Homework 2
Jordan Metz
February 4, 2019
Number 1 A. True. Because if they are not normally distributed then there could be other information that you are missing. B. False. A model with small residuals could indicate that the model is overfit. C. False. There are 4 methods to elavulate error and depending on what you are looking for another method can be a better fit. D. False. If your model doesn’t forecast well then you might wnt to think about using a differnt method. If you just make it more complicated then you might end up overfitting. E. True. Although when you have 2 models that are relatively close then it is better to o with the simpler model.
Number 2
library(fpp)## Warning: package 'fpp' was built under R version 3.4.4## Loading required package: forecast## Warning: package 'forecast' was built under R version 3.4.4## Loading required package: fma## Warning: package 'fma' was built under R version 3.4.4## Loading required package: expsmooth## Warning: package 'expsmooth' was built under R version 3.4.4## Loading required package: lmtest## Warning: package 'lmtest' was built under R version 3.4.4## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.4.4##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: tseries## Warning: package 'tseries' was built under R version 3.4.4autoplot(dowjones)
rwf(dowjones,3, drift=TRUE)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 79 121.3636 120.8129 121.9143 120.5214 122.2059
## 80 121.4973 120.7085 122.2860 120.2910 122.7035
## 81 121.6309 120.6529 122.6089 120.1352 123.1266autoplot(dowjones)+
autolayer(rwf(dowjones,4, drift=TRUE), series = "Drift", PI = FALSE)+
autolayer(snaive(dowjones,4), series = "Seasonal Naive", PI = FALSE)+
autolayer(meanf(dowjones,4), series = "Mean", PI = FALSE)+
autolayer(naive(dowjones,4), series = "Naive", PI = FALSE)
Drift is the best option for this data. The mean is not a good forecast for this because of the wide range of data. Seasonal and naive are the same in this one for there is not much seasonality therefore creating a a flat forecast.
Number 3
autoplot(ibmclose)
train <- subset(ibmclose, end = 300)
test <- subset(ibmclose, start = 301)
autoplot(train)
autoplot(test)
ibm1 <- naive(train, 69)
ibm2 <- snaive(train, 69)
ibm3 <- meanf(train, 69)
ibm4 <- rwf(train, 69, drift = TRUE)
accuracy(ibm1, test)## ME RMSE MAE MPE MAPE MASE
## Training set -0.2809365 7.302815 5.09699 -0.08262872 1.115844 1.000000
## Test set -3.7246377 20.248099 17.02899 -1.29391743 4.668186 3.340989
## ACF1 Theil's U
## Training set 0.1351052 NA
## Test set 0.9314689 2.973486accuracy(ibm2, test)## ME RMSE MAE MPE MAPE MASE
## Training set -0.2809365 7.302815 5.09699 -0.08262872 1.115844 1.000000
## Test set -3.7246377 20.248099 17.02899 -1.29391743 4.668186 3.340989
## ACF1 Theil's U
## Training set 0.1351052 NA
## Test set 0.9314689 2.973486accuracy(ibm3, test)## ME RMSE MAE MPE MAPE
## Training set 1.660438e-14 73.61532 58.72231 -2.642058 13.03019
## Test set -1.306180e+02 132.12557 130.61797 -35.478819 35.47882
## MASE ACF1 Theil's U
## Training set 11.52098 0.9895779 NA
## Test set 25.62649 0.9314689 19.05515accuracy(ibm4, test)## ME RMSE MAE MPE MAPE
## Training set 2.870480e-14 7.297409 5.127996 -0.02530123 1.121650
## Test set 6.108138e+00 17.066963 13.974747 1.41920066 3.707888
## MASE ACF1 Theil's U
## Training set 1.006083 0.1351052 NA
## Test set 2.741765 0.9045875 2.361092checkresiduals(ibm4)
##
## Ljung-Box test
##
## data: Residuals from Random walk with drift
## Q* = 22.555, df = 9, p-value = 0.007278
##
## Model df: 1. Total lags used: 10Drift looks to be the best fit forecast for this data set. The residuals look to be close to white noise with little skew to the left. There appears to be correlation accoring to the acf.
