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:

• 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?
• The model can be additive or multiplicative. When we do use an additive model? When do we use a multiplicative model?
• 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

• Construct a scatter plot with this data. Do you observe a trend? If so, what type of trend do you observe?
• Use Excel to fit a linear trend and an exponential trend to the data. Display the models and their respective r^2.
• Interpret both models. Which model seems to be more appropriate? Why?

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