1702_ts

Install packages

install.packages("readr", repos = "http://cran.us.r-project.org")

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install.packages("skimr", repos = "http://cran.us.r-project.org")

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install.packages("dplyr", repos = "http://cran.us.r-project.org")

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install.packages("tidyverse", repos = "http://cran.us.r-project.org")

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install.packages("lubridate", repos = "http://cran.us.r-project.org")

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install.packages("RMySQL", repos = "http://cran.us.r-project.org")

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install.packages("plotly", repos = "http://cran.us.r-project.org")

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install.packages("circular", repos = "http://cran.us.r-project.org")

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install.packages("ggeasy", repos = "http://cran.us.r-project.org")

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install.packages("RColorBrewer", repos = "http://cran.us.r-project.org")

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install.packages("viridis", repos = "http://cran.us.r-project.org")

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install.packages("reshape2", repos = "http://cran.us.r-project.org")

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install.packages("fpp2", repos = "http://cran.us.r-project.org")

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install.packages("shiny", repos = "http://cran.us.r-project.org")

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Load Libraries

library("readr")

## Warning: package 'readr' was built under R version 4.1.2

library("skimr")
library("dplyr")

## Warning: package 'dplyr' was built under R version 4.1.2

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## Attaching package: 'dplyr'

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library("tidyverse")

## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──

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## ✓ tidyr   1.2.0     ✓ forcats 0.5.1

## Warning: package 'tidyr' was built under R version 4.1.2

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library("lubridate")

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library("RMySQL")

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library("plotly")

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library("circular")

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library("ggeasy")
library("RColorBrewer")
library("viridis")

## Loading required package: viridisLite

library("viridisLite")
library("reshape2")

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library("forecast")

## Warning: package 'forecast' was built under R version 4.1.2

## Registered S3 method overwritten by 'quantmod':
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library("fpp2")

## ── Attaching packages ────────────────────────────────────────────── fpp2 2.4 ──

## ✓ fma       2.4     ✓ expsmooth 2.3

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library("shiny")

options(scipen = 999) # force R not to use exponential notation

TS

#write.csv(df789, file="~/2810_uc3_R/T1C4/df789.csv")

df789 <- read.csv(file="~/2810_uc3_R/T1C4/df789.csv")

df789_met<-df789%>%
  group_by(year, month)%>%
  summarise(sumKitchen=sum(Kitchen),
            sumLaundromat=sum(Laundromat),
            sumTC=sum(Temp_control),
            sumOEE=sum(otherEE),
            sumAll=sum(gapW))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

df789_met

## # A tibble: 36 × 7
## # Groups:   year [3]
##     year month sumKitchen sumLaundromat  sumTC  sumOEE   sumAll
##    <int> <chr>      <int>         <int>  <int>   <dbl>    <dbl>
##  1  2007 Apr        41591         38446 191629 317887.  589553.
##  2  2007 Aug        35834         49642 225277 256356.  567109.
##  3  2007 Dec        74090         82927 361356 690437. 1208810.
##  4  2007 Feb        47584         64623 270274 559051.  941532.
##  5  2007 Jan        56433         79251 329578 684618. 1149880.
##  6  2007 Jul        43052         55734 154973 243117.  496876.
##  7  2007 Jun        59672         69981 189615 274420.  593688.
##  8  2007 Mar        60758        104675 288235 522849.  976517.
##  9  2007 May        76235         72151 228526 356324.  733236.
## 10  2007 Nov        50823         73687 299690 507719.  931919.
## # … with 26 more rows

ts789_Kitchen <- ts(df789_met$sumKitchen, frequency = 12, start=c(2007,1))
ts789_Laundromat <- ts(df789_met$sumLaundromat, frequency = 12, start=c(2007,1))
ts789_TC <- ts(df789_met$sumTC, frequency = 12, start=c(2007,1))
ts789_OEE <- ts(df789_met$sumOEE, frequency = 12, start=c(2007,1))
ts789_all <- ts(df789_met$sumAll, frequency = 12, start=c(2007,1))

# package fpp2

ggseasonplot(ts789_Kitchen)

ggseasonplot(ts789_Laundromat)

ggseasonplot(ts789_TC)

ggseasonplot(ts789_OEE)

ggseasonplot(ts789_all)

# package fpp2

ggseasonplot(ts789_Kitchen, polar=TRUE)

ggseasonplot(ts789_Laundromat, polar=TRUE)

ggseasonplot(ts789_TC, polar=TRUE)

ggseasonplot(ts789_OEE, polar=TRUE)

ggseasonplot(ts789_all, polar=TRUE)

par(mfrow=c(3,2))

plot(ts789_Kitchen, col="orange", main="Monthly Consumption Kitchen")
plot(ts789_Laundromat, col="blue", main="Monthly Consumption Laundromat")
plot(ts789_TC, col="green", main="Monthly Consumption Temp Control")
plot(ts789_OEE, col="lightgrey", main="Monthly Consumption Everything Else")
plot(ts789_all, col="red", main="Monthly Consumption Total")

Decomposition

#decompose
tsKd <- decompose(ts789_Kitchen) #kitchen
tsLd <- decompose(ts789_Laundromat) #laundromat
tsTd <- decompose(ts789_TC) # temperature control
tsOd <- decompose(ts789_OEE) # other appliances
tsAd <- decompose(ts789_all) # total

#plot
plot(tsKd)

plot(tsLd)

plot(tsTd)

plot(tsOd)

plot(tsAd)

Forecast

Naive forecast

#naive forecasting
naiveKitchen <- naive(ts789_Kitchen, h=12)
naiveLaundromat <- naive(ts789_Laundromat, h=12)
naiveTC <- naive(ts789_TC, h=12)
naiveOEE <- naive(ts789_OEE, h=12)
naiveAll <- naive(ts789_all, h=12)

#plotting the naives
autoplot(naiveKitchen)

autoplot(naiveLaundromat)

autoplot(naiveTC)

autoplot(naiveOEE)

autoplot(naiveAll)

#summary of naives
summary(naiveKitchen)

## 
## Forecast method: Naive method
## 
## Model Information:
## Call: naive(y = ts789_Kitchen, h = 12) 
## 
## Residual sd: 21470.0437 
## 
## Error measures:
##                    ME     RMSE      MAE      MPE     MAPE     MASE       ACF1
## Training set 287.4857 21470.04 17147.43 -38.6244 68.46997 1.427827 -0.5593082
## 
## Forecasts:
##          Point Forecast      Lo 80     Hi 80      Lo 95     Hi 95
## Jan 2010          51653  24138.032  79167.97   9572.488  93733.51
## Feb 2010          51653  12740.959  90565.04  -7857.831 111163.83
## Mar 2010          51653   3995.677  99310.32 -21232.585 124538.59
## Apr 2010          51653  -3376.936 106682.94 -32508.025 135814.02
## May 2010          51653  -9872.339 113178.34 -42441.886 145747.89
## Jun 2010          51653 -15744.632 119050.63 -51422.783 154728.78
## Jul 2010          51653 -21144.763 124450.76 -59681.571 162987.57
## Aug 2010          51653 -26171.082 129477.08 -67368.663 170674.66
## Sep 2010          51653 -30891.904 134197.90 -74588.537 177894.54
## Oct 2010          51653 -35356.969 138662.97 -81417.264 184723.26
## Nov 2010          51653 -39603.825 142909.83 -87912.271 191218.27
## Dec 2010          51653 -43661.645 146967.65 -94118.171 197424.17

summary(naiveLaundromat)

