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 do we 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?

Provide an example from

your personal or professional life where time series data can be useful. where time series data can be useful