fit_EXPAR {EXPAR}

Fitting of EXPAR model with known parameters

Description

Fits an EXPAR model to the dataset for given parameter values, without any optimisation.

Usage

fit_EXPAR(ts_data, par)

Arguments

ts_data

A univariate data to which the model is to be fitted, preferably (but not limited to) a ts object.

par

The parameter vector. Any value from the parametric space of EXPAR model is permissible. Number of required parameters is 2p+1, where p is order of the model. Entries are arranged consecutively, for example, for order 2, the form of input is c(Phi1,Phi2,Pi1,Pi2,Gamma).

Details

This function uses the form of EXPAR model to generate consecutive fitted observations as theoretical values obtained from the model. The form of EXPAR model employed is given by,

y_{t+1}=\sum_{i=1}^{p}[({\phi_i+\pi_i e^{-\gamma y_t^2}})\ y_{t-i+1}\ ]+\epsilon_{t+1}

where, \gamma>0 and \{\epsilon_t\} is white noise process with zero mean and constant variance \sigma_e^2

The process of fitting involves using actual observations in the dataset in the RHS of above equation and obtaining the fitted values y_{t+1}. No optimization is done as parameter estimation is omitted. It is useful for simulation of data with given order and parameters.

Value

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

Fitted

Fitted values obtained from LHS of the aforementioned model. Due to obvious reasons, fits of the first p observations are not obtained.

Residuals

The residuals \epsilon_{t+1}, computed by iterative fitting.

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.

Examples

datats <- ts(egg_price_index[,3], start = c(2013, 1), frequency = 12)
fit_EXPAR(datats, par = c(0.45,0.68,0.48))