each disturbance path. Variables in Tbl1
represent the continuation of corresponding variables in
Presample
.
If Tbl1
is a timetable, it must represent a sample with a
regular datetime time step (see isregular
), and the datetime vector Tbl1.Time
must be
strictly ascending or descending.
If Tbl1
is a table, the last row contains the latest
observation.
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: filter(Mdl,Z,Z0=PS,X=Pred)
specifies the numeric vector of
presample disturbance data PS
to initialize the model and the exogenous
predictor data X
for the regression component.
DisturbanceVariable
— Disturbance variable zt to select from Tbl1
string scalar | character vector | integer | logical vector
Since R2023b
Disturbance variable zt to select from
Tbl1
containing the disturbance data to filter through
Mdl
, specified as one of the following data types:
String scalar or character vector containing a variable name in
Tbl1.Properties.VariableNames
Variable index (positive integer) to select from
Tbl1.Properties.VariableNames
A logical vector, where
DisturbanceVariable(
selects variablej
) = true
fromj
Tbl1.Properties.VariableNames
The selected variable must be a numeric vector and cannot contain missing values
(NaN
s).
If Tbl1
has one variable, the default specifies that variable.
Otherwise, the default matches the variable to names in
Mdl.SeriesName
.
Example: DisturbanceVariable="StockRateDist"
Example: DisturbanceVariable=[false false true false]
or
DisturbanceVariable=3
selects the third table variable as the
disturbance variable.
Data Types: double
| logical
| char
| cell
| string
Y0
— Presample response data yt
numeric column vector | numeric matrix
Presample response data yt to initialize
the model, specified as a numpreobs
-by-1 numeric column vector or a
numpreobs
-by-numprepaths
numeric matrix. Use
Y0
only when you supply the numeric array of disturbance data
Z
.
numpreobs
is the number of presample observations.
numprepaths
is the number of presample response paths.
Each row is a presample observation (sampling time), and measurements in each row
occur simultaneously. The last row contains the latest presample observation.
numpreobs
must be at least Mdl.P
to initialize
the AR model component. If numpreobs
> Mdl.P
,
filter
uses the latest required observations only.
Columns of Y0
are separate, independent presample paths. The
following conditions apply:
If
Y0
is a column vector, it represents a single response path.filter
applies it to each output path.If
Y0
is a matrix, each column represents a presample response path.filter
appliesY0(:,
to initialize pathj
)j
.numprepaths
must be at leastnumpaths
. Ifnumprepaths
>numpaths
,filter
uses the firstsize(Z,2)
columns only.
By default, filter
sets any necessary presample
responses to one of the following values:
The unconditional mean of the model when
Mdl
represents a stationary AR process without a regression componentZero when
Mdl
represents a nonstationary process or when it contains a regression component
Data Types: double
Z0
— Presample disturbance data zt
numeric column vector | numeric matrix
Presample disturbance data zt providing
initial values for the input disturbance series Z
, specified as a
numpreobs
-by-1 numeric column vector or a
numpreobs
-by-numprepaths
numeric matrix. Use
Z0
only when you supply the numeric array of disturbance data
Z
.
Each row is a presample observation (sampling time), and measurements in each row
occur simultaneously. The last row contains the latest presample observation.
numpreobs
must be at least Mdl.Q
to initialize
the MA model component. If Mdl.Variance
is a conditional variance
model (for example, a garch
model object),
filter
can require more rows than
Mdl.Q
. If numpreobs
is larger than required,
filter
uses the latest required observations only.
Columns of Z0
are separate, independent presample paths. The
following conditions apply:
If
Z0
is a column vector, it represents a single disturbance path.filter
applies it to each output path.If
Z0
is a matrix, each column represents a presample disturbance path.filter
appliesZ0(:,
to initialize pathj
)j
.numprepaths
must be at leastnumpaths
. Ifnumprepaths
>numpaths
,filter
uses the firstsize(Z,2)
columns only.
By default, filter
sets the necessary presample
disturbances to zero.
Data Types: double
V0
— Presample conditional variance data σt2
positive numeric column vector | positive numeric matrix
Presample conditional variance data
σt2 used to
initialize the conditional variance model, specified as a
numpreobs
-by-1 positive numeric column vector or a
numpreobs
-by-numprepaths
positive numeric
matrix. If the conditional variance Mdl.Variance
is constant,
filter
ignores V0
. Use
V0
only when you supply the numeric array of disturbance data
Z
.
