Question

We will be analyzing the built-in R dataset: ‘AirPassengers'. Carefully read through all the R code and associated output below. library(forecast) ## Registered s3 method overwritten by 'quantmod': ## method from ## as.zoo.data.frame zoo library(ggplot2) We first look at the time series data: ##AirPassengers time series 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 Then we plot the time series and compute a 6-number summary of the data: autoplot(AirPassengers)

Answer 1

summary(AirPassengers) ## ## Min. 1st Qu. Median 104.0 180.0 265.5 Mean 3rd Qu. 280.3 360.5 Мах. 622.0

Median=265.5

diff(AirPassengers, lag 12)

Air passengers data is differenced at lag 12

0.2 - 0.1- 0.0. -0.1 - -0.2- 0.3 -

We see that only the first lag is significant. Hence only 1 lag 1 differences are suggested.