## 
## Forecast method: Naive method
## 
## Model Information:
## Call: naive(y = ts789_Laundromat, h = 12) 
## 
## Residual sd: 18850.9605 
## 
## Error measures:
##                 ME     RMSE      MAE       MPE     MAPE      MASE       ACF1
## Training set 215.4 18850.96 15578.26 -6.448364 30.50085 0.9155087 -0.3091428
## 
## Forecasts:
##          Point Forecast      Lo 80     Hi 80      Lo 95     Hi 95
## Jan 2010          45985  21826.522  70143.48   9037.796  82932.20
## Feb 2010          45985  11819.753  80150.25  -6266.237  98236.24
## Mar 2010          45985   4141.289  87828.71 -18009.434 109979.43
## Apr 2010          45985  -2331.956  94301.96 -27909.407 119879.41
## May 2010          45985  -8034.999 100005.00 -36631.459 128601.46
## Jun 2010          45985 -13190.944 105160.94 -44516.796 136486.80
## Jul 2010          45985 -17932.325 109902.32 -51768.113 143738.11
## Aug 2010          45985 -22345.494 114315.49 -58517.473 150487.47
## Sep 2010          45985 -26490.434 118460.43 -64856.611 156826.61
## Oct 2010          45985 -30410.815 122380.82 -70852.317 162822.32
## Nov 2010          45985 -34139.607 126109.61 -76555.012 168525.01
## Dec 2010          45985 -37702.422 129672.42 -82003.868 173973.87

summary(naiveTC)

## 
## Forecast method: Naive method
## 
## Model Information:
## Call: naive(y = ts789_TC, h = 12) 
## 
## Residual sd: 92251.7255 
## 
## Error measures:
##                    ME     RMSE     MAE       MPE     MAPE     MASE       ACF1
## Training set 2977.543 92251.73 70389.2 -9.055431 32.75646 1.415657 -0.6281436
## 
## Forecasts:
##          Point Forecast       Lo 80    Hi 80      Lo 95    Hi 95
## Jan 2010         295843  177617.657 414068.3  115032.94 476653.1
## Feb 2010         295843  128647.116 463038.9   40138.96 551547.0
## Mar 2010         295843   91070.699 500615.3  -17329.21 609015.2
## Apr 2010         295843   59392.314 532293.7  -65777.12 657463.1
## May 2010         295843   31483.096 560202.9 -108460.58 700146.6
## Jun 2010         295843    6251.234 585434.8 -147049.39 738735.4
## Jul 2010         295843  -16951.857 608637.9 -182535.45 774221.5
## Aug 2010         295843  -38548.768 630234.8 -215565.08 807251.1
## Sep 2010         295843  -58833.030 650519.0 -246587.18 838273.2
## Oct 2010         295843  -78018.362 669704.4 -275928.61 867614.6
## Nov 2010         295843  -96266.104 687952.1 -303836.13 895522.1
## Dec 2010         295843 -113701.602 705387.6 -330501.42 922187.4

summary(naiveOEE)

## 
## Forecast method: Naive method
## 
## Model Information:
## Call: naive(y = ts789_OEE, h = 12) 
## 
## Residual sd: 211139.0047 
## 
## Error measures:
##                     ME   RMSE      MAE       MPE     MAPE     MASE       ACF1
## Training set -75.58096 211139 173091.3 -18.73948 51.09778 3.156825 -0.5078119
## 
## Forecasts:
##          Point Forecast      Lo 80     Hi 80       Lo 95     Hi 95
## Jan 2010       315241.2   44655.68  585826.7   -98583.65  729066.0
## Feb 2010       315241.2  -67424.52  697906.9  -269995.51  900477.9
## Mar 2010       315241.2 -153426.67  783909.1  -401524.46 1032006.9
## Apr 2010       315241.2 -225929.84  856412.2  -512408.49 1142890.9
## May 2010       315241.2 -289806.42  920288.8  -610099.28 1240581.7
## Jun 2010       315241.2 -347555.26  978037.7  -698418.51 1328900.9
## Jul 2010       315241.2 -400660.80 1031143.2  -779636.43 1410118.8
## Aug 2010       315241.2 -450090.23 1080572.6  -855232.22 1485714.6
## Sep 2010       315241.2 -496515.37 1126997.8  -926233.33 1556715.7
## Oct 2010       315241.2 -540425.35 1170907.8  -993387.86 1623870.3
## Nov 2010       315241.2 -582189.45 1212671.9 -1057260.54 1687742.9
## Dec 2010       315241.2 -622094.54 1252576.9 -1118290.11 1748772.5

summary(naiveAll)

## 
## Forecast method: Naive method
## 
## Model Information:
## Call: naive(y = ts789_all, h = 12) 
## 
## Residual sd: 325226.8157 
## 
## Error measures:
##                    ME     RMSE      MAE       MPE     MAPE     MASE       ACF1
## Training set 3404.848 325226.8 263542.6 -12.97477 40.81994 2.860911 -0.5513107
## 
## Forecasts:
##          Point Forecast     Lo 80   Hi 80       Lo 95   Hi 95
## Jan 2010       708722.2  291927.3 1125517    71289.35 1346155
## Feb 2010       708722.2  119285.2 1298159  -192743.98 1610188
## Mar 2010       708722.2  -13187.8 1430632  -395343.88 1812788
## Apr 2010       708722.2 -124867.7 1542312  -566143.49 1983588
## May 2010       708722.2 -223259.6 1640704  -716620.97 2134065
## Jun 2010       708722.2 -312212.7 1729657  -852663.02 2270107
## Jul 2010       708722.2 -394013.5 1811458  -977766.59 2395211
## Aug 2010       708722.2 -470151.9 1887596 -1094210.15 2511655
## Sep 2010       708722.2 -541662.6 1959107 -1203576.34 2621021
## Oct 2010       708722.2 -609299.1 2026744 -1307017.45 2724462
## Nov 2010       708722.2 -673630.2 2091075 -1405403.38 2822848
## Dec 2010       708722.2 -735097.8 2152542 -1499409.95 2916854

Seasonal naive forecast

#naive forecasting
snaiveKitchen <- snaive(ts789_Kitchen, h=12)
snaiveLaundromat <- snaive(ts789_Laundromat, h=12)
snaiveTC <- snaive(ts789_TC, h=12)
snaiveOEE <- snaive(ts789_OEE, h=12)
snaiveAll <- snaive(ts789_all, h=12)

#plotting the naives
autoplot(snaiveKitchen)

autoplot(snaiveLaundromat)

autoplot(snaiveTC)

autoplot(snaiveOEE)

autoplot(snaiveAll)

#summary of naives
summary(snaiveKitchen)

