This is just an ARMA model with exogenous inputs. The model is Phi(B) X_t = Theta(B) Z_t + Gamma U_{t-1} where Phi and Theta are standard autoregressive and moving average polynomials {U_t} is an exogenous time series. Much of the analysis is the same, we just have extra coefficients for the exogenous inputs, and to compute likelihoods, we have to adjust the observations appropriately. For now, we only allow a simple one-lag dependency on the exogenous series. Later I'll generalize this. More...

Inheritance diagram for CronoSeries.TimeSeries.Models.ARMAXModel:

Public Member Functions
	ARMAXModel (int arOrder, int maOrder, int exOrder, Data.TimeSeries data)
	basic constructor More...

	ARMAXModel (int arOrder, int maOrder, int exOrder, int tailDoF, Data.TimeSeries data)
	constructor for heavy-tailed ARMAX model More...

void	SetGamma (int idx, double value)
	sets gamma for the model More...

double	GetGamma (int idx)
	returns the specified gamma value More...

override string	GetParameterName (int index)

override int	NumInputs ()

override string	GetInputName (int index)

override string	GetShortDescription ()

override bool	SetInput (int socket, object item, StringBuilder failMsg)

Data.TimeSeries	GetExogenousTS (int idx)

override double	LogLikelihood (Vector< double > parameter, double penaltyFactor, bool fillOutputs)
	Returns the (possibly penalized) log-likelihood of the model with specified parameters and the current object theData. If parameter==null, it will use CURRENT parameters. If fillOutputs is true, then the residuals and any other outputs will be filled in. More...

override Vector< double >	ParameterToCube (Vector< double > param)

override Vector< double >	CubeToParameter (Vector< double > cube)

override Data.TimeSeries	SimulateData (List< DateTime > inputs, int randomSeed)
	This function must simulate from the current model. More...

override void	ResetRealTimePrediction ()

override double	Register (DateTime timeStamp, double value)

override double	Register (DateTime timeStamp, double value, double[] auxValues)

override DistributionSummary	GetCurrentPredictor (DateTime futureTime)

override List< Type >	GetAllowedInputTypesFor (int socket)

Public Member Functions inherited from CronoSeries.TimeSeries.Models.ARMAModel
	ARMAModel (int arOrder, int maOrder)

	ARMAModel (int arOrder, int maOrder, Data.TimeSeries data)
	Basic constructor for an ARMA(p,q) model with Gaussian innovations More...

	ARMAModel (int arOrder, int maOrder, Data.TimeSeries data, int tailDOF)
	basic constructor for an ARMA(p,q) model with Students T innovations More...

void	CarryOutPreMLEComputations ()

virtual MathNet.Numerics.LinearAlgebra.Vector< double >	ParameterToCube (MathNet.Numerics.LinearAlgebra.Vector< double > param)

virtual MathNet.Numerics.LinearAlgebra.Vector< double >	CubeToParameter (MathNet.Numerics.LinearAlgebra.Vector< double > cube)

virtual void	Register (Data.TimeSeries series)

override int	NumOutputs ()

override object	GetOutput (int socket)

override string	GetOutputName (int index)

override string	GetParameterDescription (int index)

void	SetARPolynomial (MathNet.Numerics.LinearAlgebra.Vector< double > p)

void	SetMAPolynomial (MathNet.Numerics.LinearAlgebra.Vector< double > p)

MathNet.Numerics.LinearAlgebra.Vector< double >	GetMAPolynomial ()

override double	LogLikelihood (MathNet.Numerics.LinearAlgebra.Vector< double > parameter, double penaltyFactor, bool fillOutputs)

override object	BuildForecasts (object otherData, object inputs)
	This function generates forecasts (or fitted values) for the specified inputs, based on the existing data object and current model parameters. Results are returned in a form that depends on the model, for example, as a TimeSeries of DistributionSummary objects More...

double	ARCoeff (int i)
	returns the i'th autoregressive coefficient: 0 = Phi_1, 1 = Phi_2, etc. More...

double	MACoeff (int i)

override MathNet.Numerics.LinearAlgebra.Vector< double >	ComputeACF (int maxLag, bool normalize)

void	EstimateByYuleWalker (double sampleMean, MathNet.Numerics.LinearAlgebra.Vector< double > acvf)
	This method fits the model by using Yule-Walker estimation. It can only handle a few particular orders for the ARMA model now. In other cases it throws an exception. More...

