Suppose that a time series consisting of six years (2011−2016) of quarterly data exhibits obvious seasonality. In fact, assume that the seasonal indexes turn out to be 0.75, 1.45, 1.25, and 0.55.

a. If the last four observations of the series (the four quarters of 2016) are 2502, 4872, 4269, and 1924, calculate the deseasonalized values for the four quarters of 2016.

b. Suppose that a plot of the deseasonalized series shows an upward linear trend, except for some random noise. Therefore, you estimate a linear regression equation for this series versus time and obtain the following equation:

Predicted deseasonalized value = 2250 + 51Quarter

Here the time variable Quarter is coded so that Quarter = 1 corresponds to first quarter 2011, Quarter = 24 corresponds to fourth quarter 2016, and the others fall in between. Forecast the actual (not deseasonalized) values for the four quarters of 2017.