Estimation of Parameters in Autoregressive Models

Özlem TÜRKER (METU)

Autoregressive models have many applications in business and economics. In this paper, we consider two regressive models

Y_i,t = m_i + d_i X_i,t + e_i,t (i = 1, 2 ; t = 1, 2, ..., n_i )

where the random errors e_i,t are autocorrelated, i.e.,

e_i,t = f_i e_i,t-1 + a_i,t , | f_i | < 1;

a_i,t are iid random errors. The autoregression coefficicents f_i (i = 1, 2) may or may not be equal. The problem is to estimate m_i , d_i and f_i and s_i² = V(a_i,t); the variances s_i² (i = 1, 2) may or may not be equal.

Traditionally, the random errors at have been assumed to be normal N(0, s²). There is now a realization that non-normal distributions are more prelavent in practice. We consider non-normal distributions and derive efficient estimators by using the methodology of modified likelihood. We also give a test for H_o: d₁ = d₂. We show that our solutions are robust to outliers and other data anomalies. Both situations are considered when X_t (1 £ t £ n) are fixed design points and when they change with Y_t (1 £ t £ n). We give real life examples.