library(forecast)
data("AirPassengers")
AirPassengers
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1949 112 118 132 129 121 135 148 148 136 119 104 118
## 1950 115 126 141 135 125 149 170 170 158 133 114 140
## 1951 145 150 178 163 172 178 199 199 184 162 146 166
## 1952 171 180 193 181 183 218 230 242 209 191 172 194
## 1953 196 196 236 235 229 243 264 272 237 211 180 201
## 1954 204 188 235 227 234 264 302 293 259 229 203 229
## 1955 242 233 267 269 270 315 364 347 312 274 237 278
## 1956 284 277 317 313 318 374 413 405 355 306 271 306
## 1957 315 301 356 348 355 422 465 467 404 347 305 336
## 1958 340 318 362 348 363 435 491 505 404 359 310 337
## 1959 360 342 406 396 420 472 548 559 463 407 362 405
## 1960 417 391 419 461 472 535 622 606 508 461 390 432
forecast(AirPassengers,12)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 1961 441.7479 420.9284 462.5675 409.9071 473.5887
## Feb 1961 433.0931 407.5924 458.5938 394.0931 472.0931
## Mar 1961 496.6067 462.3205 530.8930 444.1705 549.0430
## Apr 1961 483.5263 445.6985 521.3541 425.6737 541.3790
## May 1961 485.1026 443.0128 527.1925 420.7317 549.4735
## Jun 1961 551.1085 498.8558 603.3612 471.1949 631.0221
## Jul 1961 613.3810 550.5136 676.2484 517.2336 709.5284
## Aug 1961 610.4359 543.3613 677.5105 507.8542 713.0177
## Sep 1961 530.9494 468.8133 593.0855 435.9204 625.9783
## Oct 1961 462.5032 405.1625 519.8439 374.8081 550.1982
## Nov 1961 402.0130 349.4447 454.5813 321.6167 482.4093
## Dec 1961 450.8391 388.8923 512.7858 356.0996 545.5785
forecast(auto.arima(AirPassengers),12)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 1961 446.7582 431.6858 461.8306 423.7070 469.8094
## Feb 1961 420.7582 402.5180 438.9984 392.8622 448.6542
## Mar 1961 448.7582 427.8241 469.6923 416.7423 480.7741
## Apr 1961 490.7582 467.4394 514.0770 455.0952 526.4212
## May 1961 501.7582 476.2770 527.2395 462.7880 540.7284
## Jun 1961 564.7582 537.2842 592.2323 522.7403 606.7761
## Jul 1961 651.7582 622.4264 681.0900 606.8991 696.6173
## Aug 1961 635.7582 604.6796 666.8368 588.2275 683.2889
## Sep 1961 537.7582 505.0258 570.4906 487.6983 587.8181
## Oct 1961 490.7582 456.4516 525.0648 438.2908 543.2256
## Nov 1961 419.7582 383.9466 455.5698 364.9891 474.5273
## Dec 1961 461.7582 424.5023 499.0141 404.7803 518.7361
plot(forecast(AirPassengers,12))
plot(forecast(auto.arima(AirPassengers),12))
summary(forecast(AirPassengers,12))
##
## Forecast method: ETS(M,Ad,M)
##
## Model Information:
## ETS(M,Ad,M)
##
## Call:
## ets(y = object, lambda = lambda, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.7322
## beta = 0.0188
## gamma = 1e-04
## phi = 0.98
##
## Initial states:
## l = 120.9759
## b = 1.8015
## s=0.8929 0.7984 0.9211 1.0604 1.2228 1.2324
## 1.1107 0.9807 0.9807 1.0106 0.8843 0.9051
##
## sigma: 0.0368
##
## AIC AICc BIC
## 1395.092 1400.564 1448.548
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 1.580744 10.66828 7.728085 0.4426031 2.850202 0.2412742
## ACF1
## Training set 0.01639359
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 1961 441.7479 420.9284 462.5675 409.9071 473.5887
