bdm::ARX Class Reference

#include <arx.h>

Inheritance diagram for bdm::ARX:

Detailed Description

Linear Autoregressive model with Gaussian noise.

Regression of the following kind:

$y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t$

where unknown parameters rv are $[\theta r]$ , regression vector $\psi=\psi(y_{1:t},u_{1:t})$ is a known function of past outputs and exogeneous variables $u_t$ . Distrubances $e_t$ are supposed to be normally distributed:

$e_t \sim \mathcal{N}(0,1).$

See Theory of ARX model estimation for mathematical treatment.

The easiest way how to use the class is:

#include <estim/arx.h>
using namespace bdm;
        
// estimation of AR(0) model
int main() {
        //prior 
        mat V0 = 0.00001*eye(2); V0(0,0)= 0.1; //
        ARX Ar; 
        Ar.set_statistics(1, V0); //nu is default (set to have finite moments)
                                                          // forgetting is default: 1.0
        mat Data = concat_vertical( randn(1,100), ones(1,100) );
        Ar.bayesB( Data); 
                        
        cout << "Expected value of Theta is: " << Ar.posterior().mean() <<endl;
}


Extension to conditional BM
This extension is useful e.g. in Marginalized Particle Filter (bdm::MPF). Alternatively, it can be used for automated connection to DS when the condition is observed
const RV &	_rvc () const
	access function
virtual void	condition (const vec &val)
	Substitute `val` for `rvc`.
RV	rvc
	Name of extension variable.
Logging of results
void	set_options (const string &opt)
	Set boolean options from a string.
void	log_add (logger *L, const string &name="")
	Add all logged variables to a logger.
void	logit (logger *L)
ivec	LIDs
	IDs of storages in loggers.
bool	opt_L_bounds
	Option for logging bounds.
Public Member Functions
void	set_statistics (const BMEF *BM0)
	Set sufficient statistics.
BMEF *	_copy_ (bool changerv=false) const
	Flatten the posterior as if to keep nu0 data.
Constructors
	ARX (const double frg0=1.0)
	ARX (const ARX &A0)
ARX *	_copy_ () const
void	set_parameters (double frg0)
void	set_statistics (int dimx0, const ldmat V0, double nu0=-1.0)
Mathematical operations
void	bayes (const vec &dt, const double w)
	Weighted Bayes .
void	bayes (const vec &dt)
	Incremental Bayes rule.
double	logpred (const vec &dt) const
void	flatten (const BMEF *B)
	Flatten the posterior according to the given BMEF (of the same type!).
enorm< ldmat > *	epredictor (const vec &rgr) const
	Conditioned version of the predictor.
enorm< ldmat > *	epredictor () const
	Predictor for empty regressor.
mlnorm< ldmat > *	predictor () const
	conditional version of the predictor
mlstudent *	predictor_student () const
ivec	structure_est (egiw Eg0)
	Brute force structure estimation.
Access attributes
const egiw *	_e () const
const egiw &	posterior () const
Connection
void	set_drv (const RV &drv0)
RV &	get_yrv ()
Mathematical operations
virtual void	bayesB (const mat &Dt)
	Batch Bayes rule (columns of Dt are observations).
vec	logpred_m (const mat &dt) const
	Matrix version of logpred.
Access to attributes
const RV &	_drv () const
void	set_rv (const RV &rv)
double	_ll () const
void	set_evalll (bool evl0)
Protected Attributes
int	dimx
	size of output variable (needed in regressors)
RV	_yrv
egiw	est
	Posterior estimate of $\theta,r$ in the form of Normal-inverse Wishart density.
ldmat &	V
	cached value of est.V
double &	nu
	cached value of est.nu
double	frg
	forgetting factor
double	last_lognc
	cached value of lognc() in the previous step (used in evaluation of `ll` )
RV	drv
	Random variable of the data (optional).
double	ll
	Logarithm of marginalized data likelihood.
bool	evalll
	If true, the filter will compute likelihood of the data record and store it in `ll` . Set to false if you want to save computational time.

Member Function Documentation

ARX * bdm::ARX::_copy_ ( ) const [virtual]

Copy function required in vectors, Arrays of BM etc. Have to be DELETED manually! Prototype:

 BM* _copy_() const {return new BM(*this);}

Reimplemented from bdm::BM.

void bdm::ARX::bayes ( const vec & dt ) [inline, virtual]

Incremental Bayes rule.

Parameters:

dt

vector of input data

Reimplemented from bdm::BMEF.

References bayes().

double bdm::ARX::logpred ( const vec & dt ) const [virtual]

Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out.

Reimplemented from bdm::BM.

References bdm::egiw::_nu(), bdm::egiw::_V(), est, bdm::BM::evalll, bdm::BMEF::frg, bdm::BMEF::last_lognc, bdm::egiw::lognc(), nu, ldmat::opupdt(), bdm::egiw::pow(), and V.

mlnorm< ldmat > * bdm::ARX::predictor ( ) const [virtual]

conditional version of the predictor

<----------- TODO

Reimplemented from bdm::BM.

References bdm::epdf::dimension(), est, bdm::egiw::mean_mat(), ldmat::rows(), bdm::mlnorm< sq_T >::set_parameters(), and V.

ivec bdm::ARX::structure_est ( egiw Eg0 )

Brute force structure estimation.

Returns:: indeces of accepted regressors.

References bdm::epdf::dimension(), est, and bdm::egiw::lognc().

Member Data Documentation

RV bdm::ARX::_yrv [protected]

description of modelled data $ y_t $ in the likelihood function Do NOT access directly, only via get_yrv().

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

arx.h
bdm/estim/arx.cpp

bdm::ARX Class Reference

Detailed Description

Extension to conditional BM

Logging of results

Public Member Functions

Protected Attributes

Member Function Documentation

Member Data Documentation