public class ARSeasonalFit extends Object implements Serializable
ARMA time series modeling assumes the time series is stationary. Seasonal
trends and cycles violate this assumption, which can lead to inaccurate
predictions. However, in many cases the nonstationary series can be
transformed into a stationary series by first differencing the series. For
example, if the correlation is strong from one period to the next, the series
might be differenced by a lag of 1. Instead of fitting a model to the
original series , the model is fitted to the
transformed series: . Higher order
lags or differences are warranted if the series has cycles every 4 or 13
weeks. Class ARSeasonalFit
is designed to help identify the
optimum differencing for a series with seasonal trends or cycles.
ARSeasonalFit
assumes the original series has no missing
values, is equally spaced in time and is not centered before computing the
optimum differencing. However, by default the transformed series is centered
using the mean of that series. Users can change this default using the
setCenter
setCenter
is set to
NO_CENTER
CENTER_MEAN
CENTER_MEDIAN
setCenter
is set to CENTER_MEAN
or CENTER_MEDIAN
then the
differenced series, is centered before determination
of minimum AIC and optimum lag.
For every combination of rows in sInitial
and dInitial
, the series is converted to the seasonally
adjusted series using the following computation
sInitial
and dInitial
respectively, and m is the number of
differences, or m=sInitial[0].length
.
This transformation of the series to is computed using the Difference
class.
After this transformation the transformed series
NO_CENTER
is specified, and the
ARAutoUnivariate
This procedure is repeated for every possible combination of rows in
sInitial
and dInitial
. The series with the minimum
AIC is identified as the optimum representation and returned in the methods
getAROrder
getOptimumS
getOptimumD
getAIC
getAR
getTransformedTimeSeries
Modifier and Type  Field and Description 

static int 
CENTER_MEAN
Indicates the transformed series should be centered using the
average of the differenced series.

static int 
CENTER_MEDIAN
Indicates the transformed series should be centered using the
median of the differenced series.

static int 
NO_CENTER
Indicates the transformed series should not be centered.

Constructor and Description 

ARSeasonalFit(int maxlag,
int[][] sInitial,
double[] z)
Constructor for
ARSeasonalFit . 
Modifier and Type  Method and Description 

void 
compute()
Computes the minimum AIC and optimum values for s and d
based upon the candidates provided in
sInitial and
dInitial , and computes the values for the transformed series,
. 
double 
getAIC()
Returns the final estimate for Akaike's Information Criterion (AIC) at
the optimum.

double[] 
getAR()
Returns the final autoregressive parameter estimates at the optimum in
the transformed series .

int 
getAROrder()
Returns optimum number of lags, p, for the optimum autoregressive
AR(p) model.

int 
getCenter()
Returns the current setting for centering the input time series.

int[][] 
getDInitial()
Returns the candidate values for d to evaluate.

boolean 
getExclude()
Returns the current setting for excluding or replacing the inital values
in the transformed series.

int 
getMaxlag()
Returns the maximum lag used to fit the AR(p) model.

int 
getNLost()
Returns the number of values in the initial part of the series lost to
differencing.

int[] 
getOptimumD()
Returns the optimum values for d selected among the candidates in
dInitial . 
int[] 
getOptimumS()
Returns the optimum values for s selected among the candidates in
sInitial . 
int[][] 
getSInitial()
Returns the the candidate values for s to evaluate.

double[] 
getTimeSeries()
Returns the time series.

double[] 
getTransformedTimeSeries()
Returns the transformed series, .

void 
setCenter(int center)
Controls centering of the differenced series.

void 
setDInitial(int[][] dInitial)
Sets the candidate values for selecting the optimum seasonal adjustment
prior to calling the compute method.

void 
setExclude(boolean exclude)
Controls whether to exclude or replace the inital values in the
transformed series.