Public Member Functions inherited from CronoSeries.TimeSeries.Models.UnivariateTimeSeriesModel
override List< Type >	GetAllowedInputTypesFor (int socket)

override List< Type >	GetOutputTypesFor (int socket)

Public Member Functions inherited from CronoSeries.TimeSeries.Models.TimeSeriesModel
override int	NumInputs ()

override string	GetInputName (int socket)

override bool	InputIsFree (int socket)

override bool	SetInput (int socket, object item, StringBuilder failMsg)

override int	NumOutputs ()

override object	GetOutput (int socket)

override string	GetOutputName (int socket)

Public Member Functions inherited from CronoSeries.TimeSeries.Models.Model
string	GetDescription ()

bool	CanUseMLE ()

bool	CanUseMoM ()

bool	CanHandleNaNs ()

virtual void	FitByMLE (int numIterationsLDS, int numIterationsOpt, double consistencyPenalty, Optimizer.OptimizationCallback optCallback)

virtual void	FitByMoM ()
	Fits model by method of moments. This is the default method used of CanUseMLE is false. More...

bool	InputToOutputIsValid ()

bool	SetParameters (Vector< double > v)

Public Member Functions inherited from CronoSeries.TimeSeries.Models.IRealTimePredictable
void	Register (Data.TimeSeries series)

Public Attributes
int	NumExogenous => numExogenous

Public Attributes inherited from CronoSeries.TimeSeries.Models.ARMAModel
bool	IsShortMemory => Math.Abs(FracDiff) < 1e-10

Public Attributes inherited from CronoSeries.TimeSeries.Models.Model
object	theData

Protected Member Functions
new void	LocalInitializeParameters ()

override void	InitializeParameters ()
	This function is called after OnDataConnection. It can assume valid data is available, and it must fill in valid default parameter values. It typically also sets default parameter states, for purposes of estimation. More...

Data.TimeSeries	ComputeAdjustedValues ()
	performs adjustment to the original data based on exogenous time series, so that we can use the original likelihood function More...

override Vector< double >	ComputeConsequentialParameters (Vector< double > parameter)
	This function must fill in values of consequential parameters. These parameters are determined by the current ParameterState[] settings in ParameterStates. These can depend on the non-consequential parameters and the data set. The function should throw an exception if it is not possible. The parameter vector with parameters filled in should be returned. More...

Protected Member Functions inherited from CronoSeries.TimeSeries.Models.ARMAModel
	ARMAModel (int arOrder, int maOrder, int tailDOF)

override bool	CheckParameterValidity (MathNet.Numerics.LinearAlgebra.Vector< double > param)

MathNet.Numerics.LinearAlgebra.Vector< double >	GetLikelihoodsFromResiduals (double[] res, double[] pvars)

override MathNet.Numerics.LinearAlgebra.Vector< double >	ComputeConsequentialParameters (MathNet.Numerics.LinearAlgebra.Vector< double > parameter)

void	LocalInitializeParameters ()

double[]	ComputeSpecialResiduals (Data.TimeSeries startData, out double[] rs, int forecastHorizon, out double[] forecasts)
	This function uses the approach described in Section 8.7 of B&D if fracdiff parm==0 to get one-step predictors and residuals. More...

Protected Member Functions inherited from CronoSeries.TimeSeries.Models.UnivariateTimeSeriesModel
bool	DataIsLongitudinal ()

override bool	CheckDataValidity (object data, StringBuilder failMessage)
	This function checks to see if the object can be cast into the appropriate form for the model. More...

override void	OnDataConnection ()
	This function is called immediately after a data object is connected to the model. Any initial processing (e.g. determining dimension of parameter vector, etc.) should be done here. More...

Protected Member Functions inherited from CronoSeries.TimeSeries.Models.Model
double	NegativeLogLikelihood (Vector< double > partialCube)
	This function is a wrapper for another function, to be passed to a minimizer. More...

abstract bool	CheckParameterValidity (Vector< double > param)
	Checks for validity of parameters. More...

Protected Attributes
Data.TimeSeries[]	exogenous

int	numExogenous

Protected Attributes inherited from CronoSeries.TimeSeries.Models.ARMAModel
MathNet.Numerics.LinearAlgebra.Vector< double >	autocovariance

Data.TimeSeries	oneStepPredictors

Data.TimeSeries	oneStepPredictorsAtAvailability

Data.TimeSeries	oneStepPredStd

Data.TimeSeries	unstandardizedResiduals

Protected Attributes inherited from CronoSeries.TimeSeries.Models.UnivariateTimeSeriesModel
Longitudinal	longitudinalValues

Data.TimeSeries	values

Properties
override Vector< double >	Parameters `[get, set]`

override string???	Description `[get]`

Properties inherited from CronoSeries.TimeSeries.Models.ARMAModel
override string??	Description `[get]`

double	FracDiff `[get, set]`

double	Mu `[get, set]`

double	Sigma `[get, set]`

int	AROrder `[get]`

int	MAOrder `[get]`

int	TailDegreesOfFreedom `[get]`

Properties inherited from CronoSeries.TimeSeries.Models.TimeSeriesModel
override Vector< double >	Parameters `[get, set]`

Properties inherited from CronoSeries.TimeSeries.Models.Model
abstract string	Description `[get]`
	Should return a description of the model, including current parameter values if desired. More...

object	Residuals `[get, protected set]`

object	TheData `[get, set]`

double	GoodnessOfFit `[get, protected set]`

abstract Vector< double >	Parameters `[get, set]`

ParameterState[]	ParameterStates `[get, set]`

string	ToolTipText `[get, set]`

Properties inherited from CronoSeries.TimeSeries.Data.IConnectable
string	ToolTipText `[get, set]`

Additional Inherited Members
Public Types inherited from CronoSeries.TimeSeries.Models.Model
enum	ParameterState { Free, Locked, Consequential }

Static Protected Member Functions inherited from CronoSeries.TimeSeries.Models.ARMAModel
static double	GammaFunction (double x)

static Complex	ComplexPower (Complex c, double pow)

Static Protected Member Functions inherited from CronoSeries.TimeSeries.Models.Model
static Vector< double >	CubeFix (Vector< double > cube)
	This function makes sure that its vector argument really does contain an element of the unit hypercube. If not, it is mapped back to an element on the hypercube (the mapping is continuous). More...