Number 4
autoplot(hsales)
help("hsales")## starting httpd help server ... donetrain <- subset(hsales, end = length(hsales) - (12*2))
test <- subset(hsales, start = length(hsales) - (12*2) + 1)
autoplot(train)
autoplot(test)
sales1 <- naive(train, 24)
sales2 <- snaive(train, 24)
sales3 <- meanf(train, 24)
sales4 <- rwf(train, 24, drift = TRUE)
accuracy(sales1, test)## ME RMSE MAE MPE MAPE MASE
## Training set -0.008000 6.301111 5.000000 -0.767457 9.903991 0.5892505
## Test set 2.791667 8.628924 7.208333 2.858639 12.849194 0.8495028
## ACF1 Theil's U
## Training set 0.1824472 NA
## Test set 0.5377994 1.098358accuracy(sales2, test)## ME RMSE MAE MPE MAPE MASE
## Training set 0.1004184 10.582214 8.485356 -2.184269 17.633696 1.0000000
## Test set 1.0416667 5.905506 4.791667 0.972025 8.545729 0.5646984
## ACF1 Theil's U
## Training set 0.8369786 NA
## Test set 0.1687797 0.7091534accuracy(sales3, test)## ME RMSE MAE MPE MAPE MASE
## Training set 3.510503e-15 12.162811 9.532738 -6.144876 20.38306 1.1234341
## Test set 3.839475e+00 9.022555 7.561587 4.779122 13.26183 0.8911338
## ACF1 Theil's U
## Training set 0.8661998 NA
## Test set 0.5377994 1.131713accuracy(sales4, test)## ME RMSE MAE MPE MAPE MASE
## Training set 1.506410e-15 6.301106 4.999872 -0.7511048 9.903063 0.5892354
## Test set 2.891667e+00 8.658795 7.249000 3.0426108 12.901697 0.8542954
## ACF1 Theil's U
## Training set 0.1824472 NA
## Test set 0.5378711 1.100276checkresiduals(sales2)
##
## Ljung-Box test
##
## data: Residuals from Seasonal naive method
## Q* = 682.2, df = 24, p-value < 2.2e-16
##
## Model df: 0. Total lags used: 24Seasonal naive looks to be the best fit forecast for this data set. The residuals look to be noise but the acf and histogram tell us that they are not noise. It looks to be normal with a slight skew to the left.
Number 5
checkresiduals(snaive(WWWusage))
##
## Ljung-Box test
##
## data: Residuals from Seasonal naive method
## Q* = 145.58, df = 10, p-value < 2.2e-16
##
## Model df: 0. Total lags used: 10checkresiduals(snaive(bricksq))
##
## Ljung-Box test
##
## data: Residuals from Seasonal naive method
## Q* = 233.2, df = 8, p-value < 2.2e-16
##
## Model df: 0. Total lags used: 8Both residual graphs appear to be nosie at first glance, but the acf graph tells us they are not. The WWWusage data has a normal distrubution for the residuals. The bricksq data is skewed to the left for the residuals.
Number 6
library(fpp)
autoplot(dole)
dole1 <- cbind(Monthly = dole,
DailyAverage = dole/monthdays(dole))
autoplot(dole1, facet = TRUE)
For the dole data set, I did a calendar adjustment to smooth out the graph from daily to monthly observations.
autoplot(usgdp)
cpi <- read.csv("CPIAUCNS.csv")
cpi$DATE <- as.Date(cpi$DATE, format = "%m/%d/%Y")
start <- as.POSIXct("1947-01-01")
end <- as.POSIXct("2006-01-01")
cpi <- cpi[as.POSIXct(cpi$DATE) >= start & as.POSIXct(cpi$DATE) <= end,]
x <- seq(1,length(cpi[,1]) - 1,3)