## 
## Forecast method: Seasonal naive method
## 
## Model Information:
## Call: snaive(y = ts789_Kitchen, h = 12) 
## 
## Residual sd: 16332.9625 
## 
## Error measures:
##                     ME     RMSE      MAE       MPE     MAPE MASE      ACF1
## Training set -2078.792 16332.96 12009.46 -42.07327 62.34647    1 0.3190801
## 
## Forecasts:
##          Point Forecast     Lo 80    Hi 80       Lo 95     Hi 95
## Jan 2010          54506 33574.466 75437.53  22493.9818  86518.02
## Feb 2010          33480 12548.466 54411.53   1467.9818  65492.02
## Mar 2010          57801 36869.466 78732.53  25788.9818  89813.02
## Apr 2010          47099 26167.466 68030.53  15086.9818  79111.02
## May 2010          74650 53718.466 95581.53  42637.9818 106662.02
## Jun 2010          18226 -2705.534 39157.53 -13786.0182  50238.02
## Jul 2010          31885 10953.466 52816.53   -127.0182  63897.02
## Aug 2010          64645 43713.466 85576.53  32632.9818  96657.02
## Sep 2010          43047 22115.466 63978.53  11034.9818  75059.02
## Oct 2010          60445 39513.466 81376.53  28432.9818  92457.02
## Nov 2010          55220 34288.466 76151.53  23207.9818  87232.02
## Dec 2010          51653 30721.466 72584.53  19640.9818  83665.02

summary(snaiveLaundromat)

## 
## Forecast method: Seasonal naive method
## 
## Model Information:
## Call: snaive(y = ts789_Laundromat, h = 12) 
## 
## Residual sd: 20430.4031 
## 
## Error measures:
##                     ME    RMSE      MAE       MPE     MAPE MASE      ACF1
## Training set -10924.12 20430.4 17015.96 -26.44356 37.14882    1 0.1887518
## 
## Forecasts:
##          Point Forecast     Lo 80    Hi 80      Lo 95     Hi 95
## Jan 2010          52650 26467.385 78832.62  12607.146  92692.85
## Feb 2010          38298 12115.385 64480.62  -1744.854  78340.85
## Mar 2010          53490 27307.385 79672.62  13447.146  93532.85
## Apr 2010          50681 24498.385 76863.62  10638.146  90723.85
## May 2010          72984 46801.385 99166.62  32941.146 113026.85
## Jun 2010          42418 16235.385 68600.62   2375.146  82460.85
## Jul 2010          29789  3606.385 55971.62 -10253.854  69831.85
## Aug 2010          48348 22165.385 74530.62   8305.146  88390.85
## Sep 2010          50094 23911.385 76276.62  10051.146  90136.85
## Oct 2010          53473 27290.385 79655.62  13430.146  93515.85
## Nov 2010          53967 27784.385 80149.62  13924.146  94009.85
## Dec 2010          45985 19802.385 72167.62   5942.146  86027.85

summary(snaiveTC)

## 
## Forecast method: Seasonal naive method
## 
## Model Information:
## Call: snaive(y = ts789_TC, h = 12) 
## 
## Residual sd: 61816.5813 
## 
## Error measures:
##                    ME     RMSE      MAE      MPE     MAPE MASE      ACF1
## Training set 22247.67 61816.58 49721.92 2.136891 23.65514    1 0.0678801
## 
## Forecasts:
##          Point Forecast    Lo 80    Hi 80     Lo 95    Hi 95
## Jan 2010         305811 226589.9 385032.1 184652.73 426969.3
## Feb 2010         192081 112859.9 271302.1  70922.73 313239.3
## Mar 2010         382896 303674.9 462117.1 261737.73 504054.3
## Apr 2010         296735 217513.9 375956.1 175576.73 417893.3
## May 2010         328521 249299.9 407742.1 207362.73 449679.3
## Jun 2010         187949 108727.9 267170.1  66790.73 309107.3
## Jul 2010         260554 181332.9 339775.1 139395.73 381712.3
## Aug 2010         329213 249991.9 408434.1 208054.73 450371.3
## Sep 2010         312270 233048.9 391491.1 191111.73 433428.3
## Oct 2010         335532 256310.9 414753.1 214373.73 456690.3
## Nov 2010         328312 249090.9 407533.1 207153.73 449470.3
## Dec 2010         295843 216621.9 375064.1 174684.73 417001.3

summary(snaiveOEE)

## 
## Forecast method: Seasonal naive method
## 
## Model Information:
## Call: snaive(y = ts789_OEE, h = 12) 
## 
## Residual sd: 70314.1012 
## 
## Error measures:
##                     ME    RMSE      MAE      MPE     MAPE MASE      ACF1
## Training set -23385.64 70314.1 54830.82 -9.35725 18.93775    1 0.2771404
## 
## Forecasts:
##          Point Forecast    Lo 80    Hi 80     Lo 95    Hi 95
## Jan 2010       404128.4 314017.2 494239.5 266315.26 541941.5
## Feb 2010       219580.3 129469.2 309691.4  81767.19 357393.4
## Mar 2010       519623.9 429512.7 609735.0 381810.76 657437.0
## Apr 2010       444336.1 354224.9 534447.2 306522.96 582149.2
## May 2010       570483.4 480372.3 660594.6 432670.33 708296.5
## Jun 2010       211490.0 121378.9 301601.2  73676.93 349303.1
## Jul 2010       239249.7 149138.6 329360.9 101436.63 377062.8
## Aug 2010       470697.0 380585.9 560808.1 332883.89 608510.1
## Sep 2010       349871.8 259760.7 439983.0 212058.73 487684.9
## Oct 2010       468271.8 378160.6 558382.9 330458.66 606084.9
## Nov 2010       417280.3 327169.2 507391.4 279467.19 555093.4
## Dec 2010       315241.2 225130.1 405352.3 177428.09 453054.3

summary(snaiveAll)

## 
## Forecast method: Seasonal naive method
## 
## Model Information:
## Call: snaive(y = ts789_all, h = 12) 
## 
## Residual sd: 132935.5961 
## 
## Error measures:
##                     ME     RMSE      MAE       MPE    MAPE MASE      ACF1
## Training set -14140.89 132935.6 92118.41 -6.459704 18.2881    1 0.2250479
## 
## Forecasts:
##          Point Forecast    Lo 80     Hi 80    Lo 95     Hi 95
## Jan 2010       817095.4 646731.5  987459.2 556546.4 1077644.3
## Feb 2010       483439.3 313075.5  653803.1 222890.3  743988.3
## Mar 2010      1013810.9 843447.0 1184174.7 753261.9 1274359.8
## Apr 2010       838851.1 668487.2 1009214.9 578302.1 1099400.0
## May 2010      1046638.4 876274.6 1217002.3 786089.5 1307187.4
## Jun 2010       460083.0 289719.2  630446.9 199534.1  720632.0
## Jul 2010       561477.7 391113.9  731841.6 300928.8  822026.7
## Aug 2010       912903.0 742539.2 1083266.8 652354.0 1173452.0
## Sep 2010       755282.8 584919.0  925646.7 494733.9 1015831.8
## Oct 2010       917721.8 747357.9 1088085.6 657172.8 1178270.7
## Nov 2010       854779.3 684415.5 1025143.1 594230.3 1115328.3
## Dec 2010       708722.2 538358.4  879086.0 448173.2  969271.2

Regression

#library(forecast)

fitKitchen <- tslm(ts789_Kitchen~ trend + season)
summary(fitKitchen)

