best_EXPAR {EXPAR}

Fitting of EXPAR model

Description

Searches for the best EXPAR model among many orders (defaults upto 5), compares them using information criterion and returns the best fit.

Usage

best_EXPAR(ts_data, max.p = 5, ic = "AIC", opt_method = "BFGS")

Arguments

ts_data

A univarite time series data, to which an EXPAR model is to be fitted.

max.p

The maximum order upto which models are to be searched for comparison.

ic

Information criterion to be used for model selection: Akaike information criterion ("AIC"), corrected Akaike information criterion ("AIC_c") or Bayesian information criterion ("BIC").

opt_method

The optimization algorithm to be used for RSS minimization. Corresponds to arguments from optim() in stats. Defaults to the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm.

Details

Fits max.p number of EXPAR models to the given dataset by minimisation of RSS using optimise_EXPAR() and returns the best model among the evaluated ones. Model selection is based on the information critera given in ic.

The various information criterion are calculated (estimated) from RSS as,

\textup{AIC} = 2k + n\log(\frac{\textup{RSS}}{n})

\textup{AIC}_\textup{c} = \textup{AIC} + \frac{2k(k+1)}{n-k-1}

\textup{BIC} = k\log(n) + n\log(\frac{\textup{RSS}}{n})

where, n,k are the number of observations and the number of parameters, respectively.

Value

Returns the fitted EXPAR model as a list with the following components,

series

The data used for fitting the model.

order

Order p of the fitted EXPAR model.

n

Number of observations in series.

k

Number of parameters in the model.

par

Parameters of the fitted model.

Fitted

Fitted values obtained from the model.

Residuals

Residuals of the fitted model.

RSS

The residual sum of squares.

AIC

Akaike information criterion, evaluated from RSS.

AIC_c

Corrected Akaike information criterion, evaluated from RSS.

BIC

Bayesian information criterion, evaluated from RSS.

counts

counts returned by optim()

convergence

convergence returned by optim()

message

message returned by optim()

Author(s)

Saikath Das, Bishal Gurung, Achal Lama and KN Singh

References

Haggan and Ozaki (1981). Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model. Biometrika, 68(1):189-199. <doi:10.1093/biomet/68.1.189>.

Gurung (2015). An exponential autoregressive (EXPAR) model for the forecasting of all India annual rainfall. Mausam, 66(4):847-849. <doi:10.54302/mausam.v66i4.594>.

Examples

datats <- ts(egg_price_index[,3], start = c(2013, 1), frequency = 12)
best_EXPAR(datats)