Determining Seasonal Component in an ARIMA Model

[Tom van Oosterhout]

I understand that a SARIMA model has a structure of (p,d,q,s). I know how to get the p, d and q components but am unsure how to get the s component for the model?

This is a dataex of my data:
Code:
* Example generated by -dataex-. To install: ssc install dataex clear input double OverallInflation float n 26.7 1 26.8 2 25.5 3 25.2 4 22.6 5 23.2 6 22.6 7 25.8 8 23.4 9 20.2 10 17.5 11 15.5 12 15.5 13 16.2 14 17.2 15 16.1 16 15.4 17 15.6 18 14.5 19 15.1 20 15.4 21 12.9 22 12 23 11.5 24 9.6 25 9.8 26 10.2 27 9.8 28 9 29 8.5 30 8.7 31 9 32 9.2 33 10.1 34 10.2 35 10.7 36 11.1 37 11.3 38 11.6 39 11.3 40 10.9 41 12.2 42 12.8 43 13.7 44 14 45 14.2 46 14.9 47 15.3 48 15.5 49 15.9 50 15.6 51 15.4 52 15.8 53 15.9 54 16.2 55 16.5 56 16.7 57 17.1 58 16.6 59 16.1 60 15.8 61 15.3 62 14.9 63 12 64 11.6 65 11 66 10.5 67 10.1 68 9.6 69 9.2 70 8.6 71 8.4 72 7.9 73 7.7 74 7.4 75 7.2 76 7.1 77 7.2 78 7.4 79 7.5 80 7.7 81 8 82 8.2 83 8.1 84 7.9 85 8.5 86 8.7 87 9.1 88 9.3 89 9.4 90 9.6 91 9.9 92 10.1 93 9.7 94 9.5 95 9.2 96 8.7 97 8.4 98 8 99 7.8 100 end
Thanks

[Tom van Oosterhout]

