Approximations to the Distribution of the Sample Autocorrelation Coefficient in the Presence of Unit Roots| Chapter 2 | Research Highlights in Mathematics and Computer Science Vol. 2

In this work, we start accompanying the first order autoregressive model 

[AR (1)]  y_t=ρy_(t-1)+ε_t, t=1,2,…,n,

where y_0=0, the variables ε_1,…,ε_n are liberated and evenly distributed (iid) N(0,σ^2), |ρ|≤1 and we will study approximations to the allocation of the autocorrelation coefficient as an estimator of ρ. First, we evolve the general case for all ρ in order that |ρ|≤1 and therefore we focus our attention on the non fixed case under the presence of whole ancestries that is when |ρ|=1.The approximations are acquired using the expansions grown by Francis Ysidro Edgeworth in 1904 to approximate the distributions of estimators.We introduce a contrasting of the results from Monte Carlo simulations and our approximations. Several authors have made that Edgeworth approximations are insufficiently correct in practical positions. Indeed, Edgeworth approximations to the density function can produce negative principles on the tails of distributions. However, the benefit of these approximations is that they generate examining results (specifically, formulas) that are natural to handle and define, making them ideal for corresponding with additional methods. Our judgments are complementary to theirs.  

Author(s) Details:

Juan Carlos Abril,
Universidad Nacional de Tucumán, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina.

María De Las Mercedes Abril,
Universidad Nacional de Tucumán, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina.

Please see the link here: https://stm.bookpi.org/RHMCS-V2/article/view/8569