Each row is a presample observation (sampling time), and measurements in each row
occur simultaneously. The last row contains the latest presample observation.
numpreobs
must be at least Mdl.Q
to initialize
the conditional variance model in Mdl.Variance
. For details, see
the filter
function of conditional variance
models. If numpreobs
is larger than required,
filter
uses the latest required observations only.
Columns of V0
are separate, independent presample paths. The
following conditions apply:
If
V0
is a column vector, it represents a single path of conditional variances.filter
applies it to each output path.If
V0
is a matrix, each column represents a presample path of conditional variances.filter
appliesV0(:,
to initialize pathj
)j
.numprepaths
must be at leastnumpaths
. Ifnumprepaths
>numpaths
,filter
uses the firstsize(Z,2)
columns only.
By default, filter
sets all necessary presample
conditional variances to the unconditional variance of the conditional variance
process.
Data Types: double
Presample
— Presample data
table | timetable
Since R2023b
Presample data containing paths of response
yt, disturbance
zt, or conditional variance
σt2 series to
initialize the model, specified as a table or timetable, the same type as
Tbl1
, with numprevars
variables and
numpreobs
rows. Use Presample
only when you
supply a table or timetable of data Tbl1
.
Each selected variable is a single path (numpreobs
-by-1 vector)
or multiple paths (numpreobs
-by-numprepaths
matrix) of numpreobs
observations representing the presample of the
response, disturbance, or conditional variance series for
DisturbanceVariable
, the selected disturbance variable in
Tbl1
.
Each row is a presample observation, and measurements in each row occur
simultaneously. numpreobs
must be one of the following values:
At least
Mdl.P
whenPresample
provides only presample responsesAt least
Mdl.Q
whenPresample
provides only presample disturbances or conditional variancesAt least
max([Mdl.P Mdl.Q])
otherwise
When Mdl.Variance
is a conditional variance model,
filter
can require more than the minimum required number
of presample values.
If you supply more rows than necessary, filter
uses the
latest required number of observations only.
If Presample
is a timetable, all the following conditions
must be true:
Presample
must represent a sample with a regular datetime time step (seeisregular
).The inputs
Tbl1
andPresample
must be consistent in time such thatPresample
immediately precedesTbl1
with respect to the sampling frequency and order.The datetime vector of sample timestamps
Presample.Time
must be ascending or descending.
If Presample
is a table, the last row contains the latest
presample observation.
By default, filter
sets the following values:
For necessary presample responses:
The unconditional mean of the model when
Mdl
represents a stationary AR process without a regression componentZero when
Mdl
represents a nonstationary process or when it contains a regression component.
For necessary presample disturbances, zero.
For necessary presample conditional variances, the unconditional variance of the conditional variance model n
Mdl.Variance
.
If you specify the Presample
, you must specify the presample
response, disturbance, or conditional variance name by using the
PresampleResponseVariable
,
PresampleDisturbanceVariable
, or
PresampleVarianceVariable
name-value argument.
PresampleResponseVariable
— Response variable yt to select from Presample
string scalar | character vector | integer | logical vector
Since R2023b
Response variable yt to select from
Presample
containing presample response data, specified as one of
the following data types:
String scalar or character vector containing a variable name in
Presample.Properties.VariableNames
Variable index (positive integer) to select from
Presample.Properties.VariableNames
A logical vector, where
PresampleResponseVariable(
selects variablej
) = true
fromj
Presample.Properties.VariableNames
The selected variable must be a numeric matrix and cannot contain missing values
(NaN
s).
If you specify presample response data by using the Presample
name-value argument, you must specify
PresampleResponseVariable
.
Example: PresampleResponseVariable="Stock0"
Example: PresampleResponseVariable=[false false true false]
or
PresampleResponseVariable=3
selects the third table variable as
the presample response variable.
Data Types: double
| logical
| char
| cell
| string
PresampleDisturbanceVariable
— Disturbance variable zt to select from Presample
string scalar | character vector | integer | logical vector
Since R2023b
Disturbance variable zt to select from
Presample
containing presample disturbance data, specified as one
of the following data types:
String scalar or character vector containing a variable name in
Presample.Properties.VariableNames
Variable index (positive integer) to select from
Presample.Properties.VariableNames
A logical vector, where
PresampleDisturbanceVariable(
selects variablej
) = true
fromj
Presample.Properties.VariableNames
The selected variable must be a numeric matrix and cannot contain missing values
(NaN
s).
If you specify presample disturbance data by using the
Presample
name-value argument, you must specify
PresampleDisturbanceVariable
.
