In this question you will explore whether ˆrLS and ˆrMLE are biased.
(a) In Ror a programming language of your choice, simulate time series data, {R0,R1,…,Rn}, using the model Rt+1 = ztrRte1−Rt/k, (4) with r = 1.3, k = 100, σ = 0.1, starting at R0 = 5 and n = 50, where zt is described as in Q2. Plot your time series data with t on the x-axis and Rt on the y-axis
(b) Given your time series data, compute the values of ˆrLS, and ˆrMLE.
(c) Plot your data with Rt on the x-axis and Rt+1 on the y-axis. On top of this data plot two curves, the Ricker function, rRte1−Rt/k, with r = ˆrMLE and r = ˆrLS. Which curve looks like it fits the data better?
(d) Determine which of your estimators r = ˆrMLE and r = ˆrLS has greater bias?
(e) Which estimator is more biased? Can you guess in words why one is more biased than the other? Note you can take a guess at this question even if you were unable to do the programming for parts (a-d).
