Mean estimation bias in least squares estimation of autoregressive processes

Least squares estimation in a simple random coefficient autoregressive model.∗

The question we discuss is whether a simple random coefficient autoregressive model with infinite variance can create the long swings, or persistence, which are observed in many macro economic variables. The model is defined by yt = stρyt−1 + εt, t = 1, . . . , n, where st is an i.i.d. binary variable with p = P (st = 1), independent of εt i.i.d. with mean zero and finite variance. We say that ...

Aggregation Bias in Maximum Likelihood Estimation of Spatial Autoregressive Processes

In statistical models of spatial behavior, there is often a mismatch between the scale at which data is available and the scale at which key spatial dependencies are known to occur. However, in attempting to incorporate Þner grain information about spatial dependencies, certain estimation problems arise. Here it is shown that maximum likelihood procedures can produce signiÞcantly negative estim...

Weighted Least Squares Approximate Restricted Likelihood Estimation for Vector Autoregressive Processes

We derive a weighted least squares approximate restricted likelihood estimator for a kdimensional pth order autoregressive model with intercept, for which exact likelihood optimization is generally infeasible due to the parameter space which is complicated and highdimensional, involving pk2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error th...

Recursive Least Squares Estimation

We start with estimation of a constant based on several noisy measurements. Suppose we have a resistor but do not know its resistance. So we measure it several times using a cheap (and noisy) multimeter. How do we come up with a good estimate of the resistance based on these noisy measurements? More formally, suppose x = (x1, x2, . . . , xn) T is a constant but unknown vector, and y = (y1, y2, ...

Least Squares Estimation