Detailed Description

This is just an ARMA model with exogenous inputs. The model is Phi(B) X_t = Theta(B) Z_t + Gamma U_{t-1} where Phi and Theta are standard autoregressive and moving average polynomials {U_t} is an exogenous time series. Much of the analysis is the same, we just have extra coefficients for the exogenous inputs, and to compute likelihoods, we have to adjust the observations appropriately. For now, we only allow a simple one-lag dependency on the exogenous series. Later I'll generalize this.

Constructor & Destructor Documentation

◆ ARMAXModel() [1/2]

CronoSeries.TimeSeries.Models.ARMAXModel.ARMAXModel	(	int	arOrder,
		int	maOrder,
		int	exOrder,
		Data.TimeSeries	data
	)

inline

basic constructor

Parameters

arOrder	autoregressive order
maOrder	moving average order
exOrder	number of exogenous inputs
data	data to perform analysis on

◆ ARMAXModel() [2/2]

CronoSeries.TimeSeries.Models.ARMAXModel.ARMAXModel	(	int	arOrder,
		int	maOrder,
		int	exOrder,
		int	tailDoF,
		Data.TimeSeries	data
	)

inline

constructor for heavy-tailed ARMAX model

Parameters

arOrder	autoregressive order
maOrder	moving average order
exOrder	number of exogenous inputs
tailDoF	degrees of freedom for t-distributed innovations
data	data to perform analysis on

Member Function Documentation

◆ ComputeAdjustedValues()

Data.TimeSeries CronoSeries.TimeSeries.Models.ARMAXModel.ComputeAdjustedValues ( )

inlineprotected

performs adjustment to the original data based on exogenous time series, so that we can use the original likelihood function

Returns

◆ ComputeConsequentialParameters()

override Vector<double> CronoSeries.TimeSeries.Models.ARMAXModel.ComputeConsequentialParameters ( Vector< double > parameter )

inlineprotectedvirtual

This function must fill in values of consequential parameters. These parameters are determined by the current ParameterState[] settings in ParameterStates. These can depend on the non-consequential parameters and the data set. The function should throw an exception if it is not possible. The parameter vector with parameters filled in should be returned.

Implements CronoSeries.TimeSeries.Models.Model.

◆ GetGamma()

double CronoSeries.TimeSeries.Models.ARMAXModel.GetGamma ( int idx )

inline

returns the specified gamma value

Parameters

idx

Returns

◆ InitializeParameters()

override void CronoSeries.TimeSeries.Models.ARMAXModel.InitializeParameters ( )

inlineprotectedvirtual

This function is called after OnDataConnection. It can assume valid data is available, and it must fill in valid default parameter values. It typically also sets default parameter states, for purposes of estimation.

Reimplemented from CronoSeries.TimeSeries.Models.ARMAModel.

◆ LogLikelihood()

override double CronoSeries.TimeSeries.Models.ARMAXModel.LogLikelihood	(	Vector< double >	parameter,
		double	penaltyFactor,
		bool	fillOutputs
	)

inlinevirtual

Returns the (possibly penalized) log-likelihood of the model with specified parameters and the current object theData. If parameter==null, it will use CURRENT parameters. If fillOutputs is true, then the residuals and any other outputs will be filled in.

Returns

Implements CronoSeries.TimeSeries.Models.Model.

◆ SetGamma()

void CronoSeries.TimeSeries.Models.ARMAXModel.SetGamma	(	int	idx,
		double	value
	)

inline

sets gamma for the model

Parameters

idx	index value, starting at 0
value	value to set

◆ SimulateData()

override Data.TimeSeries CronoSeries.TimeSeries.Models.ARMAXModel.SimulateData	(	List< DateTime >	dateTimes,
		int	randomSeed
	)

inlinevirtual

This function must simulate from the current model.

Parameters

dateTimes	these may have different interpretations, but for time series, is typically an IList of DateTime objects
randomSeed	random number seed

Returns

Reimplemented from CronoSeries.TimeSeries.Models.ARMAModel.

The documentation for this class was generated from the following file:

TimeSeries/Models/ARMAXModel.cs

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Properties

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ARMAXModel() [1/2]

◆ ARMAXModel() [2/2]

Member Function Documentation

◆ ComputeAdjustedValues()

◆ ComputeConsequentialParameters()

◆ GetGamma()

◆ InitializeParameters()

◆ LogLikelihood()

◆ SetGamma()

◆ SimulateData()