## Feb 1961 433.0931 407.5924 458.5938 394.0931 472.0931
## Mar 1961 496.6067 462.3205 530.8930 444.1705 549.0430
## Apr 1961 483.5263 445.6985 521.3541 425.6737 541.3790
## May 1961 485.1026 443.0128 527.1925 420.7317 549.4735
## Jun 1961 551.1085 498.8558 603.3612 471.1949 631.0221
## Jul 1961 613.3810 550.5136 676.2484 517.2336 709.5284
## Aug 1961 610.4359 543.3613 677.5105 507.8542 713.0177
## Sep 1961 530.9494 468.8133 593.0855 435.9204 625.9783
## Oct 1961 462.5032 405.1625 519.8439 374.8081 550.1982
## Nov 1961 402.0130 349.4447 454.5813 321.6167 482.4093
## Dec 1961 450.8391 388.8923 512.7858 356.0996 545.5785
summary(forecast(auto.arima(AirPassengers),12))
##
## Forecast method: ARIMA(0,1,1)(0,1,0)[12]
##
## Model Information:
## Series: AirPassengers
## ARIMA(0,1,1)(0,1,0)[12]
##
## Coefficients:
## ma1
## -0.3184
## s.e. 0.0877
##
## sigma^2 estimated as 138.3: log likelihood=-508.32
## AIC=1020.64 AICc=1020.73 BIC=1026.39
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.2674861 11.17471 8.279565 0.03319468 2.958284 0.2584916
## ACF1
## Training set -0.005541087
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 1961 446.7582 431.6858 461.8306 423.7070 469.8094
## Feb 1961 420.7582 402.5180 438.9984 392.8622 448.6542
## Mar 1961 448.7582 427.8241 469.6923 416.7423 480.7741
## Apr 1961 490.7582 467.4394 514.0770 455.0952 526.4212
## May 1961 501.7582 476.2770 527.2395 462.7880 540.7284
## Jun 1961 564.7582 537.2842 592.2323 522.7403 606.7761
## Jul 1961 651.7582 622.4264 681.0900 606.8991 696.6173
## Aug 1961 635.7582 604.6796 666.8368 588.2275 683.2889
## Sep 1961 537.7582 505.0258 570.4906 487.6983 587.8181
## Oct 1961 490.7582 456.4516 525.0648 438.2908 543.2256
## Nov 1961 419.7582 383.9466 455.5698 364.9891 474.5273
## Dec 1961 461.7582 424.5023 499.0141 404.7803 518.7361
forecast(AirPassengers,12)$mean
## Jan Feb Mar Apr May Jun Jul
## 1961 441.7479 433.0931 496.6067 483.5263 485.1026 551.1085 613.3810
## Aug Sep Oct Nov Dec
## 1961 610.4359 530.9494 462.5032 402.0130 450.8391
forecast(auto.arima(AirPassengers),12)$mean
## Jan Feb Mar Apr May Jun Jul
## 1961 446.7582 420.7582 448.7582 490.7582 501.7582 564.7582 651.7582
## Aug Sep Oct Nov Dec
## 1961 635.7582 537.7582 490.7582 419.7582 461.7582
library(zoo)
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
apdf=data.frame(Y=as.matrix(AirPassengers),
date= as.Date(as.yearmon(time(AirPassengers))))
names(apdf)
## [1] "Y" "date"
apdf[145:156,1]=0
apdf[145:156,2]=
dts=ts(1:12, frequency = 12, start = c(1961, 1))
dts
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1961 1 2 3 4 5 6 7 8 9 10 11 12
as.Date(as.yearmon(time(dts)))
## [1] "1961-01-01" "1961-02-01" "1961-03-01" "1961-04-01" "1961-05-01"
## [6] "1961-06-01" "1961-07-01" "1961-08-01" "1961-09-01" "1961-10-01"
## [11] "1961-11-01" "1961-12-01"
apdf[145:156,2]= as.Date(as.yearmon(time(dts)))
apdf
