teo_V {sinar}

Compute the value of matrix V using the coefficients.

Description

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

\sqrt{n}(\hat{a}_{10} - a_{10}, \hat{a}_{01} - a_{01}, \hat{a}_{11} - a_{11}, \hat{\mu}_\epsilon - \mu_\epsilon)^\top \sim MNV(0, \Sigma)

where

\Sigma = 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] + \epsilon_{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] + \epsilon_{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] + \epsilon_{i,j}

mu_e

is the mean of the innovations \epsilon_{i,j}

s2_e

is the standar deviation of the innovations \epsilon_{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))