Suppose that a time series consisting of six years (2005-2010) 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 2010) are 2502, 4872, 4269, and 1924, calculate the de-seasonalized values for the four quarters of 2010.
b. Suppose that a plot of the de-seasonalized 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 de-seasonalized value = 2250 + 51Quarter Here the time variable Quarter is coded so that
Quarter = 1 corresponds to first quarter 2005,
Quarter = 24 corresponds to fourth quarter 2010, and the others fall in between. Forecast the actual (not de-seasonalized) values for the four quarters of 2011.