prove or disprove that MLE of is a consistent estimator for .? Let X1,..., X, be observations

prove or disprove that MLE of is a consistent estimator for .?

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Let X1,..., X, be observations satisfying X; = 0X;-1+ Z;, i = 2, ...,n, where X1, Z2, ..., Z, are independent with X1 ~ N(0,1) and Z; ~ = N(0, 1), i 2,..., n. The parameter space is O = {0 : -1< 0 < 1}. Let X1,..., X, be observations satisfying X; = 0X;-1+ Z;, i = 2, ...,n, where X1, Z2, ..., Z, are independent with X1 ~ N(0,1) and Z; ~ = N(0, 1), i 2,..., n. The parameter space is O = {0 : -1< 0 < 1}.

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