data("AirPassengers")
library(forecast)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: timeDate
## This is forecast 7.3
ts.plot(AirPassengers)
decompose(AirPassengers)
## $x
## 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
##
## $seasonal
## Jan Feb Mar Apr May Jun
## 1949 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1950 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1951 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1952 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1953 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1954 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1955 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1956 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1957 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1958 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1959 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## 1960 -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## Jul Aug Sep Oct Nov Dec
## 1949 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1950 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1951 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1952 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1953 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1954 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1955 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1956 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1957 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1958 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1959 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
## 1960 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
##
## $trend
## Jan Feb Mar Apr May Jun Jul
## 1949 NA NA NA NA NA NA 126.7917
## 1950 131.2500 133.0833 134.9167 136.4167 137.4167 138.7500 140.9167
## 1951 157.1250 159.5417 161.8333 164.1250 166.6667 169.0833 171.2500
## 1952 183.1250 186.2083 189.0417 191.2917 193.5833 195.8333 198.0417
## 1953 215.8333 218.5000 220.9167 222.9167 224.0833 224.7083 225.3333
## 1954 228.0000 230.4583 232.2500 233.9167 235.6250 237.7500 240.5000
## 1955 261.8333 266.6667 271.1250 275.2083 278.5000 281.9583 285.7500
## 1956 309.9583 314.4167 318.6250 321.7500 324.5000 327.0833 329.5417
## 1957 348.2500 353.0000 357.6250 361.3750 364.5000 367.1667 369.4583
## 1958 375.2500 377.9167 379.5000 380.0000 380.7083 380.9583 381.8333
## 1959 402.5417 407.1667 411.8750 416.3333 420.5000 425.5000 430.7083
## 1960 456.3333 461.3750 465.2083 469.3333 472.7500 475.0417 NA
## Aug Sep Oct Nov Dec
## 1949 127.2500 127.9583 128.5833 129.0000 129.7500
## 1950 143.1667 145.7083 148.4167 151.5417 154.7083
## 1951 173.5833 175.4583 176.8333 178.0417 180.1667
## 1952 199.7500 202.2083 206.2500 210.4167 213.3750
## 1953 225.3333 224.9583 224.5833 224.4583 225.5417
## 1954 243.9583 247.1667 250.2500 253.5000 257.1250
## 1955 289.3333 293.2500 297.1667 301.0000 305.4583
## 1956 331.8333 334.4583 337.5417 340.5417 344.0833
## 1957 371.2083 372.1667 372.4167 372.7500 373.6250
## 1958 383.6667 386.5000 390.3333 394.7083 398.6250
## 1959 435.1250 437.7083 440.9583 445.8333 450.6250
## 1960 NA NA NA NA NA
##
## $random
## Jan Feb Mar Apr May
## 1949 NA NA NA NA NA
## 1950 8.4987374 29.1047980 8.3244949 6.6199495 -7.9103535
## 1951 12.6237374 26.6464646 18.4078283 6.9116162 9.8396465
## 1952 12.6237374 29.9797980 6.1994949 -2.2550505 -6.0770202
## 1953 4.9154040 13.6881313 17.3244949 20.1199495 9.4229798
## 1954 0.7487374 -6.2702020 4.9911616 1.1199495 2.8813131
## 1955 4.9154040 2.5214646 -1.8838384 1.8282828 -3.9936869
## 1956 -1.2095960 -1.2285354 0.6161616 -0.7133838 -1.9936869
## 1957 -8.5012626 -15.8118687 0.6161616 -5.3383838 -4.9936869
## 1958 -10.5012626 -23.7285354 -15.2588384 -23.9633838 -13.2020202
## 1959 -17.7929293 -28.9785354 -3.6338384 -12.2967172 4.0063131
## 1960 -14.5845960 -34.1868687 -43.9671717 -0.2967172 3.7563131
## Jun Jul Aug Sep Oct
## 1949 NA -42.6224747 -42.0732323 -8.4785354 11.0593434
## 1950 -25.1527778 -34.7474747 -35.9898990 -4.2285354 5.2260101
## 1951 -26.4861111 -36.0808081 -37.4065657 -7.9785354 5.8093434
## 1952 -13.2361111 -31.8724747 -20.5732323 -9.7285354 5.3926768
## 1953 -17.1111111 -25.1641414 -16.1565657 -4.4785354 7.0593434
## 1954 -9.1527778 -2.3308081 -13.7815657 -4.6868687 -0.6073232
## 1955 -2.3611111 14.4191919 -5.1565657 2.2297980 -2.5239899
## 1956 11.5138889 19.6275253 10.3434343 4.0214646 -10.8989899
## 1957 19.4305556 31.7108586 32.9684343 15.3131313 -4.7739899
## 1958 18.6388889 45.3358586 58.5101010 0.9797980 -10.6906566
## 1959 11.0972222 53.4608586 61.0517677 8.7714646 -13.3156566
## 1960 24.5555556 NA NA NA NA
## Nov Dec
## 1949 28.5934343 16.8699495
## 1950 16.0517677 13.9116162
## 1951 21.5517677 14.4532828
## 1952 15.1767677 9.2449495
## 1953 9.1351010 4.0782828
## 1954 3.0934343 0.4949495
## 1955 -10.4065657 1.1616162
## 1956 -15.9482323 -9.4633838
## 1957 -14.1565657 -9.0050505
## 1958 -31.1148990 -33.0050505
## 1959 -30.2398990 -17.0050505
## 1960 NA NA
##
## $figure
## [1] -24.748737 -36.188131 -2.241162 -8.036616 -4.506313 35.402778
## [7] 63.830808 62.823232 16.520202 -20.642677 -53.593434 -28.619949
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"
plot(decompose(AirPassengers))
b=auto.arima(AirPassengers)
forecast(b,24)
## 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
## Jan 1962 476.5164 431.4567 521.5761 407.6036 545.4292
## Feb 1962 450.5164 400.9938 500.0390 374.7781 526.2547
## Mar 1962 478.5164 424.9010 532.1318 396.5188 560.5141
## Apr 1962 520.5164 463.0993 577.9335 432.7045 608.3283
## May 1962 531.5164 470.5341 592.4987 438.2520 624.7808
## Jun 1962 594.5164 530.1661 658.8667 496.1011 692.9317
## Jul 1962 681.5164 613.9659 749.0670 578.2068 784.8261
## Aug 1962 665.5164 594.9105 736.1223 557.5340 773.4988
## Sep 1962 567.5164 493.9820 641.0508 455.0552 679.9776
## Oct 1962 520.5164 444.1657 596.8671 403.7481 637.2847
## Nov 1962 449.5164 370.4497 528.5831 328.5943 570.4385
## Dec 1962 491.5164 409.8239 573.2089 366.5785 616.4543
plot(forecast(b,24))