public static final int CENTER_MEAN
public static final int CENTER_MEDIAN
public static final int NO_CENTER
public ARSeasonalFit(int maxlag, int[][] sInitial, double[] z)
ARSeasonalFit
.maxlag
 an int
scalar specifying the maximum lag
allowed when fitting an AR(p) model.sInitial
 an int
matrix where each row represents
seasonal differences to evaluate. The number of columns
in sInitial
represent the number of
differences to perform. All values of sInitial
must be greater than zero.z
 an input double
array containing the time
series.public void compute() throws ARMA.MatrixSingularException, ARMA.TooManyCallsException, ARMA.IncreaseErrRelException, ARMA.NewInitialGuessException, ARMA.IllConditionedException, ARMA.TooManyITNException, ARMA.TooManyFcnEvalException, ARMA.TooManyJacobianEvalException, ARAutoUnivariate.TriangularMatrixSingularException, ARMAMaxLikelihood.NonInvertibleException, ARMAMaxLikelihood.NonStationaryException, ARMAMaxLikelihood.InitialMAException
sInitial
and
dInitial
, and computes the values for the transformed series,
.
Warnings are printed if a row in sInitial
is skipped due
to too many observations lost in the differenced series or if problems
occurred computing the optimum AIC using the differenced series.
ARMA.MatrixSingularException
 is thrown if the input matrix is
singularARMA.TooManyCallsException
 is thrown if the number of calls
to the function has exceeded the maximum number of
iterations times the number of moving average (MA)
parameters + 1.ARMA.IncreaseErrRelException
 is thrown if the bound for the
relative error is too smallARMA.NewInitialGuessException
 is thrown if the iteration has
not made good progressARMA.IllConditionedException
 is thrown if the problem is
illconditionedARMA.TooManyITNException
 is thrown if the maximum number of
iterations is exceededARMA.TooManyFcnEvalException
 is thrown if the maximum number
of function evaluations is exceededARMA.TooManyJacobianEvalException
 is thrown if the maximum
number of Jacobian evaluations is exceededARMAMaxLikelihood.NonStationaryException
 is thrown if the
final maximum likelihood estimates for the time series
are nonstationaryARMAMaxLikelihood.NonInvertibleException
 is thrown if the
final maximum likelihood estimates for the time series
are noninvertibleARMAMaxLikelihood.InitialMAException
 is thrown if the initial
values provided for the moving average terms using
setMA
are noninvertible. In this case,
ARMAMaxLikelihood
terminates and does not compute
the time series estimates.ARAutoUnivariate.TriangularMatrixSingularException
 is thrown
if the input triangular matrix is singular.public double getAIC()
double
equal to , where L is the value of the maximum
likelihood function evalutated at the parameter estimates.public double[] getAR() throws ARMA.MatrixSingularException, ARMA.TooManyCallsException, ARMA.IncreaseErrRelException, ARMA.NewInitialGuessException, ARMA.IllConditionedException, ARMA.TooManyITNException, ARMA.TooManyFcnEvalException, ARMA.TooManyJacobianEvalException, ARAutoUnivariate.TriangularMatrixSingularException, ARMAMaxLikelihood.NonInvertibleException, ARMAMaxLikelihood.NonStationaryException, ARMAMaxLikelihood.InitialMAException
double
array containing the estimates for the
autoregressive parametersARMA.MatrixSingularException
 is thrown if the input matrix is
singularARMA.TooManyCallsException
 is thrown if the number of calls
to the function has exceeded the maximum number of
iterations times the number of moving average (MA)
parameters + 1.ARMA.IncreaseErrRelException
 is thrown if the bound for the
relative error is too smallARMA.NewInitialGuessException
 is thrown if the iteration has
not made good progressARMA.IllConditionedException
 is thrown if the problem is
illconditionedARMA.TooManyITNException
 is thrown if the maximum number of
iterations is exceededARMA.TooManyFcnEvalException
 is thrown if the maximum number
of function evaluations is exceededARMA.TooManyJacobianEvalException
 is thrown if the maximum
number of Jacobian evaluations is exceededARMAMaxLikelihood.NonStationaryException
 is thrown if the
final maximum likelihood estimates for the time series
are nonstationaryARMAMaxLikelihood.NonInvertibleException
 is thrown if the
final maximum likelihood estimates for the time series
are noninvertibleARMAMaxLikelihood.InitialMAException
 is thrown if the initial
values provided for the moving average terms using
setMA
are noninvertible. In this case,
ARMAMaxLikelihood
terminates and does not compute
the time series estimates.ARAutoUnivariate.TriangularMatrixSingularException
 is thrown
if the input triangular matrix is singular.public int getAROrder()
int
containing the optimum number of lags in the
autoregressive model used to fit the transformed series
.public int getCenter()
int
containing the setting for center equal to 0,
1, or 2, which implies
NO_CENTER
CENTER_MEAN
CENTER_MEDIAN
public int[][] getDInitial()
int
matrix containing the candidate values for
d to evaluatepublic boolean getExclude()
If exclude is true
, then inital values in the transformed