## 
## Call:
## tslm(formula = ts789_Kitchen ~ trend + season)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -20522.7  -5210.9    228.9   6728.7  16700.9 
## 
## Coefficients:
##             Estimate Std. Error t value    Pr(>|t|)    
## (Intercept)  50158.4     7294.5   6.876 0.000000519 ***
## trend         -173.2      200.7  -0.863      0.3970    
## season2     -23337.4     9635.6  -2.422      0.0237 *  
## season3      11439.5     9641.8   1.186      0.2476    
## season4      -2428.3     9652.3  -0.252      0.8036    
## season5      17067.9     9666.9   1.766      0.0907 .  
## season6     -10843.2     9685.6  -1.120      0.2745    
## season7       6561.4     9708.5   0.676      0.5059    
## season8      15963.3     9735.4   1.640      0.1147    
## season9      10934.9     9766.4   1.120      0.2744    
## season10     10097.8     9801.4   1.030      0.3136    
## season11      1509.7     9840.3   0.153      0.8794    
## season12      6254.9     9883.2   0.633      0.5331    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11800 on 23 degrees of freedom
## Multiple R-squared:  0.5796, Adjusted R-squared:  0.3602 
## F-statistic: 2.642 on 12 and 23 DF,  p-value: 0.02186

fitLaundromat <- tslm(ts789_Laundromat~ trend + season)
summary(fitLaundromat)

## 
## Call:
## tslm(formula = ts789_Laundromat ~ trend + season)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -26462  -4047   1225   6742  16873 
## 
## Coefficients:
##             Estimate Std. Error t value     Pr(>|t|)    
## (Intercept)  65818.8     7709.9   8.537 0.0000000138 ***
## trend         -910.3      212.1  -4.292     0.000272 ***
## season2     -16071.3    10184.3  -1.578     0.128210    
## season3       6460.7    10190.9   0.634     0.532358    
## season4       6076.4    10201.9   0.596     0.557253    
## season5      21360.7    10217.4   2.091     0.047807 *  
## season6      -2197.6    10237.2  -0.215     0.831916    
## season7       5901.1    10261.3   0.575     0.570821    
## season8      29802.1    10289.8   2.896     0.008142 ** 
## season9      13676.1    10322.5   1.325     0.198225    
## season10     15214.8    10359.5   1.469     0.155466    
## season11     23513.8    10400.7   2.261     0.033541 *  
## season12     11337.4    10446.0   1.085     0.289018    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12470 on 23 degrees of freedom
## Multiple R-squared:  0.6518, Adjusted R-squared:  0.4702 
## F-statistic: 3.588 on 12 and 23 DF,  p-value: 0.00413

fitTC <- tslm(ts789_TC~ trend + season)
summary(fitTC)

## 
## Call:
## tslm(formula = ts789_TC ~ trend + season)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -86828 -18452   4621  17636  82260 
## 
## Coefficients:
##              Estimate Std. Error t value       Pr(>|t|)    
## (Intercept)  240955.0    23239.4  10.368 0.000000000385 ***
## trend          1854.0      639.4   2.900        0.00808 ** 
## season2     -101645.6    30697.9  -3.311        0.00305 ** 
## season3       82068.1    30717.9   2.672        0.01363 *  
## season4        4049.8    30751.2   0.132        0.89637    
## season5       50948.4    30797.7   1.654        0.11165    
## season6      -84333.5    30857.3  -2.733        0.01185 *  
## season7      -29516.8    30930.1  -0.954        0.34985    
## season8       20293.9    31015.9   0.654        0.51941    
## season9       -2941.8    31114.6  -0.095        0.92549    
## season10      23236.6    31226.1   0.744        0.46433    
## season11       3909.6    31350.2   0.125        0.90184    
## season12     -16529.4    31486.9  -0.525        0.60463    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 37590 on 23 degrees of freedom
## Multiple R-squared:  0.7566, Adjusted R-squared:  0.6297 
## F-statistic: 5.959 on 12 and 23 DF,  p-value: 0.0001292

fitOe <- tslm(ts789_OEE~ trend + season)
summary(fitOe)

## 
## Call:
## tslm(formula = ts789_OEE ~ trend + season)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -90659 -22182   -120  25076  78527 
## 
## Coefficients:
##              Estimate Std. Error t value         Pr(>|t|)    
## (Intercept)  396144.6    28934.4  13.691 0.00000000000152 ***
## trend         -1948.8      796.1  -2.448         0.022415 *  
## season2     -176222.7    38220.7  -4.611         0.000123 ***
## season3      221611.7    38245.6   5.794 0.00000665375944 ***
## season4      126314.8    38287.0   3.299         0.003137 ** 
## season5      271446.8    38344.9   7.079 0.00000032704706 ***
## season6     -119610.9    38419.2  -3.113         0.004891 ** 
## season7      -89280.7    38509.8  -2.318         0.029671 *  
## season8      141989.0    38616.6   3.677         0.001250 ** 
## season9        -745.4    38739.5  -0.019         0.984815    
## season10     173279.4    38878.3   4.457         0.000180 ***
## season11      86897.8    39032.9   2.226         0.036076 *  
## season12     -19856.1    39203.0  -0.506         0.617330    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 46800 on 23 degrees of freedom
## Multiple R-squared:  0.9297, Adjusted R-squared:  0.893 
## F-statistic: 25.33 on 12 and 23 DF,  p-value: 0.0000000002065

fitAll <- tslm(ts789_all~ trend + season)
summary(fitAll)

## 
## Call:
## tslm(formula = ts789_all ~ trend + season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -211944  -32155   -9648   43483  137689 
## 
## Coefficients:
##             Estimate Std. Error t value         Pr(>|t|)    
## (Intercept)   753077      54488  13.821 0.00000000000126 ***
## trend          -1178       1499  -0.786         0.439867    
## season2      -317277      71976  -4.408         0.000204 ***
## season3       321580      72022   4.465         0.000177 ***
## season4       134013      72100   1.859         0.075915 .  
## season5       360824      72210   4.997 0.00004700251521 ***
## season6      -216985      72349  -2.999         0.006403 ** 
## season7      -106335      72520  -1.466         0.156110    
## season8       208048      72721   2.861         0.008838 ** 
## season9        20924      72953   0.287         0.776823    
## season10      221828      73214   3.030         0.005957 ** 
## season11      115831      73505   1.576         0.128723    
## season12      -18793      73825  -0.255         0.801324    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 88130 on 23 degrees of freedom
## Multiple R-squared:  0.8882, Adjusted R-squared:  0.8298 
## F-statistic: 15.22 on 12 and 23 DF,  p-value: 0.00000003464

forecastfitKitchen <- forecast(fitKitchen, h=12)
plot(forecastfitKitchen)

forecastfitLaundromat <- forecast(fitLaundromat, h=12)
plot(forecastfitLaundromat)

forecastfitTC <- forecast(fitTC, h=12)
plot(forecastfitTC)

forecastfitOe <- forecast(fitOe, h=12)
plot(forecastfitOe)

forecastfitAll <- forecast(fitAll, h=12)
plot(forecastfitAll)

Holt-Winters

fcKitchen <- hw(ts789_Kitchen, seasonal="additive", h=12)

checkresiduals(fcKitchen)

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 29.152, df = 3, p-value = 0.000002081
## 
## Model df: 16.   Total lags used: 19

autoplot(fcKitchen)

fcLaundromat <- hw(ts789_Laundromat, seasonal="additive", h=12)

checkresiduals(fcLaundromat)

