hard · Quantitative Finance

Consider the AR(1) process X_t=φ X_t-1+varepsilon_t with varepsilon_t i.i.d. N(0,σ^2) and |φ|<1, in stationarity. You compute the OLS estimator hatφ from T observations. Which statement about hatφ is correct?

1. hatφ is biased downward in finite samples (toward zero / its sign), with bias of order -1/T, even though it is consistent and asymptotically normal
2. hatφ is unbiased for every T because the regression error is conditionally mean-zero
3. hatφ is biased upward, overstating persistence, because positive autocorrelation reinforces itself
4. hatφ is inconsistent because the regressor X_t-1 is correlated with past errors

Sign up free to see the explanation and track your rank →