Week 6 Assignment 1 Of 2 Due Date Is Thursday, October 1 ✓ Solved

Week 6 Assignment 1 Of 2 Due Date Is Thursday October 1, 2020time 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 do 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 - 817 million, 1950 - 206 million, 1955 - 921 million, 1960 - 686 million, 1965 - 338 million. 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?

Sample Paper For Above instruction

Time series analysis is an essential tool in understanding and forecasting variables that fluctuate over time, such as revenues, costs, and profits. Decomposition of a time series involves breaking down the observed data into several components: trend (T), cycle (C), seasonal (S), and irregular (I). Each component captures different aspects of the data's underlying patterns. The trend component reflects the long-term movement or directional change in the data, indicating whether the variable is generally increasing or decreasing over time. The cycle component embodies repetitive fluctuations that occur at irregular intervals, often influenced by economic or environmental factors. Seasonal components represent regular, predictable patterns that recur within specific periods, such as quarterly or annually. Lastly, the irregular component captures random or unforeseen fluctuations that cannot be explained by the other components, often considered noise.

The choice between additive and multiplicative models depends on the nature of the data. An additive model assumes the relationship Y = T + C + S + I, where the components add together, making it suitable when the magnitude of seasonal variations remains constant over time. Conversely, a multiplicative model follows the form Y = T × C × S × I, appropriate when seasonal variations change proportionally with the level of the series—meaning the seasonal fluctuations increase or decrease with the trend.

Analyzing the U.S. gross federal debt data from 1945 to 2000 reveals intriguing insights. Plotting the data on a scatter plot indicates an upward trend in federal debt over time, suggesting that the debt has generally increased across decades. Visual inspection hints at exponential growth, especially in the later years, which implies that an exponential trend model might better capture this trend compared to a linear model.

Using Excel, both linear and exponential trend lines were fitted to the data, with the corresponding R-squared values computed to assess fit quality. The linear trend model provides a straightforward approximation, indicating a constant rate of increase in debt over time, but with a lower R-squared value. The exponential model fits the data more closely, as evidenced by a higher R-squared, signaling that federal debt growth accelerates over time, consistent with exponential growth patterns.

Interpretation of the models reinforces these observations. The linear trend suggests a steady increase in debt per five-year interval, but the exponential model emphasizes the compounding nature of debt accumulation, which may be more accurate in capturing the growth dynamics during this period. Given the higher R-squared and the observed curve sharper ascent towards the later years, the exponential model appears more appropriate for forecasting future debt levels. It indicates that without intervention, federal debt might continue to grow exponentially, raising concerns about fiscal sustainability.

References

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