series that cannot be computed are set to missing, NaN
. This
ensures that the length of the transformed series is equal to the length of the time series, z.length
. If exclude is set to false
, then inital values in
the transformed series that cannot be computed
are removed. This makes the length of the transformed series equal to z.length
nLost where nLost
is the number of lost values obtained from method
getNLost
public int getMaxlag()
int
scalar containing the maximum lag allowed
when fitting an AR(p) modelpublic int getNLost() throws ARMA.MatrixSingularException, ARMA.TooManyCallsException, ARMA.IncreaseErrRelException, ARMA.NewInitialGuessException, ARMA.IllConditionedException, ARMA.TooManyITNException, ARMA.TooManyFcnEvalException, ARMA.TooManyJacobianEvalException, ARAutoUnivariate.TriangularMatrixSingularException, ARMAMaxLikelihood.NonInvertibleException, ARMAMaxLikelihood.NonStationaryException, ARMAMaxLikelihood.InitialMAException
int
containing the number of values in the
initial part of the series lost to differencing. These lost
values will be set to missing or dropped in the transformed
series, depending upon the setting for exclude.ARMA.MatrixSingularException
 is thrown if the input matrix is
singularARMA.TooManyCallsException
 is thrown if the number of calls
to the function has exceeded the maximum number of
iterations times the number of moving average (MA)
parameters + 1.ARMA.IncreaseErrRelException
 is thrown if the bound for the
relative error is too smallARMA.NewInitialGuessException
 is thrown if the iteration has
not made good progressARMA.IllConditionedException
 is thrown if the problem is
illconditionedARMA.TooManyITNException
 is thrown if the maximum number of
iterations is exceededARMA.TooManyFcnEvalException
 is thrown if the maximum number
of function evaluations is exceededARMA.TooManyJacobianEvalException
 is thrown if the maximum
number of Jacobian evaluations is exceededARMAMaxLikelihood.NonStationaryException
 is thrown if the
final maximum likelihood estimates for the time series
are nonstationaryARMAMaxLikelihood.NonInvertibleException
 is thrown if the
final maximum likelihood estimates for the time series
are noninvertibleARMAMaxLikelihood.InitialMAException
 is thrown if the initial
values provided for the moving average terms using
setMA
are noninvertible. In this case,
ARMAMaxLikelihood
terminates and does not compute
the time series estimates.ARAutoUnivariate.TriangularMatrixSingularException
 is thrown
if the input triangular matrix is singular.public int[] getOptimumD() throws ARMA.MatrixSingularException, ARMA.TooManyCallsException, ARMA.IncreaseErrRelException, ARMA.NewInitialGuessException, ARMA.IllConditionedException, ARMA.TooManyITNException, ARMA.TooManyFcnEvalException, ARMA.TooManyJacobianEvalException, ARAutoUnivariate.TriangularMatrixSingularException, ARMAMaxLikelihood.NonInvertibleException, ARMAMaxLikelihood.NonStationaryException, ARMAMaxLikelihood.InitialMAException
dInitial
.int
array of length dInitial[0].length
containing the optimum values for d selected
among the candidates in dInitial
ARMA.MatrixSingularException
 is thrown if the input matrix is
singularARMA.TooManyCallsException
 is thrown if the number of calls
to the function has exceeded the maximum number of
iterations times the number of moving average (MA)
parameters + 1.ARMA.IncreaseErrRelException
 is thrown if the bound for the
relative error is too smallARMA.NewInitialGuessException
 is thrown if the iteration has
not made good progressARMA.IllConditionedException
 is thrown if the problem is
illconditionedARMA.TooManyITNException
 is thrown if the maximum number of
iterations is exceededARMA.TooManyFcnEvalException
 is thrown if the maximum number
of function evaluations is exceededARMA.TooManyJacobianEvalException
 is thrown if the maximum
number of Jacobian evaluations is exceededARMAMaxLikelihood.NonStationaryException
 is thrown if the
final maximum likelihood estimates for the time series
are nonstationaryARMAMaxLikelihood.NonInvertibleException
 is thrown if the
final maximum likelihood estimates for the time series
are noninvertibleARMAMaxLikelihood.InitialMAException
 is thrown if the initial
values provided for the moving average terms using
setMA
are noninvertible. In this case,
ARMAMaxLikelihood
terminates and does not compute
the time series estimates.ARAutoUnivariate.TriangularMatrixSingularException
 is thrown
if the input triangular matrix is singular.public int[] getOptimumS() throws ARMA.MatrixSingularException, ARMA.TooManyCallsException, ARMA.IncreaseErrRelException, ARMA.NewInitialGuessException, ARMA.IllConditionedException, ARMA.TooManyITNException, ARMA.TooManyFcnEvalException, ARMA.TooManyJacobianEvalException, ARAutoUnivariate.TriangularMatrixSingularException, ARMAMaxLikelihood.NonInvertibleException, ARMAMaxLikelihood.NonStationaryException, ARMAMaxLikelihood.InitialMAException
sInitial
.int
array of length sInitial[0].length
containing the optimum values for s selected among
the candidates in sInitial
