ESTIMATING OF PARAMETERS: NUAR(1) PROCESS

Miroslav M. Risti\'c and Biljana \v C. Popovi\'c

Abstract: We applied the method of conditional least squares for estimating parameters of NUAR(1). This process can be represented as the random coefficient autoregressive time series of the form $$ X_n=U_n X_{n-1}+V_n, $$ where $\{(U_n,V_n)\}$ is the sequence of independent identically distributed random vectors such that supply the elements of the sequence $\{X_n\}$ with $\mathcal{U}(0,1)$ marginal distribution. Defined estimates were the functions of the estimates of moments $E(U_n)$ and $E(U_n V_n)$ and they are strong consistent and asymptotically normally distributed.

Keywords: conditional least squares estimation; uniform autoregressive process; asymptotic normality; strong consistency

Classification (MSC2000): 62M10

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