Business Finance Homework Help

• 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?

Reply to at least 2 of your classmates or your faculty member, and/or discuss any of the following subjects:

1. Give an example of an irregular trend and explain how this one-time event might impact future operations.
2. When might you use an exponential trend line? When might you choose not to use an exponential trend line?
3. Define the most commonly used time series model at your workplace. How is it used?
4. How do you view Data Analytics and Statistics differently, now that we are in the 6th week of this course?

Be constructive and professional.

Nichole Taylor

Hi teacher and class,

A time series can be break down into systematic and unsystematic components. Systematic means that the components have consistency or recurrence and therefore can be modeled or described. Unsystematic or Non-systematic means that the components cannot be directly modeled. It is also called noise.

The components are defined as:

• Level: The average value in the series.
• Trend: The increasing or decreasing value in the series.
• Seasonality: The repeating short-term cycle in the series.
• Noise: The random variation in the series.

A model can be additive or multiplicative. The additive model is useful when the seasonal variation is relatively constant over time, and the multiplicative model is useful when the seasonal variation increases over time.

For the problem given, we have systematic components, and it is a trend since the debts are increasing period after period.

The linear regression gives R-squared=0.7202. This means that more than 72% of the data fits the model. Nevertheless the average slope =92146 shows that There is an increase of nearly $92146 per period. This is not consistent with the data.

The exponential model fits more the data. R-squared=0.8913 means that more than 89% of the data fits the model. The exponential regression is more accurate than the linear regression in this case. Nevertheless the slope 6-E49 or nearly zero is not really consistent.

The quadratic regression is the one that fits most the data as the number of years increases. R-squared=0.9708 meaning that more than 97% of the data fits the model. The quadratic regression is more accurate to predict future debts while the exponential regression is more accurate for predicting debts between 1940 and 1980. This means also that for the periods 1940 to 1980 and 1980 to 2000 the factors that are explaining the increase of debts are not totally the same

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 trend is defined as movement over years and is steady and predictable. Seasonal is a repetitive cyclical pattern within a year. The cycle is a repetitive pattern, with movement up and down, around a trend that is over several years. Irregular is defined as randomness that follows no particular pattern. Also known as the error component or random noise, irregularity affects all factors other than trend, cycle, and seasonality.

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

Additive models are valuable when their seasonal variations are constant over time versus multiplicative models are most valuable when there are seasonal increases over time.

Interpret both models. Which model seems to be more appropriate? Why?

Exponential trends are most appropriate for time series data that exhibit growth or decline at the same rate in each period. Conversely, the linear trend is best used for time series data that increase or decrease by the same amount in each period. For the federal debt time series data the exponential trend is most appropriate, there is a constant rate of increase.

Linear

Exponential