cpi_q <- seq(1,length(cpi[,1]) - 1,3)
x## [1] 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
## [18] 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100
## [35] 103 106 109 112 115 118 121 124 127 130 133 136 139 142 145 148 151
## [52] 154 157 160 163 166 169 172 175 178 181 184 187 190 193 196 199 202
## [69] 205 208 211 214 217 220 223 226 229 232 235 238 241 244 247 250 253
## [86] 256 259 262 265 268 271 274 277 280 283 286 289 292 295 298 301 304
## [103] 307 310 313 316 319 322 325 328 331 334 337 340 343 346 349 352 355
## [120] 358 361 364 367 370 373 376 379 382 385 388 391 394 397 400 403 406
## [137] 409 412 415 418 421 424 427 430 433 436 439 442 445 448 451 454 457
## [154] 460 463 466 469 472 475 478 481 484 487 490 493 496 499 502 505 508
## [171] 511 514 517 520 523 526 529 532 535 538 541 544 547 550 553 556 559
## [188] 562 565 568 571 574 577 580 583 586 589 592 595 598 601 604 607 610
## [205] 613 616 619 622 625 628 631 634 637 640 643 646 649 652 655 658 661
## [222] 664 667 670 673 676 679 682 685 688 691 694 697 700 703 706num <- 1
for (i in x){
print(cpi[i,2])
cpi_avg <- (cpi[i,2] + cpi[i + 1,2] + cpi[i + 2,2])/3
cpi_q[num] <- cpi_avg
num <- num + 1
}## [1] 21.5
## [1] 21.9
## [1] 22.5
## [1] 23.1
## [1] 23.5
## [1] 23.9
## [1] 24.5
## [1] 24.2
## [1] 23.8
## [1] 23.8
## [1] 23.8
## [1] 23.8
## [1] 23.5
## [1] 23.7
## [1] 24.3
## [1] 24.7
## [1] 25.7
## [1] 25.9
## [1] 25.9
## [1] 26.4
## [1] 26.3
## [1] 26.4
## [1] 26.7
## [1] 26.7
## [1] 26.5
## [1] 26.7
## [1] 26.9
## [1] 26.9
## [1] 26.9
## [1] 26.9
## [1] 26.9
## [1] 26.8
## [1] 26.7
## [1] 26.7
## [1] 26.8
## [1] 26.9
## [1] 26.8
## [1] 27
## [1] 27.3
## [1] 27.5
## [1] 27.7
## [1] 28
## [1] 28.3
## [1] 28.4
## [1] 28.6
## [1] 28.9
## [1] 28.9
## [1] 29
## [1] 28.9
## [1] 29
## [1] 29.2
## [1] 29.4
## [1] 29.4
## [1] 29.5
## [1] 29.6
## [1] 29.8
## [1] 29.8
## [1] 29.8
## [1] 29.9
## [1] 30
## [1] 30.1
## [1] 30.2
## [1] 30.3
## [1] 30.4
## [1] 30.4
## [1] 30.5
## [1] 30.7
## [1] 30.8
## [1] 30.9
## [1] 30.9
## [1] 31
## [1] 31.2
## [1] 31.2
## [1] 31.4
## [1] 31.6
## [1] 31.7
## [1] 32
## [1] 32.3
## [1] 32.7
## [1] 32.9
## [1] 32.9
## [1] 33.2
## [1] 33.5
## [1] 33.8
## [1] 34.2
## [1] 34.5
## [1] 35
## [1] 35.4
## [1] 35.8
## [1] 36.4
## [1] 37
## [1] 37.5
## [1] 38
## [1] 38.6
## [1] 39
## [1] 39.6
## [1] 39.9
## [1] 40.3
## [1] 40.8
## [1] 40.9
## [1] 41.3
## [1] 41.6
## [1] 42
## [1] 42.4
## [1] 42.9
## [1] 43.9
## [1] 45.1
## [1] 45.9
## [1] 47.2
## [1] 48.6
## [1] 50
## [1] 51.5
## [1] 52.5
## [1] 53.2
## [1] 54.3
## [1] 55.3
## [1] 55.8
## [1] 56.5
## [1] 57.4
## [1] 58
## [1] 59.1
## [1] 60.3
## [1] 61.2
## [1] 61.9
## [1] 62.9
## [1] 64.5
## [1] 66
## [1] 67.4
## [1] 69.1
## [1] 71.5
## [1] 73.8
## [1] 75.9
## [1] 78.9
## [1] 81.8
## [1] 83.3
## [1] 85.5
## [1] 87.9
## [1] 89.8
## [1] 92.3
## [1] 93.7
## [1] 94.6
## [1] 95.8
## [1] 97.7
## [1] 98
## [1] 97.9
## [1] 99.2
## [1] 100.2
## [1] 101.2
## [1] 