Teachers’ Retirement System of the City of New York offers several types of investments for its members. Among the choices are investments with fixed and variable rates of return. There are several categories of variable-return investments. The Diversified Equity Fund consists of investments that are primarily made in stocks, and the Stable-Value Fund consists of investments in corporate bonds and other types of lower-risk instruments. The data in TRSNYC represent the value of a unit of each type of variable-return investment at the beginning of each year from 1984 to 2017.

Source: Data extracted from “Historical Data-Unit Values, Teachers’ Retirement System of the City of New York,” bit.ly/SESJF5.

For each of the two time series,

a. Plot the data.

b. Compute the linear trend forecasting equation.

c. Compute the quadratic trend forecasting equation.

d. Compute the exponential trend forecasting equation.

e. Determine the best-fitting autoregressive model, using α = 0.05.

f. Perform a residual analysis for each of the models in (b) through (e).

g. Compute the standard error of the estimate (SYX) and the MAD for each corresponding model in (f).

h. On the basis of your results in (f) and (g), along with a consideration of the principle of parsimony, which model would you select for purposes of forecasting? Discuss.

i. Using the selected model in (h), forecast the unit values for 2018.

j. Based on the results of (a) through (i), what investment strategy would you recommend for a member of the Teachers’ Retirement System of the City of New York? Explain.