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 27.308, df = 3, p-value = 0.000005074
## 
## Model df: 16.   Total lags used: 19

autoplot(fcLaundromat)

fcTC <- hw(ts789_TC, seasonal="additive", h=12)

checkresiduals(fcTC)

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 39.339, df = 3, p-value = 0.00000001471
## 
## Model df: 16.   Total lags used: 19

autoplot(fcTC)

fcOe <- hw(ts789_OEE, seasonal="additive", h=12)

checkresiduals(fcOe)

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 26.731, df = 3, p-value = 0.000006704
## 
## Model df: 16.   Total lags used: 19

autoplot(fcOe)

fcAll <- hw(ts789_all, seasonal="additive", h=12)

checkresiduals(fcAll)

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 25.04, df = 3, p-value = 0.00001515
## 
## Model df: 16.   Total lags used: 19

autoplot(fcAll)

Check residuals

Residuals should look like white noise+ Assumptions: - residuals are uncorrelated - mean(residuals=0) - variance of residuals is constant - residuals are normally distributed

checkresiduals(forecastfitKitchen) #regression

## 
##  Ljung-Box test
## 
## data:  Residuals from Linear regression model
## Q* = 36.665, df = 3, p-value = 0.00000005416
## 
## Model df: 13.   Total lags used: 16

checkresiduals(snaiveKitchen) #seasonal naive

## 
##  Ljung-Box test
## 
## data:  Residuals from Seasonal naive method
## Q* = 11.881, df = 7, p-value = 0.1046
## 
## Model df: 0.   Total lags used: 7

checkresiduals(fcKitchen) #holtwinters

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 29.152, df = 3, p-value = 0.000002081
## 
## Model df: 16.   Total lags used: 19

checkresiduals(forecastfitLaundromat) #regression

## 
##  Ljung-Box test
## 
## data:  Residuals from Linear regression model
## Q* = 20.741, df = 3, p-value = 0.0001192
## 
## Model df: 13.   Total lags used: 16

checkresiduals(snaiveLaundromat) #seasonal naive

## 
##  Ljung-Box test
## 
## data:  Residuals from Seasonal naive method
## Q* = 5.7088, df = 7, p-value = 0.5741
## 
## Model df: 0.   Total lags used: 7

checkresiduals(fcLaundromat) #holtwinters

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 27.308, df = 3, p-value = 0.000005074
## 
## Model df: 16.   Total lags used: 19

checkresiduals(forecastfitTC) #regression

## 
##  Ljung-Box test
## 
## data:  Residuals from Linear regression model
## Q* = 37.52, df = 3, p-value = 0.00000003572
## 
## Model df: 13.   Total lags used: 16

checkresiduals(snaiveTC) #seasonal naive

## 
##  Ljung-Box test
## 
## data:  Residuals from Seasonal naive method
## Q* = 8.077, df = 7, p-value = 0.3259
## 
## Model df: 0.   Total lags used: 7

checkresiduals(fcTC) #holtwinters

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 39.339, df = 3, p-value = 0.00000001471
## 
## Model df: 16.   Total lags used: 19

checkresiduals(forecastfitOe) #regression

## 
##  Ljung-Box test
## 
## data:  Residuals from Linear regression model
## Q* = 25.748, df = 3, p-value = 0.00001077
## 
## Model df: 13.   Total lags used: 16

checkresiduals(snaiveOEE) #seasonal naive

## 
##  Ljung-Box test
## 
## data:  Residuals from Seasonal naive method
## Q* = 3.6713, df = 7, p-value = 0.8168
## 
## Model df: 0.   Total lags used: 7

checkresiduals(fcOe) #holtwinters

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 26.731, df = 3, p-value = 0.000006704
## 
## Model df: 16.   Total lags used: 19

checkresiduals(forecastfitAll) #regression

## 
##  Ljung-Box test
## 
## data:  Residuals from Linear regression model
## Q* = 26.729, df = 3, p-value = 0.00000671
## 
## Model df: 13.   Total lags used: 16

checkresiduals(snaiveAll) #seasonal naive

## 
##  Ljung-Box test
## 
## data:  Residuals from Seasonal naive method
## Q* = 3.1215, df = 7, p-value = 0.8735
## 
## Model df: 0.   Total lags used: 7

checkresiduals(fcAll) #holtwinters

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' additive method
## Q* = 25.04, df = 3, p-value = 0.00001515
## 
## Model df: 16.   Total lags used: 19

#Plot overlay actual vs. fitted

autoplot(ts789_Kitchen, series="Actual values")+
  autolayer(fitted(fcKitchen), series="Fitted values")+
  ggtitle("Electricity consumption - Kitchen")

autoplot(ts789_Laundromat, series="Actual values")+
  autolayer(fitted(fcLaundromat), series="Fitted values")+
  ggtitle("Electricity consumption - Laundromat")

autoplot(ts789_TC, series="Actual values")+
  autolayer(fitted(fcTC), series="Fitted values")+
  ggtitle("Electricity consumption - Temp control")

autoplot(ts789_OEE, series="Actual values")+
  autolayer(fitted(fcOe), series="Fitted values")+
  ggtitle("Electricity consumption - Other appliances")

autoplot(ts789_all, series="Actual values")+
  autolayer(fitted(fcAll), series="Fitted values")+
  ggtitle("Electricity consumption - Total")

#Prep test set

# bind together Date and Time, which are now chr

#write_csv(yr_2010, file="~/2810_uc3_R/T1C4/yr_2010.csv")

yr_2010 <- read_csv(file="~/2810_uc3_R/T1C4/yr_2010.csv")

## Rows: 457394 Columns: 10
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl  (8): id, Global_active_power, Global_reactive_power, Global_intensity, ...
## date (1): Date
## time (1): Time
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

df10 <- cbind(yr_2010, paste(yr_2010$Date,yr_2010$Time), stringsAsFactors=FALSE)

## Give the new attribute in the 9th column a header name
colnames(df10)[11] <-"DateTime"

# since we're at renaming columns, will rename the sub_meters too

colnames(df10)[8] <-"Kitchen"
colnames(df10)[9] <-"Laundromat"
colnames(df10)[10] <-"Temp_control"

#move the DateTime attribute within the dataset

df10 <- df10[,c(ncol(df10),1:(ncol(df10)-1))]

# drop original date and time columns, ID and voltage

df10 <- subset(df10, select = -c(Date, Time, id, Voltage))

#convert from chr to POSIXct
df10$DateTime <- as.POSIXct(df10$DateTime, "%Y-%m-%d %H:%M:%S") 

## Warning in strptime(xx, f, tz = tz): unknown timezone '%Y-%m-%d %H:%M:%S'

## Warning in as.POSIXct.POSIXlt(x): unknown timezone '%Y-%m-%d %H:%M:%S'

## Warning in strptime(x, f, tz = tz): unknown timezone '%Y-%m-%d %H:%M:%S'

## Warning in as.POSIXct.POSIXlt(as.POSIXlt(x, tz, ...), tz, ...): unknown timezone
## '%Y-%m-%d %H:%M:%S'

#set time-zone
attr(df10$DateTime, "tzone") <- "GMT"

#inspect new data types
str(df10)

