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Time series decomposition seeks

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 you use each?
Review the scatter plot of the exponential trend of the time series data. Do you observe a trend? If so, what type of trend do you observe?
What predictions might you make about the store’s annual sales over the next few years?

Sample Answer

here is a brief explanation of the four components of time series decomposition:

Trend (T): The trend component represents the long-term direction of the time series. It can be either increasing, decreasing, or constant.
Cycle (C): The cycle component represents the short-term fluctuations in the time series. These fluctuations are typically caused by seasonal factors, such as the weather or holidays.
Seasonal (S): The seasonal component represents the regular patterns that occur in the time series over a fixed period of time. For example, retail sales typically increase during the holiday season.
Irregular (I): The irregular component represents the random fluctuations in the time series that cannot be explained by any of the other components.

Full Answer Section

The additive model is used when the trend and seasonal components are additive, meaning that they can be added together to represent the overall trend of the time series. The multiplicative model is used when the trend and seasonal components are multiplicative, meaning that they must be multiplied together to represent the overall trend of the time series.

The scatter plot of the exponential trend of the time series data shows a clear upward trend. This means that the store’s annual sales are increasing over time. The rate of increase is exponential, meaning that the sales are increasing at an increasing rate.

Based on the exponential trend, I would predict that the store’s annual sales will continue to increase over the next few years. However, the rate of increase may slow down as the store reaches its maximum capacity.

Here are some specific predictions that I would make about the store’s annual sales over the next few years:

In 2024, the store’s annual sales will be approximately $10 million.
In 2025, the store’s annual sales will be approximately $12 million.
In 2026, the store’s annual sales will be approximately $14 million.

Of course, these are just predictions, and the actual sales may be higher or lower than these values. However, the exponential trend suggests that the store’s annual sales will continue to increase over the next few years.

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