Problem: Time Series Modeling
Time series are particularly useful to track variables such as revenues, costs, and profits over time. Time series models help evaluate performance and make predictions. Consider the following and respond in a minimum of 175 words:
1. Time series decomposition seeks to separate the time series (Y) into 4 components: trend (T), cycle (C), seasonal (S), and irregular (I). What is the difference between these components?
2. The model can be additive or multiplicative. When we do use an additive model? When do we use a multiplicative model?
3. The following list gives the gross federal debt (in millions of dollars) for the U.S. every 5 years from 1945 to 2000:
Year Gross Federal Debt ($millions)
1945 260,123
1950 256,853
1955 274,366
1960 290,525
1965 322,318
1970 380,921
1975 541,925
1980 909,050
1985 1,817,521
1990 3,206,564
1995 4,921,005
2000 5,686,338
a) Construct a scatter plot with this data. Do you observe a trend? If so, what type of trend do you observe?
b) Use Excel to fit a linear trend and an exponential trend to the data. Display the models and their respective r^2.
c) Interpret both models. Which model seems to be more appropriate? Why?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.