Please thoroughly explain.

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.

• 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:

YearGross Federal Debt ($millions)

1945260,123

1950256,853

1955274,366

1960290,525

1965322,318

1970380,921

1975541,925

1980909,050

19851,817,521

19903,206,564

19954,921,005

20005,686,338

• 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?