/* Table A.9: Average Daily Calls to Directory Assistance, Cincinnati, Ohio in Hundreds of Calls as reported in Applied Time Series and Box-Jenkins Models by Walter Vandaele, Academic Press, Orlando, Fla., 1983, p. 355. Original source: McCleary, R., and R.A. Hay, Jr. (1980). Applied Time Series Analysis for the Social Sciences. Beverly Hill, CA: Sage Publications, 316. Vandaele analyzes this data in Section 14.3 of his book, pp. 343 - 347. */ data calls; format date monyy5.; input date:monyy5. calls @@; cards; jan62 350 feb62 339 mar62 351 apr62 364 may62 369 jun62 331 jul62 331 aug62 340 sep62 346 oct62 341 nov62 357 dec62 398 jan63 381 feb63 367 mar63 383 apr63 375 may63 353 jun63 361 jul63 375 aug63 371 sep63 373 oct63 366 nov63 382 dec63 429 jan64 406 feb64 403 mar64 429 apr64 425 may64 427 jun64 409 jul64 402 aug64 409 sep64 419 oct64 404 nov64 429 dec64 463 jan65 428 feb65 449 mar65 444 apr65 467 may65 474 jun65 463 jul65 432 aug65 453 sep65 462 oct65 456 nov65 474 dec65 514 jan66 489 feb66 475 mar66 492 apr66 525 may66 527 jun66 533 jul66 527 aug66 522 sep66 526 oct66 513 nov66 564 dec66 599 jan67 572 feb67 587 mar67 599 apr67 601 may67 611 jun67 620 jul67 579 aug67 582 sep67 592 oct67 581 nov67 630 dec67 663 jan68 638 feb68 631 mar68 645 apr68 682 may68 601 jun68 595 jul68 521 aug68 521 sep68 516 oct68 496 nov68 538 dec68 575 jan69 537 feb69 534 mar69 542 apr69 538 may69 547 jun69 540 jul69 526 aug69 548 sep69 555 oct69 545 nov69 594 dec69 643 jan70 625 feb70 616 mar70 640 apr70 625 may70 637 jun70 634 jul70 621 aug70 641 sep70 654 oct70 649 nov70 662 dec70 699 jan71 672 feb71 704 mar71 700 apr71 711 may71 715 jun71 718 jul71 652 aug71 664 sep71 695 oct71 704 nov71 733 dec71 772 jan72 716 feb72 712 mar72 732 apr72 755 may72 761 jun72 748 jul72 748 aug72 750 sep72 744 oct72 731 nov72 782 dec72 810 jan73 777 feb73 816 mar73 840 apr73 868 may73 872 jun73 811 jul73 810 aug73 762 sep73 634 oct73 626 nov73 649 dec73 697 jan74 657 feb74 549 mar74 162 apr74 177 may74 175 jun74 162 jul74 161 aug74 165 sep74 170 oct74 172 nov74 178 dec74 186 jan75 178 feb75 178 mar75 189 apr75 205 may75 202 jun75 185 jul75 193 aug75 200 sep75 196 oct75 204 nov75 206 dec75 227 jan76 225 feb76 217 mar76 219 apr76 236 may76 253 jun76 213 jul76 205 aug76 210 sep76 216 oct76 218 nov76 235 dec76 241 ; run; data calls; set calls; calls1 = calls - lag1(calls); calls112 = calls1 - lag12(calls1); pulse = (_n_ = 144); run; /* Use the first 144 bservations to get the systematic dynamic for the data. Seasonality seems to be present in the data. */ proc arima data= calls(obs=144); identify var = calls nlag = 24; identify var = calls(1) nlag = 24; identify var = calls(12) nlag = 24; identify var = calls(1,12) nlag = 24; estimate q = (12); estimate q = (1)(12); estimate p = (12) q = (12); run; /* The pre-intervention systematic dynamics seems to be modeled well by q = (12) model. */ /* Model the intervention at obs = 144 as a temporary intervention (i.e. use a pulse dummy). */ proc arima data = calls; identify var = pulse noprint; identify var = calls(1,12) crosscorr = (pulse) noprint; estimate q = (12) input = ((1)/(1,2)pulse) method=ml; estimate input = ((1)/(1,2)pulse) method=ml; estimate input = (/(1,2)pulse) method=ml; estimate q = (12) input = (/(1,2)pulse) method=ml; /* This last model is almost it but residuals are still not white noise. Let's see if we can get white noise errors by modeling the autocorrelation. */ estimate q = (1)(12) input = (/(1,2)pulse) method=ml; estimate p = 1 q = (12) input = (/(1,2)pulse) method=ml; estimate p = (1)(12) q = (12) input = (/(1,2)pulse) method=ml; /* These last 3 models provide only a marginally better fit. In the SBC measures are larger. Can't get rid of autocorrelation in the errors so adopt the model q = (12) input = (/(1,2)pulse). */ run; run;