bdm::ARX Class Reference

Linear Autoregressive model with Gaussian noise. More...

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;
}

Todo:: sort out constant terms - bayes should accept vec without additional 1s

#include <arx.h>

List of all members.

Public Member Functions
void	set_statistics (const BMEF *BM0)
	Set sufficient statistics.
void	from_setting (const Setting &set)
void	validate ()
	This method TODO.
virtual void	set_statistics (const BMEF *BM0)
	get statistics from another model
virtual void	flatten (const BMEF *B)
	Flatten the posterior according to the given BMEF (of the same type!).
virtual string	to_string ()
	This method returns a basic info about the current instance.
virtual void	to_setting (Setting &set) const
	This method save all the instance properties into the Setting structure.
Constructors

	ARX (const double frg0=1.0)
	ARX (const ARX &A0)
ARX *	_copy_ () const
	Copy function required in vectors, Arrays of BM etc. Have to be DELETED manually! Prototype:.
void	set_parameters (double frg0)
void	set_constant (bool const0)
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)
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.
ivec	structure_est_LT (egiw Eg0)
	Smarter structure estimation by Ludvik Tesar.
Access attributes

const egiw &	posterior () const
Connection

void	set_rv (const RV &yrv0, const RV &rgrrv0)
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_drv (const RV &rv)
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
RV	rgrrv
	rv of regressor
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
bool	have_constant
	switch if constant is modelled or not
vec	_dt
	cached value of data vector for have_constant =true
egiw	alter_est
	Alternative estimate of parameters, used in stabilized forgetting, see [Kulhavy].
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.
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

virtual void	set_options (const string &opt)
	Set boolean options from a string, recognized are: "logbounds,logll".
virtual void	log_add (logger &L, const string &name="")
	Add all logged variables to a logger.
virtual void	logit (logger &L)
	Save results to the given logger, details of what is stored is configured by `LIDs` and `options`.
ivec	LIDs
	IDs of storages in loggers 4:[1=mean,2=lb,3=ub,4=ll].
ivec	LFlags
	Flags for logging - same size as LIDs, each entry correspond to the same in LIDs.

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::BMEF.

Reimplemented in bdm::ARXfrg.

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

Incremental Bayes rule.

Parameters:

dt

vector of input data

Reimplemented from bdm::BMEF.

References bayes().

void bdm::ARX::from_setting ( const Setting & set ) [virtual]

UI for ARX estimator

        class = 'ARX';
        rv    = RV({names_of_dt} )                 // description of output variables
        rgr   = RV({names_of_regressors}, [-1,-2]} // description of regressor variables
        constant = 1;                              // 0/1 switch if the constant term is modelled or not

        --- optional ---
        V0  = [1 0;0 1];                           // Initial value of information matrix V
          --- OR ---
        dV0 = [1e-3, 1e-5, 1e-5, 1e-5];            // Initial value of diagonal of information matrix V
                                                                                           // default: 1e-3 for rv, 1e-5 for rgr
        nu0 = 6;                                                   // initial value of nu, default: rgrlen + 2
        frg = 1.0;                                 // forgetting, default frg=1.0

        rv_param   = RV({names_of_parameters}}     // description of parametetr names 
                                                                                           // default: ["theta_i" and "r_i"]