Week 6 Discussion
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Industrial Engineering
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Nov 24, 2024
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Week 6 Discussion: Time Series Models and Visualizing Information
Part 1
Time series decomposition is an important method for separating a time series (Y) into its
underlying components which are the trend (T), Cycle (C), seasonal (S) and irregular (I). These
components can be defined as below:
a)
Trend (T) is an important component that showcases the long-term changes within the
time series. Generally, this component describes the overall trajectory of the data over
time. The component can either be increasing, decreasing or even flat.
b)
Cycle (C) represent the periodic fluctuations within the time series that happen within a
timeframe of more than one year. Additionally, this component has close relationship
with economic and business cycles.
c)
Seasonal (S) showcases the periodic changes in the time series that happen within one
year. This component is related with seasonal factors including holiday sales, climatic
patterns and various other recurrent events.
d)
Irregular (I) is another important component which represents the haphazard or
unpredictable changes within the time series that are not accounted for by other relevant
elements.
It is possible to utilize the trend component of the time series model to forecast the store's yearly
sales over the following several years. The trend component, which indicates the overall
direction of the data across time, plays a significant role in describing the long-term fluctuations
within the time series. The upward trend in this instance indicates that the store's sales are rising
over time. The given model predicts that the store's yearly sales will rise by $460,655 per year.
We would simply add this amount to the sales from the prior year in order to produce a
projection for that particular year. If the store's sales in 2022 were $10 million, for instance, we
may anticipate that they would be $10.46 million in 2023 ($10 million + $460,655). By
continuing to add $460,655 to the sales from the prior year, we might similarly forecast the
store's revenues for subsequent years.
Part 2
The decision to choose either an additive or multiplicative model primarily relies on if the
magnitude of the seasonal fluctuations corresponds to the trend’s magnitude. In this respect, it is
worth acknowledging that the additive model is characterized by seasonal fluctuations which are
independent of the trend. In contrast, the seasonal fluctuations of multiplicative model are
perceived to be proportional to the trend. Based on the details of the scatter plot of the time
series’ exponential trend, a clear upward trend is apparent.
2010
2012
2014
2016
2018
2020
2022
$0
$1,000,000
$2,000,000
$3,000,000
$4,000,000
$5,000,000
$6,000,000
f(x) = 460654.89 x − 926877641.62
R² = 0.72
Sales
The upward trend indicates that the sales made by the store are constantly increasing. As per the
provided regression model, the yearly sales made by the store are expected to increase by
$460,655 annually. In this respect, the R-squared value stands at 0.7202. By projecting the trend
component from this model, we may forecast the store's yearly sales over the following several
years. It is crucial to keep in mind that this forecast depends on the underlying variables
influencing the time series remaining constant, which may not always be the case.
Part 3
Time series models are helpful for monitoring variables like revenues, expenses, and profits over
time, in conclusion. Time series are divided into four categories by time series decomposition:
trend, cycle, seasonality, and irregularity. The connection between the amplitude of the seasonal
variations and the trend determines whether an additive or multiplicative model should be used.
We can see a definite increasing tendency based on the scatter plot of the exponential trend of the
time series data. By projecting the trend component, we can forecast the store's yearly sales over
the following several years, but it's vital to keep in mind that external events might impact those
sales and should be taken into consideration when making decisions based on the projections.
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