Solution HW4
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Georgia Institute Of Technology *
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6501
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Industrial Engineering
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Feb 20, 2024
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Question 7.1
Describe a situation or problem from your job, everyday life, current events, etc., for which exponential smoothing would be appropriate. What data would you need? Would you expect the value of
(the first smoothing parameter) to be closer to 0 or 1, and why?
Ans: In my role as analytics lead focused on customer data and improving customer relationships, exponential smoothing can be a valuable technique for forecasting and addressing churn, customer experience, and happiness. Exponential smoothing is a time series forecasting method that assigns exponentially decreasing weights to past observations, with a parameter called α (alpha) that determines the weight assigned to the most recent data point. Let's consider a specific scenario where exponential smoothing could be applied:
Scenario
: Predicting Monthly Customer Churn Rate
Data Needed
: Monthly customer churn rate data, which is the percentage of customers who stopped using your product or service in each month. Historical data on factors that might influence churn, such as customer satisfaction scores, customer support interactions, product usage statistics, and marketing campaigns.
Application of Exponential Smoothing
: In this scenario, I want to predict the future monthly churn rate to proactively address potential issues and reduce churn. Exponential smoothing can help by providing a
smoother, more stable estimate of the churn rate. Initialize
: Start with an initial estimate of the churn rate for the first month.
Update
: As each new month's data becomes available, update the estimate of the churn rate using exponential smoothing. The formula for updating is as follows:
New Estimate = α * New Data + (1 - α) * Previous Estimate
New Data: The actual churn rate for the current month.
Previous Estimate: The estimated churn rate from the previous month.
α (Alpha): The smoothing parameter that determines the weight given to the new data.
Forecast: Use the updated estimate to forecast the churn rate for the next month.
Choice of α (Smoothing Parameter):
The choice of α is crucial in this context. A lower α (closer to 0) gives more weight to historical data, making the forecast smoother and less responsive to recent changes in churn rate. A higher α (closer to 1) gives more weight to the most recent data, making the forecast more responsive to recent changes.
In this scenario, I would likely want α to be closer to 0. Here's why:
Stability
: Churn rate data may be noisy and subject to random fluctuations. Using a smaller α helps in stabilizing the forecasts by giving more weight to historical trends, which are often more stable than short-term fluctuations.
Customer Behavior Changes
: Customer behavior changes often occur gradually. A smaller α helps in capturing these gradual changes over time and provides a more reliable indication of trends in churn rate.
Reducing False Alarms
: A smaller α reduces the likelihood of reacting to short-term spikes or dips in churn rate, which might not represent a real change in customer behavior.
However, it's essential to strike a balance because setting α too low might make the model too sluggish to respond to actual changes in customer churn patterns. Therefore, I will need to experiment and fine-
tune the value of α based on the specific characteristics of my data and the desired trade-off between responsiveness and stability in my churn rate forecasts.
Question 7.2
Using the 20 years of daily high temperature data for Atlanta (July through October) from Question 6.2 (file temps.txt
), build and use an exponential smoothing model to help make a judgment of whether the unofficial end of summer has gotten later over the 20 years. (Part of the point of this assignment is for you to think about how you might use exponential smoothing to answer this question. Feel free to combine it with other models if you’d like to. There’s certainly more than one reasonable approach.) Note: in R, you can use either HoltWinters
(simpler to use) or the smooth
package’s es
function (harder to use, but more general). If you use es
, the Holt-Winters model uses model=”AAM”
in the function call (the first and second constants are used “A”dditively, and the third (seasonality) is used “M”ultiplicatively; the documentation doesn’t make that clear). Ans:
I.
I first downloaded the data and converted it into a timeseries for further process:
From the chart we can see that there is seasonality in our data.
II.
I further used Holt Winters to smooth the data. I set alpha beta gamma to null so function will find optimal values based on data. I smoothen the data with seasonal factors as both multiplicative and additive. I calculated sum of squared errors for both of them and chose additive as it had smaller sum of squared errors.
III.
I then evaluated the summary stats of the smoothened data:
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From the plot of fitted model and from the trend factor, we can see that there is almost no trend. Hence, we do not have evidence to conclude if summers are getting hotter or if the length of summer season is getting longer with time.
IV.
To explore further, we will perform CUSUM method to see if we can use Holtwinters model’s components to detect when unofficial summer ends. 1.
For which we will first extract the seasonality factors from above analysis into a separate
object and add the row/column names.
2.
Mean: I then calculated the average seasonality factor for each year for unofficial summer period: July, August, September. Unofficial summer period is identified based on temperature trends over months (graph used from answer to question 6.2: analysis for same data)
3.
For CUSUM analysis we need mean, C and T. a.
Mean we will choose as average of seasonality factor for summer months of first year : meanSFEachYear[1](refer the screenshot above)
b.
C we will use as 0.5 times standard deviation of seasonality factor for summer months of first year.
c.
T we will use as 3 times standard deviation of seasonality factor for summer months of first year.
d.
We are choosing seasonality factor of summer months of first year as baseline period for CUSUM analysis because we want to calculate seasonality drift both from summer seasonality (to show when summer ended each year) as well as seasonality drift in comparison to first year seasonality.
e.
The CUSUM function for reference:
4.
I will next run CUSUM analysis for each year to identify on what day of the year the running average of seasonality factor crossed the threshold we set.
5.
The resulting days of the year on which running average of seasonality factor crossed the threshold we set or the days which represent as summer end are as follows:
V.
It seems that the day unofficial summer ended has changed and increased over the years. However, the overall time-period of unofficial summer's end over the years is quite consistent. The days are within a one-week range.
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