SCENARIO 16-13 Given Below Is the Monthly Time Series Data for U.S.retail

Short Answer

SCENARIO 16-13
Given below is the monthly time series data for U.S.retail sales of building materials over a specific year.
The results of the linear trend,quadratic trend,exponential trend,first-order autoregressive,second-order autoregressive and third-order autoregressive model are presented below in which the coded month for the 1^st month is 0:
Linear trend model:

Quadratic trend model:
Third-order autoregressive::

Below is the residual plot of the various models:

-Referring to Scenario 16-13,what is the exponentially smoothed value for the first month using a smoothing coefficient of W = 0.5?