ARMA.MatrixSingularException
 is thrown if the input matrix is
singularARMA.TooManyCallsException
 is thrown if the number of calls
to the function has exceeded the maximum number of
iterations times the number of moving average (MA)
parameters + 1.ARMA.IncreaseErrRelException
 is thrown if the bound for the
relative error is too smallARMA.NewInitialGuessException
 is thrown if the iteration has
not made good progressARMA.IllConditionedException
 is thrown if the problem is
illconditionedARMA.TooManyITNException
 is thrown if the maximum number of
iterations is exceededARMA.TooManyFcnEvalException
 is thrown if the maximum number
of function evaluations is exceededARMA.TooManyJacobianEvalException
 is thrown if the maximum
number of Jacobian evaluations is exceededARMAMaxLikelihood.NonStationaryException
 is thrown if the
final maximum likelihood estimates for the time series
are nonstationaryARMAMaxLikelihood.NonInvertibleException
 is thrown if the
final maximum likelihood estimates for the time series
are noninvertibleARMAMaxLikelihood.InitialMAException
 is thrown if the initial
values provided for the moving average terms using
setMA
are noninvertible. In this case,
ARMAMaxLikelihood
terminates and does not compute
the time series estimates.ARAutoUnivariate.TriangularMatrixSingularException
 is thrown
if the input triangular matrix is singular.public int[][] getSInitial()
int
matrix containing the candidate values for
s to evaluatepublic double[] getTimeSeries()
double
array containing the time series valuespublic double[] getTransformedTimeSeries() throws ARMA.MatrixSingularException, ARMA.TooManyCallsException, ARMA.IncreaseErrRelException, ARMA.NewInitialGuessException, ARMA.IllConditionedException, ARMA.TooManyITNException, ARMA.TooManyFcnEvalException, ARMA.TooManyJacobianEvalException, ARAutoUnivariate.TriangularMatrixSingularException, ARMAMaxLikelihood.NonInvertibleException, ARMAMaxLikelihood.NonStationaryException, ARMAMaxLikelihood.InitialMAException
is an array of length z.length
or z.lengthnLost
containing the optimum seasonally
adjusted, autoregressive series, where nLost
is the first
lost observations in this series that are dropped due to differencing. If
the missing values are not dropped the first nLost
values of
will be set (Double.NaN
). The
getNLost
nLost
.
The seasonal adjustment is done by selecting optimum values for
,
(m is number of differences or sIinitial[0].length
)
and p in the AR model:
double
array of length z.length
or
z.lengthnLost
, depending upon the setting for
setExclude
ARMA.MatrixSingularException
 is thrown if the input matrix is
singularARMA.TooManyCallsException
 is thrown if the number of calls
to the function has exceeded the maximum number of
iterations times the number of moving average (MA)
parameters + 1.ARMA.IncreaseErrRelException
 is thrown if the bound for the
relative error is too smallARMA.NewInitialGuessException
 is thrown if the iteration has
not made good progressARMA.IllConditionedException
 is thrown if the problem is
illconditionedARMA.TooManyITNException
 is thrown if the maximum number of
iterations is exceededARMA.TooManyFcnEvalException
 is thrown if the maximum number
of function evaluations is exceededARMA.TooManyJacobianEvalException
 is thrown if the maximum
number of Jacobian evaluations is exceededARMAMaxLikelihood.NonStationaryException
 is thrown if the
final maximum likelihood estimates for the time series
are nonstationaryARMAMaxLikelihood.NonInvertibleException
 is thrown if the
final maximum likelihood estimates for the time series
are noninvertibleARMAMaxLikelihood.InitialMAException
 is thrown if the initial
values provided for the moving average terms using
setMA
are noninvertible. In this case,
ARMAMaxLikelihood
terminates and does not compute
the time series estimates.ARAutoUnivariate.TriangularMatrixSingularException
 is thrown
if the input triangular matrix is singular.public void setCenter(int center)
center
 an int
scalar value equal
NO_CENTER
CENTER_MEAN
CENTER_MEDIAN
center=CENTER_MEAN
public void setDInitial(int[][] dInitial)
dInitial
 an int
array of candidate values for d
to evaluate. All values must be nonnegative.
dInitial
must have the same number of
differences (columns) as sInitial
. By
default, dInitial
is initialized to all
ones.public void setExclude(boolean exclude)
If exclude is true
, then inital values in the transformed
series that cannot be computed are set to missing, NaN
. This
ensures that the length of the transformed series is equal to the length of the time series, z.length
. If exclude is set to false
, then inital values in
the transformed series that cannot be computed
are removed. This makes the length of the transformed series equal to z.length
nLost where nLost
is the number of lost values obtained from method
getNLost
exclude
 a boolean
value that controls whether values
in that cannot be calculated are
dropped or set to missing. Missing values are set to
Double.NaN
. By default, exclude
=true
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Built October 13 2015.