homework 4 with Correct Answers Georgia Institute Of Technology ISYE 6501

ISYE 6501 19SP1 HW 4 solution


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?

Solution 7.1

Exponential smoothing would be appropriate to be used in forecasting USA Gross domestic product
(GDP). The Gross domestic Product (GDP) is the market value of all final goods and services produced
within a country in a given period of time. For USA quarterly GDP data, we can download the Federal
Reserve website (​https://fred.stlouisfed.org/series/GDP​).

I expect the smoothing parameter, alpha, is closer 1 in USA GDP forecasting as the economy of USA. It
means that more weight is given to the actual data. As US economy is huge and has many types goods
and service produces, the randomness of overall US economy should be less.


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).

,Solution 7.2

HoltWinters function is used to generate 4 exponential smoothing models: single, double, triple with
additive seasonality and triple with multiplicative seasonality. The results from exponential
smoothing models do not support the unofficial end of summer has gotten later over the 20 years.

Sample result & chart from Triple exponential smoothing model with multiplicative seasonality. It is
observed that there is not trend variation in the temperature data set.
​## HoltWinters(x = temp_ts, seasonal = "multiplicative")

## Smoothing parameters:

## alpha: 0.615003

## beta : 0

## gamma: 0.5495256

##

## Coefficients:

## [,1]

## a 73.679517064

## b -0.004362918

## s1 1.239022317

..

..

,Result from Triple exponential smoothing model with multiplicative seasonality is used to generated
season data set for later cucum calculation for verify if there is any significant change in temperate
over the years (1996 to 2005)

Please note that the generated season date set is from 1997 to 2005 only as the very first predicted
value (year 1996) is empty.

Code of cucum calculation is from previous homework. In the Code, qcc.cucum function is used.
Various decision.interval and se.shift parameter values have been used to generate the cusum
models to figure out the unofficial summer end-day data set of each year from 1997 to 2005. The
cusum models of all these date set do not show significant increases or decreases of summer end day
change from 1997 to 2005.
Sample year over year summer end day cusum chart

, Code for homework 7
clear the environment & load data
rm(list = ls())
set.seed(123)

# ---------------------------- Data manipulation
-------------------------------------

data <- read.table("temps.txt", header = TRUE, stringsAsFactors = FALSE)

head(data)
#convert data into vector
temp_vec <- as.vector(unlist(data[,2:21]))
plot (temp_vec)




cat('temp_vec class is', class(temp_vec), '\n')