mlmts (version 1.1.2)

dis_var_2: Model-based dissimilarity proposed by Maharaj (1999)

Description

dis_var_2 returns a pairwise distance matrix based on testing whether each pair of series are or not generated from the same VARMA model maharaj1999comparisonmlmts.

Usage

dis_var_2(X, max_p = 2, criterion = "BIC")

Value

The computed pairwise distance matrix.

Arguments

X

A list of MTS (numerical matrices).

max_p

The maximum order considered with respect to the fitting of VAR models.

criterion

The criterion used to determine the VAR order.

Author

Ángel López-Oriona, José A. Vilar

Details

Given a collection of MTS, the function returns the pairwise distance matrix, where the distance between two MTS \(\boldsymbol X_T\) and \(\boldsymbol Y_T\) is defined as \(1-p\), where \(p\) is the \(p\)-value of the test of hypothesis proposed by . This test is based on checking the equality of the underlying VARMA models of both series. The VARMA structures are approximated by truncated VAR(\(\infty)\) models with a common order \(k = \max{(k_x, k_y)}\), where \(k_x\) and \(k_y\) are determined by the BIC or AIC criterion. The VAR coefficients are automatically fitted. The dissimilarity between both series is given by \(1-p\) because this quantity is expected to take larger values the more different both generating processes are. The procedure is able to compare two dependent MTS.

References

maharaj1999comparisonmlmts

See Also

dis_var_1, diss.AR.MAH

Examples

toy_dataset <- Libras$data[c(1, 2)] # Selecting the first two MTS from the
# dataset Libras
distance_matrix <- dis_var_2(toy_dataset, max_p = 1) # Computing the pairwise
# distance matrix based on the distance dis_var_2