## Y date
## 1 112 1949-01-01
## 2 118 1949-02-01
## 3 132 1949-03-01
## 4 129 1949-04-01
## 5 121 1949-05-01
## 6 135 1949-06-01
## 7 148 1949-07-01
## 8 148 1949-08-01
## 9 136 1949-09-01
## 10 119 1949-10-01
## 11 104 1949-11-01
## 12 118 1949-12-01
## 13 115 1950-01-01
## 14 126 1950-02-01
## 15 141 1950-03-01
## 16 135 1950-04-01
## 17 125 1950-05-01
## 18 149 1950-06-01
## 19 170 1950-07-01
## 20 170 1950-08-01
## 21 158 1950-09-01
## 22 133 1950-10-01
## 23 114 1950-11-01
## 24 140 1950-12-01
## 25 145 1951-01-01
## 26 150 1951-02-01
## 27 178 1951-03-01
## 28 163 1951-04-01
## 29 172 1951-05-01
## 30 178 1951-06-01
## 31 199 1951-07-01
## 32 199 1951-08-01
## 33 184 1951-09-01
## 34 162 1951-10-01
## 35 146 1951-11-01
## 36 166 1951-12-01
## 37 171 1952-01-01
## 38 180 1952-02-01
## 39 193 1952-03-01
## 40 181 1952-04-01
## 41 183 1952-05-01
## 42 218 1952-06-01
## 43 230 1952-07-01
## 44 242 1952-08-01
## 45 209 1952-09-01
## 46 191 1952-10-01
## 47 172 1952-11-01
## 48 194 1952-12-01
## 49 196 1953-01-01
## 50 196 1953-02-01
## 51 236 1953-03-01
## 52 235 1953-04-01
## 53 229 1953-05-01
## 54 243 1953-06-01
## 55 264 1953-07-01
## 56 272 1953-08-01
## 57 237 1953-09-01
## 58 211 1953-10-01
## 59 180 1953-11-01
## 60 201 1953-12-01
## 61 204 1954-01-01
## 62 188 1954-02-01
## 63 235 1954-03-01
## 64 227 1954-04-01
## 65 234 1954-05-01
## 66 264 1954-06-01
## 67 302 1954-07-01
## 68 293 1954-08-01
## 69 259 1954-09-01
## 70 229 1954-10-01
## 71 203 1954-11-01
## 72 229 1954-12-01
## 73 242 1955-01-01
## 74 233 1955-02-01
## 75 267 1955-03-01
## 76 269 1955-04-01
## 77 270 1955-05-01
## 78 315 1955-06-01
## 79 364 1955-07-01
## 80 347 1955-08-01
## 81 312 1955-09-01
## 82 274 1955-10-01
## 83 237 1955-11-01
## 84 278 1955-12-01
## 85 284 1956-01-01
## 86 277 1956-02-01
## 87 317 1956-03-01
## 88 313 1956-04-01
## 89 318 1956-05-01
## 90 374 1956-06-01
## 91 413 1956-07-01
## 92 405 1956-08-01
## 93 355 1956-09-01
## 94 306 1956-10-01
## 95 271 1956-11-01
## 96 306 1956-12-01
## 97 315 1957-01-01
## 98 301 1957-02-01
## 99 356 1957-03-01
## 100 348 1957-04-01
## 101 355 1957-05-01
## 102 422 1957-06-01
## 103 465 1957-07-01
## 104 467 1957-08-01
## 105 404 1957-09-01
## 106 347 1957-10-01
## 107 305 1957-11-01
## 108 336 1957-12-01
## 109 340 1958-01-01
## 110 318 1958-02-01
## 111 362 1958-03-01
## 112 348 1958-04-01
## 113 363 1958-05-01
## 114 435 1958-06-01
## 115 491 1958-07-01
## 116 505 1958-08-01
## 117 404 1958-09-01
## 118 359 1958-10-01
## 119 310 1958-11-01
## 120 337 1958-12-01
## 121 360 1959-01-01
## 122 342 1959-02-01
## 123 406 1959-03-01
## 124 396 1959-04-01
## 125 420 1959-05-01
## 126 472 1959-06-01
## 127 548 1959-07-01
## 128 559 1959-08-01
## 129 463 1959-09-01
## 130 407 1959-10-01
## 131 362 1959-11-01
## 132 405 1959-12-01
## 133 417 1960-01-01
## 134 391 1960-02-01
## 135 419 1960-03-01
## 136 461 1960-04-01
## 137 472 1960-05-01
## 138 535 1960-06-01
## 139 622 1960-07-01
## 140 606 1960-08-01
## 141 508 1960-09-01
## 142 461 1960-10-01
## 143 390 1960-11-01
## 144 432 1960-12-01
## 145 0 1961-01-01
## 146 0 1961-02-01
## 147 0 1961-03-01
## 148 0 1961-04-01
## 149 0 1961-05-01
## 150 0 1961-06-01
## 151 0 1961-07-01
## 152 0 1961-08-01
## 153 0 1961-09-01
## 154 0 1961-10-01
## 155 0 1961-11-01
## 156 0 1961-12-01
apdf$Y1=apdf$Y
apdf[145:156,1]=forecast(AirPassengers,12)$mean
apdf[145:156,3]=forecast(auto.arima(AirPassengers),12)$mean
library(ggplot2)
names(apdf)
## [1] "Y" "date" "Y1"
ggplot(apdf, aes(date)) +
geom_line(aes(y=Y, colour = "Y"))+
geom_line(aes(y=Y1, colour = "Y1"))