102.4
## [1] 103.4
## [1] 104.5
## [1] 105.3
## [1] 106
## [1] 107.3
## [1] 108
## [1] 109
## [1] 109.3
## [1] 108.9
## [1] 109.7
## [1] 110.4
## [1] 111.6
## [1] 113.1
## [1] 114.4
## [1] 115.4
## [1] 116
## [1] 117.5
## [1] 119
## [1] 120.3
## [1] 121.6
## [1] 123.8
## [1] 124.6
## [1] 125.9
## [1] 128
## [1] 129.2
## [1] 131.6
## [1] 133.8
## [1] 134.8
## [1] 135.6
## [1] 136.6
## [1] 137.8
## [1] 138.6
## [1] 139.7
## [1] 140.9
## [1] 142
## [1] 143.1
## [1] 144.2
## [1] 144.8
## [1] 145.8
## [1] 146.7
## [1] 147.5
## [1] 149
## [1] 149.7
## [1] 150.9
## [1] 152.2
## [1] 152.9
## [1] 153.6
## [1] 154.9
## [1] 156.6
## [1] 157.3
## [1] 158.6
## [1] 159.6
## [1] 160.1
## [1] 160.8
## [1] 161.5
## [1] 161.9
## [1] 162.8
## [1] 163.4
## [1] 164
## [1] 164.5
## [1] 166.2
## [1] 167.1
## [1] 168.3
## [1] 169.8
## [1] 171.5
## [1] 172.8
## [1] 174.1
## [1] 175.8
## [1] 177.7
## [1] 177.5
## [1] 177.4
## [1] 177.8
## [1] 179.8
## [1] 180.7
## [1] 181.3
## [1] 183.1
## [1] 183.5
## [1] 184.6
## [1] 184.5
## [1] 186.2
## [1] 189.1
## [1] 189.5
## [1] 191
## [1] 191.8
## [1] 194.4
## [1] 196.4
## [1] 197.6cpi_q## [1] 21.76667 22.03333 22.83333 23.40000 23.56667 24.13333 24.46667
## [8] 24.10000 23.83333 23.80000 23.80000 23.63333 23.56667 23.86667
## [15] 24.43333 25.03333 25.76667 25.90000 26.06667 26.46667 26.33333
## [22] 26.53333 26.70000 26.66667 26.56667 26.76667 26.93333 26.90000
## [29] 26.86667 26.90000 26.83333 26.73333 26.70000 26.73333 26.86667
## [36] 26.83333 26.83333 27.20000 27.40000 27.56667 27.80000 28.13333
## [43] 28.30000 28.46667 28.76667 28.93333 28.90000 28.96667 28.93333
## [50] 29.10000 29.30000 29.36667 29.43333 29.56667 29.66667 29.80000
## [57] 29.80000 29.86667 29.96667 30.00000 30.13333 30.23333 30.36667
## [64] 30.40000 30.46667 30.60000 30.73333 30.86667 30.90000 31.00000
## [71] 31.06667 31.20000 31.30000 31.53333 31.63333 31.76667 32.13333
## [78] 32.40000 32.76667 32.90000 33.00000 33.30000 33.60000 33.93333
## [85] 34.30000 34.70000 35.13333 35.50000 36.06667 36.60000 37.13333
## [92] 37.66667 38.23333 38.80000 39.20000 39.73333 40.00000 40.53333
## [99] 40.83333 41.03333 41.40000 41.73333 42.13333 42.50000 43.26667
## [106] 44.13333 45.30000 46.23333 47.66667 49.00000 50.56667 51.83333
## [113] 52.70000 53.66667 54.60000 55.46667 55.93333 56.80000 57.63333
## [120] 58.23333 59.53333 60.66667 61.40000 62.16667 63.40000 65.13333
## [127] 66.53333 67.80000 69.83333 72.30000 74.53333 76.80000 80.00000
## [134] 82.40000 84.03333 86.26667 88.50000 90.66667 92.96667 94.00000
## [141] 94.66667 96.76667 97.93333 97.80000 98.13333 99.53333 100.63333
## [148] 101.46667 102.70000 103.73333 104.93333 105.36667 106.43333 107.56667
## [155] 108.33333 109.30000 108.90000 109.30000 110.06667 110.70000 112.13333
## [162] 113.46667 114.90000 115.50000 116.53333 118.00000 119.66667 120.63333
## [169] 122.33333 124.10000 125.06667 126.46667 128.53333 129.83333 132.60000
## [176] 