ConsRegArima {ConsReg}

Fit regression model with Arma errors to univariate time series

Description

ConsRegArima is a function that allows to estimate a regression model with errors following an ARMA process (p,q). It allows the introduction of restrictions (both lower and upper limits) and restrictions between the coefficients (in the form, for example, of a>b). Largely a wrapper for the arima function in the stats package but easier to include regressors.

Usage

ConsRegArima(...)

## Default S3 method:
ConsRegArima(x, y, order, seasonal, optimizer,
  LOWER = NULL, UPPER = NULL, penalty = 1000, constraints = NULL,
  ini.pars.coef, model_fit = NULL, ...)

## S3 method for class 'formula'
ConsRegArima(formula, data = list(),
  optimizer = c("solnp"), order = c(0, 0), seasonal = list(order =
  c(0, 0), period = NA), LOWER = NULL, UPPER = NULL, penalty = 1000,
  constraints = NULL, ini.pars.coef = NULL, na.action = "na.omit",
  ...)

Arguments

...

additional parameters passed in the optimizer (number of iterations, ...)

x

matrix of predictive variables

y

vector of outcome variable

order

Arma component (p, q)

seasonal

A specification of the seasonal part of the ARMA model (P,Q), plus the period (which defaults to 1).

optimizer

Optimizer package used for fit the model (include bayesian and genetic algorithm optimization). Possible values are: "solnp" (default) (Rsolnp), "gosonlp" (Rsolnp), "optim" (stats::optim), "nloptr" (nloptr), DEoptim ("DEoptim"), "dfoptim" (dfoptim), "mcmc" (FME::modMCMC), "MCMCmetrop" (MCMCpack::MCMCmetrop1R), 'adaptMCMC'(adaptMCMC::MCMC), "GA" (GA package), "GenSA" (GenSA package)

LOWER

(default NULL) vector of lower bounds for the coefficients. If the lenght of LOWER is not equal with the length of the coeefficients, then, the rest will be equal to -Inf

UPPER

(default NULL) vector of lower bounds for the coefficients. If the lenght of UPPER is not equal with the length of the coeefficients, then, the rest will be equal to +Inf

penalty

(default 1000) penalty to the objective function if some constraints do not fullfill

constraints

vector of constraints (see details)

ini.pars.coef

vector of initial parameters. In case there is some constraint, then the ini.pars.coef should fulfill the constraints. This vector is only for regression component.

model_fit

object of class ConsRegArima to update the Arma part and fix the coefficient from a previous model

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.

na.action

na.action to the data

Details

Several optimizers of various R packages are implemented, including methods typically used in Bayesian regressions like Markov Chain Monte Carlo simulation.

Constraints will be a string: For example, if x1 and x2 are two coefficient names, then a constraint could be: "x1 > x2" or "x1+x2 > 2". For some constraints, one can write: "x1+x2>2, x1 > 1". Each constraint will be separate by commas.

Important: if there are some constraints that do not fulfill in a model without those constraints, it is recommended to use ini.pars.coef parameter to set initial values that fulfill constraints. See the example

On the other hand, aic value is computed as auto.arima function computes the AIC when method == 'CSS':

AIC = n * log(sigma2) + npar * 2

Where npar I set the number of coefficients.

Value

An object of class "ConsRegArima".

coefficients

Coefficients (regression + arma errors)

hessian

hessian matrix if the optimizer can return it

optimizer

optimizer object return (see details of each optimization package)

optimizer.name

name of the optimizer

df

nrow(data) - number of coefficients

rank

number of coefficients

objective_function

objective_function used

model

A list representing the Kalman Filter used in the fitting

sigma2

the MLE of the innovations variance

residuals

residuals of the model

fitted

fitted values of the model

fitted_regression

fitted values only of the regression part

fitted_arima

fitted values only of the arma part

metrics

Accuracy metrics of the model (accuracy function of the forecast package)

call

the matched call

y

objective series

x

regressors

formula

formula term

aic

the AIC value (see details)

bic

the BIC value

aicc

the AICc value

Author(s)

Josep Puig Salles

References

Peiris, M. & Perera, B. (1988), On prediction with fractionally Hyndman RJ, Khandakar Y (2008). “Automatic time series forecasting: the forecast package for R.”

Examples

data('series')
fit1 = ConsRegArima(formula = y ~ x1+x2 +x3+x4,
                    order = c(2, 1), data = series)
summary(fit1)
fit2 = ConsRegArima(formula = y ~ x1+x2 +x3+x4, order = c(2, 1),
                    data = series, constraints = '(x3 +.1) > x1',
                    ini.pars.coef = c(.96, .2, -.8, .4), UPPER = 1, LOWER = -1)

fit1$coefficients
fit2$coefficients