Homework4
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School
Florida State University *
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Course
6501
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
docx
Pages
4
Uploaded by tkumar001
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?
Answer: I think exponential smoothing would be a really good model for my monthly
expenses and predicting how much I can expect to spend in upcoming month. This is
because it mostly contains recurring expenses and the variable expenses are not as big
component of monthly expenses. I would also like to include trend and cyclicality in my
model. This is because trend will be a good way to capture the inflation effects on my
monthly spend. Cyclicality would be a really good way to capture vacation expenses and
other activities that mostly vary by season.
I would choose value of
to be closer to 0 (approx 0.2 to 0.25). The reason for that is,
because biggest component of my monthly expense is mortgage and a car loan which are
both fixed expenses and hence my current month expense even if very high for some reason
should not change my baseline expenses very much as I don’t expect variable expenses to
be same next month.
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).
Answer: For this question, I will import the data from file and run holt winters model on
that data. Then we can look at the coefficients of the model to make some estimates if there
is any change in ending of summer.
#First we will start by clearing the environment
rm
(
list =
ls
())
#Reading the data and converting to time series
temps
<-
read.delim
(
"C:/GeorgiaTech/ISYE6501/Homework4/data
7.2/temps.txt"
,
stringsAsFactors=
TRUE
)
temps_vector
<-
as.vector
(
unlist
(temps[,
2
:
21
]))
temps_ts
<-
ts
(temps_vector,
start =
1996
,
frequency =
123
)
#check the data with a plot
plot
(temps_ts)
plot
(
decompose
(temps_ts))
Checking which
plot, we see that our data is showing some trend. Now we will run the exponential
smoothing method on this data.
#Run Holt Winsters model
Model_HW
<-
HoltWinters
(temps_ts,
seasonal =
c
(
"additive"
,
"multiplicative"
))
#Check important values for our model
Model_HW
$
SSE
## [1] 66244.25
Model_HW
$
alpha
##
alpha
## 0.6610618
Model_HW
$
beta
## beta
##
0
Here we see that trend on data after fitting our model shows 0. Which means that there is
no trend in our data.
Model_HW
$
gamma
##
gamma
## 0.6248076
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This shows that we have high degree of seasonality which is usual because we are dealing
with weather data.
#plot the output from Holt winters
plot
(Model_HW
$
fitted)
As we can see from
this above plot, we dot see any trend and there is no significant change in seasonality. So I
would say they there is no significant change in ending dates for summer season.