134.06667 135.00000 135.93333 137.06667 137.93333 139.13333 140.13333
## [183] 141.33333 142.16667 143.56667 144.33333 145.20000 145.93333 147.10000
## [190] 147.96667 149.30000 149.90000 151.40000 152.40000 153.26667 153.83333
## [197] 155.63333 156.76667 157.80000 158.76667 159.93333 160.30000 161.20000
## [204] 161.46667 162.20000 163.00000 163.66667 164.06667 165.23333 166.36667
## [211] 167.73333 168.46667 170.76667 172.23333 173.50000 174.40000 176.30000
## [218] 177.73333 177.83333 177.06667 178.80000 179.93333 181.00000 181.30000
## [225] 183.70000 183.70000 184.93333 184.66667 187.20000 189.40000 190.10000
## [232] 190.66667 193.23333 194.76667 198.13333 197.56667cpi[,2]## [1] 21.5 21.9 21.9 21.9 22.0 22.2 22.5 23.0 23.0 23.1 23.4
## [12] 23.7 23.5 23.4 23.8 23.9 24.1 24.4 24.5 24.5 24.4 24.2
## [23] 24.1 24.0 23.8 23.8 23.9 23.8 23.9 23.7 23.8 23.9 23.7
## [34] 23.8 23.6 23.5 23.5 23.6 23.6 23.7 23.8 24.1 24.3 24.4
## [45] 24.6 24.7 25.0 25.4 25.7 25.8 25.8 25.9 25.9 25.9 25.9
## [56] 26.1 26.2 26.4 26.5 26.5 26.3 26.3 26.4 26.4 26.5 26.7
## [67] 26.7 26.7 26.7 26.7 26.7 26.6 26.5 26.6 26.6 26.7 26.8
## [78] 26.8 26.9 26.9 27.0 26.9 26.9 26.9 26.9 26.9 26.8 26.9
## [89] 26.9 26.9 26.9 26.8 26.8 26.8 26.7 26.7 26.7 26.7 26.7
## [100] 26.7 26.7 26.8 26.8 26.9 26.9 26.9 26.8 26.8 26.8 26.8
## [111] 26.9 27.0 27.2 27.4 27.3 27.4 27.5 27.5 27.6 27.6 27.7
## [122] 27.8 27.9 28.0 28.1 28.3 28.3 28.3 28.3 28.4 28.4 28.6
## [133] 28.6 28.8 28.9 28.9 28.9 29.0 28.9 28.9 28.9 29.0 28.9
## [144] 29.0 28.9 28.9 29.0 29.0 29.1 29.2 29.2 29.3 29.4 29.4
## [155] 29.4 29.3 29.4 29.4 29.5 29.5 29.6 29.6 29.6 29.6 29.8
## [166] 29.8 29.8 29.8 29.8 29.8 29.8 29.8 29.8 30.0 29.9 30.0
## [177] 30.0 30.0 30.0 30.0 30.1 30.1 30.2 30.2 30.2 30.3 30.3
## [188] 30.4 30.4 30.4 30.4 30.4 30.4 30.5 30.5 30.5 30.6 30.7
## [199] 30.7 30.7 30.8 30.8 30.9 30.9 30.9 30.9 30.9 30.9 31.0
## [210] 31.1 31.0 31.1 31.1 31.2 31.2 31.2 31.2 31.3 31.4 31.4
## [221] 31.6 31.6 31.6 31.6 31.7 31.7 31.8 31.8 32.0 32.1 32.3
## [232] 32.3 32.4 32.5 32.7 32.7 32.9 32.9 32.9 32.9 32.9 33.0
## [243] 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9 34.1 34.2
## [254] 34.3 34.4 34.5 34.7 34.9 35.0 35.1 35.3 35.4 35.5 35.6
## [265] 35.8 36.1 36.3 36.4 36.6 36.8 37.0 37.1 37.3 37.5 37.7
## [276] 37.8 38.0 38.2 38.5 38.6 38.8 39.0 39.0 39.2 39.4 39.6
## [287] 39.8 39.8 39.9 40.0 40.1 40.3 40.6 40.7 40.8 40.8 40.9
## [298] 40.9 41.1 41.1 41.3 41.4 41.5 41.6 41.7 41.9 42.0 42.1
## [309] 42.3 42.4 42.5 42.6 42.9 43.3 43.6 43.9 44.2 44.3 45.1
## [320] 45.2 45.6 45.9 46.2 46.6 47.2 47.8 48.0 48.6 49.0 49.4
## [331] 50.0 50.6 51.1 51.5 51.9 52.1 52.5 52.7 52.9 53.2 53.6
## [342] 54.2 54.3 54.6 54.9 55.3 55.5 55.6 55.8 55.9 56.1 56.5
## [353] 56.8 57.1 57.4 57.6 57.9 58.0 58.2 58.5 59.1 59.5 60.0
## [364] 60.3 60.7 61.0 61.2 61.4 61.6 61.9 62.1 62.5 62.9 63.4
## [375] 63.9 64.5 65.2 65.7 66.0 66.5 67.1 67.4 67.7 68.3 69.1
## [386] 69.8 70.6 