## 'data.frame':    457394 obs. of  7 variables:
##  $ DateTime             : POSIXct, format: "2010-01-01 00:00:00" "2010-01-01 00:01:00" ...
##  $ Global_active_power  : num  1.79 1.78 1.78 1.75 1.69 ...
##  $ Global_reactive_power: num  0.236 0.234 0.234 0.186 0.102 0.1 0.1 0.102 0.072 0 ...
##  $ Global_intensity     : num  7.4 7.4 7.4 7.2 7 7 7 7 6.8 6.6 ...
##  $ Kitchen              : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Laundromat           : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Temp_control         : num  18 18 19 18 18 19 18 18 19 18 ...

df10$year <- year(df10$DateTime)
df10$month <- month(df10$DateTime, label=TRUE)
df10$week <- week(df10$DateTime)
df10$day <- day(df10$DateTime)
df10$hour <- hour(df10$DateTime)
df10$minute <- minute(df10$DateTime)
df10$quarter <- quarter(df10$DateTime)
df10$weekDay <- wday(df10$DateTime, label=TRUE, week_start=getOption("lubridate.week.start", 1))

# sum sub meters
df10$sumMeters <- df10$Kitchen + df10$Laundromat + df10$Temp_control

# compute total consumption
df10$gapW <- df10$Global_active_power*1000/60

# compute other electricals
df10$otherEE <- df10$gapW - df10$sumMeters

df10_met<-df10%>%
  group_by(year, month)%>%
  summarise(sumKitchen=sum(Kitchen),
            sumLaundromat=sum(Laundromat),
            sumTC=sum(Temp_control),
            sumOEE=sum(otherEE),
            sumAll=sum(gapW))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

df10_met

## # A tibble: 11 × 7
## # Groups:   year [1]
##     year month sumKitchen sumLaundromat  sumTC  sumOEE  sumAll
##    <dbl> <ord>      <dbl>         <dbl>  <dbl>   <dbl>   <dbl>
##  1  2010 Jan        53887         56568 395913 483293. 989661.
##  2  2010 Feb        49268         53590 411714 409956. 924528.
##  3  2010 Mar        35089         60872 324352 382285. 802598.
##  4  2010 Apr        38196         36476 336091 328872. 739635.
##  5  2010 May        48107         52376 364625 349765. 814873.
##  6  2010 Jun        65747         47675 306934 277734. 698090.
##  7  2010 Jul        17667         34359 192912 291525. 536463.
##  8  2010 Aug        12499         26983 160189 168719. 368390.
##  9  2010 Sep        36865         32508 257861 277923. 605157.
## 10  2010 Oct        48199         60220 315669 441461. 865549.
## 11  2010 Nov        46162         42282 247113 407749. 743306.

ts10_Kitchen <- ts(df10_met$sumKitchen, frequency = 11, start=c(2010,1))
ts10_Laundromat <- ts(df10_met$sumLaundromat, frequency = 11, start=c(2010,1))
ts10_TC <- ts(df10_met$sumTC, frequency = 11, start=c(2010,1))
ts10_OEE <- ts(df10_met$sumOEE, frequency = 11, start=c(2010,1))
ts10_all <- ts(df10_met$sumAll, frequency = 11, start=c(2010,1))

Predict the future

trainingK <- ts789_Kitchen
testK <- ts10_Kitchen

fcK <- hw(trainingK, h=11)
autoplot(fcK)+autolayer(testK, series="Test data: Kitchen")

accuracy(fcK,testK)

##                       ME     RMSE       MAE       MPE     MAPE      MASE
## Training set    10.37171 10341.45  8305.971 -13.79947 29.79065 0.6916191
## Test set     -6087.30633 26579.96 22266.747 -57.83856 86.58067 1.8541008
##                    ACF1 Theil's U
## Training set 0.08740131        NA
## Test set     0.01092548  1.481096

summary(fcK)

## 
## Forecast method: Holt-Winters' additive method
## 
## Model Information:
## Holt-Winters' additive method 
## 
## Call:
##  hw(y = trainingK, h = 11) 
## 
##   Smoothing parameters:
##     alpha = 0.0001 
##     beta  = 0.0001 
##     gamma = 0.0001 
## 
##   Initial states:
##     l = 54001.5701 
##     b = -187.0126 
##     s = 1031.819 -5047.28 3193.73 13016.58 9631.69 12388.69
##            -16727.38 18925.23 -5184.269 4158.327 -30663.85 -4723.291
## 
##   sigma:  13874.51
## 
##      AIC     AICc      BIC 
## 828.5686 862.5686 855.4884 
## 
## Error measures:
##                    ME     RMSE      MAE       MPE     MAPE      MASE       ACF1
## Training set 10.37171 10341.45 8305.971 -13.79947 29.79065 0.6916191 0.08740131
## 
## Forecasts:
##          Point Forecast     Lo 80    Hi 80      Lo 95    Hi 95
## Jan 2010       42356.71 24575.817 60137.61  15163.178 69550.25
## Feb 2010       16229.96 -1550.933 34010.86 -10963.572 43423.50
## Mar 2010       50865.16 33084.258 68646.05  23671.619 78058.69
## Apr 2010       41334.23 23553.331 59115.13  14140.691 68527.77
## May 2010       65255.37 47474.470 83036.27  38061.829 92448.91
## Jun 2010       29418.12 11637.215 47199.03   2224.573 56611.67
## Jul 2010       58343.70 40562.794 76124.61  31150.149 85537.26
## Aug 2010       55403.38 37622.464 73184.29  28209.816 82596.94
## Sep 2010       58598.77 40817.852 76379.70  31405.201 85792.35
## Oct 2010       48591.65 30810.718 66372.58  21398.061 75785.24
## Nov 2010       40163.56 22382.622 57944.51  12969.960 67357.17

trainingL <- ts789_Laundromat
testL <- ts10_Laundromat

fcL <- hw(trainingL, h=11)
autoplot(fcL)+autolayer(testL, series="Test data: Laundromat")

accuracy(fcL,testL)

##                    ME     RMSE       MAE       MPE     MAPE      MASE      ACF1
## Training set -102.333 10488.65  8152.085 -3.540696 16.67837 0.4790847 0.2459795
## Test set     9479.141 22907.35 18091.734  9.527445 40.37041 1.0632216 0.3691601
##              Theil's U
## Training set        NA
## Test set      1.429546

summary(fcL)

## 
## Forecast method: Holt-Winters' additive method
## 
## Model Information:
## Holt-Winters' additive method 
## 
## Call:
##  hw(y = trainingL, h = 11) 
## 
##   Smoothing parameters:
##     alpha = 0.0001 
##     beta  = 0.0001 
##     gamma = 0.0001 
## 
##   Initial states:
##     l = 75383.3826 
##     b = -903.0244 
##     s = -602.9715 12743.48 2428.693 1329.752 26907.62 1760.726
##            -11384.39 12241.64 -3134.848 -6587.58 -28648.49 -7053.634
## 
##   sigma:  14072
## 
##      AIC     AICc      BIC 
## 829.5862 863.5862 856.5060 
## 
## Error measures:
##                    ME     RMSE      MAE       MPE     MAPE      MASE      ACF1
## Training set -102.333 10488.65 8152.085 -3.540696 16.67837 0.4790847 0.2459795
## 
## Forecasts:
##          Point Forecast     Lo 80    Hi 80      Lo 95    Hi 95
## Jan 2010       34908.60 16874.601 52942.60   7327.979 62489.22
## Feb 2010       12412.01 -5621.992 30446.01 -15168.614 39992.63
## Mar 2010       33569.66 15535.662 51603.66   5989.040 61150.28
## Apr 2010       36117.85 18083.846 54151.85   8537.223 63698.47
## May 2010       50590.91 32556.912 68624.92  23010.287 78171.54
## Jun 2010       26061.51  8027.501 44095.51  -1519.126 53642.14
## Jul 2010       38301.71 20267.704 56335.72  10721.075 65882.35
## Aug 2010       62544.84 44510.825 80578.86  34964.193 90125.49
## Sep 2010       36066.41 18032.389 54100.44   8485.754 63647.07
## Oct 2010       36262.09 18228.059 54296.12   8681.418 63842.76
## Nov 2010       45672.88 27638.832 63706.92  18092.186 73253.57

trainingTC <- ts789_TC
testTC <- ts10_TC

fcTC <- hw(trainingTC, h=11)
autoplot(fcTC)+autolayer(testTC, series="Test data: Temperature control")

accuracy(fcTC,testTC)

