An Autoregressive Order 1 Process with Time Varying Coefficient
نویسنده
چکیده
( ) ( ) ( ) t t / L L e 1 1 e t + − = ρ and 1 Y L − + = t t β α , that is, we investigate the nonlinear least squares estimator. Starting with the simplest case 0 = β , we find that ( ) ( ) ( ) 1 e 1 e t + − = α α ρ / which is just a constant so the estimator that minimizes the error sum of squares must be ( ) ( ) ( ) ρ ρ α ˆ / ˆ ˆ − + = 1 1 ln where ρ̂ is the usual regression estimate of (the constant) ρ . Expanding in Taylor's series we have
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