Example: PresampleDisturbanceVariable="StockRateDist0"
Example: PresampleDisturbanceVariable=[false false true false]
or PresampleDisturbanceVariable=3
selects the third table variable
as the presample disturbance variable.
Data Types: double
| logical
| char
| cell
| string
PresampleVarianceVariable
— Conditional variance variable σt2 to select from
Presample
string scalar | character vector | integer | logical vector
Since R2023b
Conditional variance variable
σt2 to select
from Presample
containing presample conditional variance data,
specified as one of the following data types:
String scalar or character vector containing a variable name in
Presample.Properties.VariableNames
Variable index (positive integer) to select from
Presample.Properties.VariableNames
A logical vector, where
PresampleVarianceVariable(
selects variablej
) = true
fromj
Presample.Properties.VariableNames
The selected variable must be a numeric vector and cannot contain missing values
(NaN
s).
If you specify presample conditional variance data by using the
Presample
name-value argument, you must specify
PresampleVarianceVariable
.
Example: PresampleVarianceVariable="StockRateVar0"
Example: PresampleVarianceVariable=[false false true false]
or
PresampleVarianceVariable=3
selects the third table variable as
the presample conditional variance variable.
Data Types: double
| logical
| char
| cell
| string
X
— Exogenous predictor data
numeric matrix
Exogenous predictor data for the regression component in the model, specified as a
numeric matrix with numpreds
columns. numpreds
is the number of predictor variables (numel(Mdl.Beta)
). Use
X
only when you supply the numeric array of disturbance data
Z
.
X
must have at least numobs
rows. The last
row contains the latest predictor data. If X
has more than
numobs
rows, filter
uses only the
latest numobs
rows. Each row of X
corresponds to
each period in Z
(period for which
filter
filters errors; the period after the
presample).
filter
does not use the regression component in the
presample period.
Columns of X
are separate predictor variables.
filter
applies X
to each filtered
path; that is, X
represents one path of observed predictors.
By default, filter
excludes the regression component,
regardless of its presence in Mdl
.
Data Types: double
PredictorVariables
— Exogenous predictor variables xt to select from Tbl1
string vector | cell vector of character vectors | vector of integers | logical vector
Since R2023b
Exogenous predictor variables xt to select
from Tbl1
containing predictor data for the regression component,
specified as one of the following data types:
String vector or cell vector of character vectors containing
numpreds
variable names inTbl1.Properties.VariableNames
A vector of unique indices (positive integers) of variables to select from
Tbl1.Properties.VariableNames
A logical vector, where
PredictorVariables(
selects variablej
) = true
fromj
Tbl1.Properties.VariableNames
The selected variables must be numeric vectors and cannot contain missing values
(NaN
s).
By default, filter
excludes the regression component,
regardless of its presence in Mdl
.
Example: PredictorVariables=["M1SL" "TB3MS" "UNRATE"]
Example: PredictorVariables=[true false true false]
or
PredictorVariable=[1 3]
selects the first and third table
variables to supply the predictor data.
Data Types: double
| logical
| char
| cell
| string
Note
NaN
values inZ
,X
,Y0
,Z0
, andV0
indicate missing values.filter
removes missing values from specified data by list-wise deletion.For the presample,
filter
horizontally concatenates the possibly jagged arraysY0
,Z0
, andV0
with respect to the last rows, and then it removes any row of the concatenated matrix containing at least oneNaN
.For in-sample data,
filter
horizontally concatenates the possibly jagged arraysZ
andX
, and then it removes any row of the concatenated matrix containing at least oneNaN
.
This type of data reduction reduces the effective sample size and can create an irregular time series.
For numeric data inputs,
filter
assumes that you synchronize the presample data such that the latest observations occur simultaneously.filter
issues an error when any table or timetable input contains missing values.
Output Arguments
Y
— Simulated response paths yt
numeric column vector | numeric matrix
Simulated response paths yt, returned as a
length numobs
column vector or a
numobs
-by-numpaths
numeric matrix.
filter
returns Y
only when you supply
the input Z
.
For each
= 1, …,
t
numobs
, the simulated response at time
t
Y(
corresponds to the filtered
disturbance at time t
,:)t
Z(
and response path
t
,:)j
Y(:,
corresponds to the filtered
disturbance path j
)j
Z(:,
.j
)
Y
represents the continuation of the presample response paths
in Y0
.
E
— Simulated paths of model innovations εt
numeric column vector | numeric matrix
Simulated paths of model innovations εt,
returned as a length numobs
column vector or a
numobs
-by-numpaths
numeric matrix.
filter
returns E
only when you supply
the input Z
. The dimensions of Y
and
E
correspond.
