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;
}


Public Member Functions
void	set_statistics (const BMEF *BM0)
	Set sufficient statistics.
BMEF *	_copy_ (bool changerv=false)
	Flatten the posterior as if to keep nu0 data.
Constructors
	ARX (const double frg0=1.0)
	ARX (const ARX &A0)
ARX *	_copy_ ()
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.