ISYE 6501 Week 4 homework

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SYE 6501 Week 4 homework Exponential Smoothing Exponential smoothing assists with change detection as it smoothes out the data. The benfits of exponential smoothing are that it gives you smoother data (less noisy data) and the ability to forecast using trends and seanolaity for time series data. Additionally, data can be made to be less noisy for more confidence in a CUSUM change detection model, which will see in this assignment. Let’s pull in the data again. rm(list = ls()) temps <- read.table("/Users/paris.piotis/Desktop/OMSA/temps.txt", stringsAsFactors = FALSE, header=TRUE) head(temps) ## DAY X1996 X1997 X1998 X1999 X2000 X2001 X2002 X2003 X2004 X2005 X2006 X2007 ## 1 1-Jul 98 86 91 84 89 84 90 73 82 91 93 95 ## 2 2-Jul 97 90 88 82 91 87 90 81 81 89 93 85 ## 3 3-Jul 97 93 91 87 93 87 87 87 86 86 93 82 ## 4 4-Jul 90 91 91 88 95 84 89 86 88 86 91 86 ## 5 5-Jul 89 84 91 90 96 86 93 80 90 89 90 88 ## 6 6-Jul 93 84 89 91 96 87 93 84 90 82 81 87 ## X2008 X2009 X2010 X2011 X2012 X2013 X2014 X2015 ## 1 85 95 87 92 105 82 90 85 ## 2 87 90 84 94 93 85 93 87 ## 3 91 89 83 95 99 76 87 79 ## 4 90 91 85 92 98 77 84 85 ## 5 88 80 88 90 100 83 86 84 ## 6 82 87 89 90 98 83 87 84 tail(temps) ## DAY X1996 X1997 X1998 X1999 X2000 X2001 X2002 X2003 X2004 X2005 X2006 ## 118 26-Oct 75 71 79 69 75 64 68 68 79 61 62 ## 119 27-Oct 75 57 79 75 78 51 69 64 81 63 66 ## 120 28-Oct 81 55 79 73 80 55 75 57 78 62 63 ## 121 29-Oct 82 64 78 72 75 63 75 70 75 64 72 ## 122 30-Oct 82 66 82 75 77 72 68 77 78 69 73 ## 123 31-Oct 81 60 79 75 78 71 60 75 82 70 68 ## X2007 X2008 X2009 X2010 X2011 X2012 X2013 X2014 X2015 ## 118 68 70 65 85 77 80 61 84 67 ## 119 67 59 60 76 79 70 69 84 56 ## 120 70 50 71 74 74 56 64 77 78 ## 121 62 59 75 68 59 56 75 73 70 ## 122 67 65 66 71 61 56 78 68 70 ## 123 71 67 69 75 65 65 74 63 62 Note that there are 123 rows per year. 16/09/2020 ISYE 6501 Week 4 homework file:///Users/paris.piotis/Desktop/ISYE-6501-Week-4-Homework.html 2/96 Data transformation Holt winters exponential smoothing requires a time series input, so we need to transform the data into time series data. First, we transform the data table into a vector: temps_vec <- as.vector(unlist(temps[,2:21])) head(temps_vec) ## [1] 98 97 97 90 89 93 plot(temps_vec) Then we transform into time series We know from our data exploration that there are 123 days per cycle, that’s why frequency gets set to 123 and starts at 1996. temps_ts <- ts(temps_vec, start = 1996, frequency = 123) head(temps_ts) ## [1] 98 97 97 90 89 93

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