##                     ME      RMSE      MAE        MPE     MAPE      MASE
## Training set -2631.161  31029.56 23925.06  -4.050852 11.70847 0.4811773
## Test set     -4028.034 103129.77 81511.91 -11.251604 31.58864 1.6393558
##                    ACF1 Theil's U
## Training set 0.01681433        NA
## Test set     0.25253908  1.473236

summary(fcTC)

## 
## Forecast method: Holt-Winters' additive method
## 
## Model Information:
## Holt-Winters' additive method 
## 
## Call:
##  hw(y = trainingTC, h = 11) 
## 
##   Smoothing parameters:
##     alpha = 0.0005 
##     beta  = 0.0001 
##     gamma = 0.0001 
## 
##   Initial states:
##     l = 243861.8042 
##     b = 1617.2792 
##     s = -6309.157 5998.606 29127.61 -290.1132 23068.28 -18412.04
##            -69008.79 46779.39 5510.321 76802.22 -107168.9 13902.59
## 
##   sigma:  41630.52
## 
##      AIC     AICc      BIC 
## 907.6808 941.6808 934.6006 
## 
## Error measures:
##                     ME     RMSE      MAE       MPE     MAPE      MASE
## Training set -2631.161 31029.56 23925.06 -4.050852 11.70847 0.4811773
##                    ACF1
## Training set 0.01681433
## 
## Forecasts:
##          Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## Jan 2010       317288.7 263937.1 370640.4 235694.4 398883.1
## Feb 2010       197830.6 144479.0 251182.3 116236.3 279425.0
## Mar 2010       383409.2 330057.5 436760.9 301814.8 465003.6
## Apr 2010       313722.8 260371.1 367074.5 232128.4 395317.1
## May 2010       356601.0 303249.3 409952.8 275006.6 438195.5
## Jun 2010       242414.4 189062.7 295766.2 160820.0 324008.9
## Jul 2010       294620.0 241268.2 347971.8 213025.5 376214.5
## Aug 2010       337710.3 284358.5 391062.2 256115.8 419304.9
## Sep 2010       315959.5 262607.6 369311.4 234364.8 397554.1
## Oct 2010       346983.7 293631.8 400335.7 265389.0 428578.5
## Nov 2010       325463.4 272111.4 378815.4 243868.5 407058.2

trainingOe <- ts789_OEE
testOe <- ts10_OEE

fcOe <- hw(trainingOe, h=11)
autoplot(fcOe)+autolayer(testOe, series="Test data: Other appliances")

accuracy(fcOe,testOe)

##                      ME      RMSE       MAE        MPE     MAPE      MASE
## Training set  -4325.446  39330.59  31813.66  -3.111138  9.82253 0.5802149
## Test set     -44808.030 171227.44 145471.13 -23.221811 48.88759 2.6530903
##                    ACF1 Theil's U
## Training set 0.29015475        NA
## Test set     0.03576891  1.504348

summary(fcOe)

## 
## Forecast method: Holt-Winters' additive method
## 
## Model Information:
## Holt-Winters' additive method 
## 
## Call:
##  hw(y = trainingOe, h = 11) 
## 
##   Smoothing parameters:
##     alpha = 0.0001 
##     beta  = 0.0001 
##     gamma = 0.0001 
## 
##   Initial states:
##     l = 441866.5723 
##     b = -1414.2471 
##     s = -69023.76 39974.06 142206.3 -62656.2 89631.23 -137596
##            -157525.5 210773.4 68147.97 162556.5 -235285.9 -51202.11
## 
##   sigma:  52767.53
## 
##      AIC     AICc      BIC 
## 924.7493 958.7493 951.6691 
## 
## Error measures:
##                     ME     RMSE      MAE       MPE    MAPE      MASE      ACF1
## Training set -4325.446 39330.59 31813.66 -3.111138 9.82253 0.5802149 0.2901547
## 
## Forecasts:
##          Point Forecast    Lo 80    Hi 80     Lo 95    Hi 95
## Jan 2010       338289.1 270664.7 405913.4 234866.60 441711.5
## Feb 2010       152777.6  85153.3 220401.9  49355.15 256200.1
## Mar 2010       549190.1 481565.7 616814.4 445767.59 652612.5
## Apr 2010       453351.3 385727.0 520975.6 349928.81 556773.8
## May 2010       594547.5 526923.2 662171.8 491125.01 697970.0
## Jun 2010       224811.8 157187.4 292436.1 121389.29 328234.3
## Jul 2010       243314.4 175690.1 310938.8 139891.88 346736.9
## Aug 2010       469112.9 401488.5 536737.3 365690.32 572535.4
## Sep 2010       315398.3 247773.9 383022.7 211975.73 418820.9
## Oct 2010       518821.6 451197.2 586446.1 415398.97 622244.3
## Nov 2010       415164.1 347539.7 482788.6 311741.43 518586.9

trainingA <- ts789_all
testA <- ts10_all

fcA <- hw(trainingA, h=11)
autoplot(fcA)+autolayer(testA, series="Test data: Everything")

accuracy(fcA,testA)

##                       ME     RMSE       MAE        MPE      MAPE      MASE
## Training set    690.2251  71966.0  53500.31  -2.210425  9.407374 0.5807776
## Test set     -28823.5231 288684.7 232674.76 -13.585037 36.598130 2.5258225
##                   ACF1 Theil's U
## Training set 0.1984186        NA
## Test set     0.1229548  1.423504

summary(fcA)