Columns of E
are scaled disturbance paths (innovations) such
that, for a particular path
V
— Conditional variance paths σt2
numeric column vector | numeric matrix
Conditional variance paths
σt2, returned as
a length numobs
column vector or
numobs
-by-numpaths
numeric matrix.
filter
returns V
only when you supply
the input Z
. The dimensions of Y
and
V
correspond.
If Z
is a matrix, then the columns of V
are
the filtered conditional variance paths corresponding to the columns of
Z
.
Columns of V
are conditional variance paths of corresponding
paths of innovations εt
(E
) such that, for a particular path
V
represents the continuation of the presample conditional
variance paths in V0
.
Tbl2
— Simulated response yt, innovation εt, and conditional variance
σt2
paths
table | timetable
Since R2023b
Simulated response yt, innovation
εt, and conditional variance
σt2 paths,
returned as a table or timetable, the same data type as Tbl1
.
filter
returns Tbl2
only when you
supply the input Tbl1
.
Tbl2
contains the following variables:
The simulated response paths, which are in a
numobs
-by-numpaths
numeric matrix, with rows representing observations and columns representing independent paths, each corresponding to the input observations and paths of the disturbance variable inTbl1
.filter
names the simulated response variable inTbl2
, whereresponseName
_Response
isresponseName
Mdl.SeriesName
. For example, ifMdl.SeriesName
isStockReturns
,Tbl2
contains a variable for the corresponding simulated response paths with the nameStockReturns_Response
.The simulated innovation paths, which are in a
numobs
-by-numpaths
numeric matrix, with rows representing observations and columns representing independent paths, each corresponding to the input observations and paths of the disturbance variable inTbl1
.filter
names the simulated innovation variable inTbl2
, whereresponseName
_Innovation
isresponseName
Mdl.SeriesName
. For example, ifMdl.SeriesName
isStockReturns
,Tbl2
contains a variable for the corresponding simulated innovation paths with the nameStockReturns_Innovation
.The simulated conditional variances paths, which are in a
numobs
-by-numpaths
numeric matrix, with rows representing observations and columns representing independent paths, each corresponding to the input observations and paths of the disturbance variable inTbl1
.filter
names the simulated conditional variance variable inTbl2
, whereresponseName
_Variance
isresponseName
Mdl.SeriesName
. For example, ifMdl.SeriesName
isStockReturns
,Tbl2
contains a variable for the corresponding simulated conditional variance paths with the nameStockReturns_Variance
.All variables
Tbl1
.
If Tbl1
is a timetable, row times of Tbl1
and Tbl2
are equal.
Alternative Functionality
filter
generalizes simulate
; both functions filter a series of disturbances to produce output
responses, innovations, and conditional variances. However, simulate
autogenerates a series of mean zero, unit variance, independent and identically distributed
(iid) disturbances according to the distribution in Mdl
. In contrast,
filter
enables you to directly specify custom disturbances.
References
[1] Box, George E. P., Gwilym M. Jenkins, and Gregory C. Reinsel. Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.
[2] Enders, Walter. Applied Econometric Time Series. Hoboken, NJ: John Wiley & Sons, Inc., 1995.
[3] Hamilton, James D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
Version History
Introduced in R2012bR2023b: filter
accepts input data in tables and timetables, and returns results in tables and timetables
In addition to accepting input data (in-sample and presample) in numeric arrays,
filter
accepts input data in tables or regular timetables. When
you supply data in a table or timetable, the following conditions apply:
filter
chooses the default in-sample disturbance series and predictor data on which to operate, but you can use the specified optional name-value argument to select a different series.If you specify optional presample data to initialize the model, you must also specify the presample response, disturbance, or conditional variance series name.
filter
returns results in a table or timetable.
Name-value arguments to support tabular workflows include:
DisturbanceVariable
specifies the name of the disturbance series to select from the input data to filter through the model.Presample
specifies the input table or timetable of presample response, disturbance, and conditional variance data.PresampleResponseVariable
specifies the name of the response series to select fromPresample
.PresampleDisturbanceVariable
specifies the name of the disturbance series to select fromPresample
.PresampleVarianceVariable
specifies the name of the conditional variance series to select fromPresample
.PredictorVariables
specifies the names of the predictor series to select from the input data for a model regression component.
Comando de MATLAB
Ha hecho clic en un enlace que corresponde a este comando de MATLAB:
Ejecute el comando introduciéndolo en la ventana de comandos de MATLAB. Los navegadores web no admiten comandos de MATLAB.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)