teo_V: Compute the value of matrix V using the coefficients.

In sinar: Conditional Least Squared (CLS) Method for the Model SINAR(1,1)

Description

V is the theoretical matrix from Klimko-Nelson for the SINAR(1,1) model. Basically, we know

√{n}(\hat{a}_{10} - a_{10}, \hat{a}_{01} - a_{01}, \hat{a}_{11} - a_{11}, \hat{μ}_ε - μ_ε)^\top \sim MNV(0, Σ)

where

Σ = V^{-1}W V^{-1}.

For more details, check Klimko and Nelson (1978).

Usage

teo_V(a10, a01, a11, mu_e, s2_e)

Arguments

a10	is the parameter in the equation X[i, j]a_{10}X[i - 1, j] + a_{01}X[i, j - 1] + a_{11}X[i - 1, j - 1] + ε_{i,j}
a01	is the parameter in the equation X[i, j]a_{10}X[i - 1, j] + a_{01}X[i, j - 1] + a_{11}X[i - 1, j - 1] + ε_{i,j}
a11	is the parameter in the equation X[i, j]a_{10}X[i - 1, j] + a_{01}X[i, j - 1] + a_{11}X[i - 1, j - 1] + ε_{i,j}
mu_e	is the mean of the innovations ε_{i,j}
s2_e	is the standar deviation of the innovations ε_{i,j}

Value

The matrix V estimated empirically.

Examples

n_row <- 20
n_col <- 50
a10 <- 0.2
a01 <- 0.2
a11 <-  0.5
l <- 1 # mean and variance for poison innovations

teo_V(a10, a01, a11, l, sqrt(l))

sinar documentation built on Jan. 13, 2021, 6 p.m.