71.5 72.3 73.1 73.8 74.6 75.2 75.9 76.7 77.8
## [397] 78.9 80.1 81.0 81.8 82.7 82.7 83.3 84.0 84.8 85.5 86.3
## [408] 87.0 87.9 88.5 89.1 89.8 90.6 91.6 92.3 93.2 93.4 93.7
## [419] 94.0 94.3 94.6 94.5 94.9 95.8 97.0 97.5 97.7 97.9 98.2
## [430] 98.0 97.6 97.8 97.9 97.9 98.6 99.2 99.5 99.9 100.2 100.7
## [441] 101.0 101.2 101.3 101.9 102.4 102.6 103.1 103.4 103.7 104.1 104.5
## [452] 105.0 105.3 105.3 105.3 105.5 106.0 106.4 106.9 107.3 107.6 107.8
## [463] 108.0 108.3 108.7 109.0 109.3 109.6 109.3 108.8 108.6 108.9 109.5
## [474] 109.5 109.7 110.2 110.3 110.4 110.5 111.2 111.6 112.1 112.7 113.1
## [485] 113.5 113.8 114.4 115.0 115.3 115.4 115.4 115.7 116.0 116.5 117.1
## [496] 117.5 118.0 118.5 119.0 119.8 120.2 120.3 120.5 121.1 121.6 122.3
## [507] 123.1 123.8 124.1 124.4 124.6 125.0 125.6 125.9 126.1 127.4 128.0
## [518] 128.7 128.9 129.2 129.9 130.4 131.6 132.7 133.5 133.8 133.8 134.6
## [529] 134.8 135.0 135.2 135.6 136.0 136.2 136.6 137.2 137.4 137.8 137.9
## [540] 138.1 138.6 139.3 139.5 139.7 140.2 140.5 140.9 141.3 141.8 142.0
## [551] 141.9 142.6 143.1 143.6 144.0 144.2 144.4 144.4 144.8 145.1 145.7
## [562] 145.8 145.8 146.2 146.7 147.2 147.4 147.5 148.0 148.4 149.0 149.4
## [573] 149.5 149.7 149.7 150.3 150.9 151.4 151.9 152.2 152.5 152.5 152.9
## [584] 153.2 153.7 153.6 153.5 154.4 154.9 155.7 156.3 156.6 156.7 157.0
## [595] 157.3 157.8 158.3 158.6 158.6 159.1 159.6 160.0 160.2 160.1 160.3
## [606] 160.5 160.8 161.2 161.6 161.5 161.3 161.6 161.9 162.2 162.5 162.8
## [617] 163.0 163.2 163.4 163.6 164.0 164.0 163.9 164.3 164.5 165.0 166.2
## [628] 166.2 166.2 166.7 167.1 167.9 168.2 168.3 168.3 168.8 169.8 171.2
## [639] 171.3 171.5 172.4 172.8 172.8 173.7 174.0 174.1 174.0 175.1 175.8
## [650] 176.2 176.9 177.7 178.0 177.5 177.5 178.3 177.7 177.4 176.7 177.1
## [661] 177.8 178.8 179.8 179.8 179.9 180.1 180.7 181.0 181.3 181.3 180.9
## [672] 181.7 183.1 184.2 183.8 183.5 183.7 183.9 184.6 185.2 185.0 184.5
## [683] 184.3 185.2 186.2 187.4 188.0 189.1 189.7 189.4 189.5 189.9 190.9
## [694] 191.0 190.3 190.7 191.8 193.3 194.6 194.4 194.5 195.4 196.4 198.8
## [705] 199.2 197.6 196.8 198.3cpi_q[length(cpi_q) + 1] <- cpi[length(cpi[,2]),2]
help(usgdp)
usgdp1 <- cbind(Nominal = usgdp,
Inflation_Adjusted = usgdp/cpi_q)
autoplot(usgdp1, facet = TRUE)
For the usgdp data set, I found a data set of comsumer price index taken on the first day of the month every month from 1913-2018, then applied it to the graph to adjust for inflation.
autoplot(bricksq)
lambda2 <- BoxCox.lambda(bricksq)
autoplot(BoxCox(bricksq, lambda2))
For the bricksq data set, I applied a box cox transformation.
autoplot(enplanements)
help(enplanements)
enp1 <- cbind(Monthly = enplanements,
DailyAverage = enplanements/monthdays(enplanements))
autoplot(enp1, facet = TRUE)
For the enplanements data, set I did a calendar adjustment to smooth out the graph from daily to monthly observations just as was done to the dole data set.