## 
## Forecast method: Holt-Winters' additive method
## 
## Model Information:
## Holt-Winters' additive method 
## 
## Call:
##  hw(y = trainingA, h = 11) 
## 
##   Smoothing parameters:
##     alpha = 0.0001 
##     beta  = 0.0001 
##     gamma = 0.0001 
## 
##   Initial states:
##     l = 815113.4406 
##     b = -1311.6344 
##     s = -76788.74 50968.87 175971.8 -48599.95 149238.7 -141858.7
##            -254646.1 288217.4 57157.85 244691 -394851.5 -49500.58
## 
##   sigma:  96552.52
## 
##       AIC      AICc       BIC 
##  968.2510 1002.2510  995.1708 
## 
## Error measures:
##                    ME  RMSE      MAE       MPE     MAPE      MASE      ACF1
## Training set 690.2251 71966 53500.31 -2.210425 9.407374 0.5807776 0.1984186
## 
## Forecasts:
##          Point Forecast    Lo 80     Hi 80    Lo 95     Hi 95
## Jan 2010       717123.3 593386.3  840860.3 527883.8  906362.8
## Feb 2010       370471.7 246734.6  494208.7 181232.2  559711.1
## Mar 2010      1008704.9 884967.8 1132441.9 819465.4 1197944.4
## Apr 2010       819862.6 696125.5  943599.7 630623.1 1009102.1
## May 2010      1049611.8 925874.7 1173348.9 860372.3 1238851.3
## Jun 2010       505428.7 381691.6  629165.7 316189.1  694668.2
## Jul 2010       616906.3 493169.2  740643.4 427666.7  806145.9
## Aug 2010       906701.6 782964.5 1030438.8 717462.0 1095941.3
## Sep 2010       707557.1 583819.8  831294.3 518317.3  896796.8
## Oct 2010       930812.6 807075.3 1054549.9 741572.8 1120052.4
## Nov 2010       804506.3 680768.9  928243.6 615266.3  993746.2

Autoarima

fcArimaK <- auto.arima(trainingK)

forKitchenArima <- forecast(fcArimaK, h=length(testK))

autoplot(forKitchenArima)+autolayer(testK, series="Test data: Kitchen")

accuracy(forKitchenArima,testK)

##                      ME     RMSE       MAE       MPE     MAPE      MASE
## Training set  -417.1997 13366.14  9682.022 -34.91416 49.14496 0.8061997
## Test set     -9409.6426 20295.43 16242.987 -58.97536 69.99768 1.3525162
##                     ACF1 Theil's U
## Training set  0.06349605        NA
## Test set     -0.01046993  1.266538

fcArimaL <- auto.arima(trainingL)

forLaundromatArima <- forecast(fcArimaL, h=length(testL))

autoplot(forLaundromatArima)+autolayer(testL, series="Test data: Laundromat")

accuracy(forLaundromatArima,testL)

##                      ME     RMSE      MAE       MPE     MAPE      MASE
## Training set  -659.0812 14216.38 10297.84 -8.288154 21.24246 0.6051873
## Test set     -1166.2209 11206.85 10099.82 -9.553697 25.28697 0.5935498
##                     ACF1 Theil's U
## Training set -0.02126564        NA
## Test set      0.23195550 0.8530575

fcArimaTC <- auto.arima(trainingTC)

forTCArima <- forecast(fcArimaTC, h=length(testTC))

autoplot(forTCArima)+autolayer(testTC, series="Test data: Temperature control")

accuracy(forTCArima,testTC)

##                     ME      RMSE      MAE        MPE      MAPE      MASE
## Training set -1143.872  29540.11 19216.78  -3.391218  9.628482 0.3864852
## Test set     -1664.921 114786.50 84532.35 -11.239243 32.682680 1.7001025
##                    ACF1 Theil's U
## Training set 0.02449484        NA
## Test set     0.25498464  1.580597

fcArimaOe <- auto.arima(trainingOe)

forOEArima <- forecast(fcArimaOe, h=length(testOe))

autoplot(forOEArima)+autolayer(testOe, series="Test data: Other electronics")

accuracy(forOEArima,testOe)

##                       ME      RMSE       MAE        MPE      MAPE     MASE
## Training set    137.7839  40527.94  24958.83  -1.909886  8.778239 0.455197
## Test set     -32579.6514 167739.75 140015.99 -19.327530 47.150300 2.553600
##                     ACF1 Theil's U
## Training set -0.03533667        NA
## Test set      0.03561466  1.464766

fcArimaAll <- auto.arima(trainingA)

forAllArima <- forecast(fcArimaAll, h=length(testA))

autoplot(forAllArima)+autolayer(testA, series="Test data: Everything")

accuracy(forAllArima,testA)

##                      ME      RMSE       MAE        MPE      MAPE      MASE
## Training set  -6157.267  69375.87  41094.14  -3.559722  8.178051 0.4461012
## Test set     -48874.646 306400.93 245102.24 -16.889687 38.843626 2.6607302
##                    ACF1 Theil's U
## Training set -0.1073350        NA
## Test set      0.1621909  1.546002

#Forecasts:

accHWk <- accuracy(fcK,testK)
accAaK <- accuracy(forKitchenArima,testK)

accHWk <- as.data.frame(accHWk)
accHWk$run <- c("Holt-Winters")
accHWk$tt <- row.names(accHWk)


accAaK <- as.data.frame(accAaK)
accAaK$run <- c("Auto Arima")
accAaK$tt <- row.names(accAaK)


accK <- bind_rows(accAaK, accHWk)

row.names(accK) <- NULL

accK <- accK[,c(ncol(accK),1:(ncol(accK)-1))]
accK <- accK[,c(ncol(accK),1:(ncol(accK)-1))]

accK

##            run           tt          ME     RMSE       MAE       MPE     MAPE
## 1   Auto Arima Training set  -417.19972 13366.14  9682.022 -34.91416 49.14496
## 2   Auto Arima     Test set -9409.64257 20295.43 16242.987 -58.97536 69.99768
## 3 Holt-Winters Training set    10.37171 10341.45  8305.971 -13.79947 29.79065
## 4 Holt-Winters     Test set -6087.30633 26579.96 22266.747 -57.83856 86.58067
##        MASE        ACF1 Theil's U
## 1 0.8061997  0.06349605        NA
## 2 1.3525162 -0.01046993  1.266538
## 3 0.6916191  0.08740131        NA
## 4 1.8541008  0.01092548  1.481096

autoplot(window(ts789_Kitchen, start=2007))+
  autolayer(fcK$mean, series="Holt-Winters")+
  autolayer(forKitchenArima$mean, series="Auto Arima")+
  autolayer(ts10_Kitchen, series="Real values")+
  xlab("Year") + ylab("Kilowatts")+
  ggtitle("2010 Forecast: Kitchen")

autoplot(window(ts789_Laundromat, start=2007))+
  autolayer(fcL$mean, series="Holt-Winters")+
  autolayer(forLaundromatArima$mean, series="Auto Arima")+
  autolayer(ts10_Laundromat, series="Real values")+
  xlab("Year") + ylab("Kilowatts")+
    ggtitle("2010 Forecast: Laundromat")

autoplot(window(ts789_TC, start=2007))+
  autolayer(fcTC$mean, series="Holt-Winters")+
  autolayer(forTCArima$mean, series="Auto Arima")+
  autolayer(ts10_TC, series="Real values")+
  xlab("Year") + ylab("Kilowatts")+
    ggtitle("2010 Forecast: Temp Control")

autoplot(window(ts789_OEE, start=2007))+
  autolayer(fcOe$mean, series="Holt-Winters")+
  autolayer(forOEArima$mean, series="Auto Arima")+
  autolayer(ts10_OEE, series="Real values")+
  xlab("Year") + ylab("Kilowatts")+
    ggtitle("2010 Forecast: Other Apliances")

autoplot(window(ts789_all, start=2007))+
  autolayer(fcA$mean, series="Holt-Winters")+
  autolayer(forAllArima$mean, series="Auto Arima")+
  autolayer(ts10_all, series="Real values")+
  xlab("Year") + ylab("Kilowatts")+
    ggtitle("2010 Forecast: Everything")