* Example generated by -dataex-. To install: ssc install dataex
clear
input int Year str3 Month double(OverallCPI OverallInflation FoodCPI FoodInflation NonFoodCPI NonFoodInflation) float(mdate loginflation n banknote rainfall OverallInflationehat logfoodinflation lognonfoodinflation smooth ehat)
2001 "Jan"   121 26.7 118.1 18.1 122.3 22.3 492  3.284664   1 0 1          .  2.895912 3.1045866      22.3          .
2001 "Feb" 123.8 26.8 121.6 21.6 124.2 24.2 493  3.288402   2 0 1  -3.692002  3.072693  3.186353        24   1.938587
2001 "Mar" 122.3 25.5 118.8 18.1 125.3 25.3 494 3.2386785   3 0 1  -5.060277  2.895912 3.2308044    25.375   1.138587
2001 "Apr" 121.2 25.2 115.4 15.4 126.7 26.7 495  3.226844   4 0 1 -4.1143637 2.7343676  3.284664    26.625   1.438587
2001 "May" 120.6 22.6 113.4 13.4 127.8 27.8 496   3.11795   5 0 0  -6.407156  2.595255  3.325036    27.525   1.138587
2001 "Jun" 116.7 23.2 106.3  6.3 128.1 28.1 497  3.144152   6 0 0 -3.3409245 1.8405496   3.33577      27.8    .338587
2001 "Jul" 117.6 22.6 108.2  8.2 127.5 27.5 498   3.11795   7 0 0  -4.478553  2.104134  3.314186    27.725 -.56141305
2001 "Aug" 117.4 25.8 107.5  7.5 128.2 28.2 499 3.2503746   8 0 0  -.6897338  2.014903  3.339322    27.575    .738587
2001 "Sep" 123.4 23.4 118.4 18.4 127.9 26.9 500  3.152736   9 0 0  -6.067998  2.912351  3.292126     27.35  -1.261413
2001 "Oct" 120.2 20.2 123.3 23.3 126.9 26.9 501  3.005683  10 0 0  -6.989508 3.1484535  3.292126     27.05  .03858696
2001 "Nov" 117.5 17.5 128.5 28.5 128.8 28.8 502  2.862201  11 0 0  -6.660053  3.349904 3.3603754      26.9   1.938587
2001 "Dec" 115.5 15.5 132.4 32.4 129.6 29.6 503   2.74084  12 0 0   -6.09995 3.4781585 3.3877745     22.95    .838587
2002 "Jan" 139.8 15.5 141.4 19.7 134.8 10.2 504   2.74084  13 0 1 -4.1969423  2.980619 2.3223877     15.05 -19.361414
2002 "Feb" 143.9 16.2 146.6 20.6 137.3 10.6 505  2.785011  14 0 1  -3.471347  3.025291  2.360854      11.1  .43858695
2002 "Mar" 143.3 17.2 144.1   22 139.2 11.1 506 2.8449094  15 0 1  -3.102846 3.0910425  2.406945      11.1    .538587
2002 "Apr" 140.7 16.1 138.1 19.7 141.2 11.5 507  2.778819  16 0 1  -5.115957  2.980619  2.442347      11.1  .43858695
2002 "May" 139.2 15.4   135   19 141.6 10.8 508 2.7343676  17 0 0 -4.7577844  2.944439 2.3795462    11.675   -.661413
2002 "Jun" 134.9 15.6 127.6   20 141.9 10.8 509  2.747271  18 0 0  -3.875095  2.995732 2.3795462    13.175  .03858696
2002 "Jul" 134.6 14.5 123.8 14.4 146.4 14.8 510 2.6741486  19 0 0   -5.13724  2.667228  2.694627    14.625   4.038587
2002 "Aug" 135.1 15.1 124.4 15.7   149 16.2 511  2.714695  20 0 0  -3.479068  2.753661  2.785011      15.5   1.438587
2002 "Sep" 142.7 15.4 136.7 15.5 147.7 15.5 512 2.7343676  21 0 0  -3.716697   2.74084   2.74084    16.075   -.661413
2002 "Oct" 142.3 12.9 135.8 10.1   148 16.6 513 2.5572274  22 0 0  -6.472713 2.3125355  2.809403     16.35   1.138587
2002 "Nov" 145.4   12 139.9  8.9 149.9 16.4 514  2.484907  23 0 0  -5.000352 2.1860514  2.797281      16.4 -.16141304
2002 "Dec" 147.6 11.5 143.3  8.2 150.2 15.9 515  2.442347  24 0 0  -4.629921  2.104134  2.766319      16.4  -.4614131
2003 "Jan" 159.4  9.6 143.8  2.8 181.2 18.3 516  2.261763  25 0 1  -6.034973 1.0296195  2.906901      16.4   2.438587
2003 "Feb" 162.1  9.8 147.6    3 182.2 18.6 517 2.2823825  26 0 1 -4.0258355 1.0986123 2.9231615      15.8    .338587
2003 "Mar"   158 10.2 155.2  7.7 158.3 13.7 518 2.3223877  27 0 1  -3.787981 2.0412204  2.617396      14.6  -4.861413
2003 "Apr" 154.5  9.8 148.9  7.8 158.8 12.5 519 2.2823825  28 0 1  -4.537868 2.0541236  2.525729        14 -1.1614131
2003 "May" 151.7    9 142.7  5.7 164.2 15.9 520 2.1972246  29 0 0   -4.93679  1.740466  2.766319        14   3.438587
2003 "Jun" 146.4  8.5 132.7    4 161.7   14 521 2.1400661  30 0 0   -4.66023 1.3862944 2.6390574        14  -1.861413
2003 "Jul" 146.3  8.7 130.4  5.3 168.4 12.5 522  2.163323  31 0 0 -3.9652815  1.667707  2.525729     14.65  -1.461413
2003 "Aug" 147.3    9 130.8  5.1 172.3 13.2 523 2.1972246  32 0 0  -3.827427 1.6292405  2.580217 16.350002    .738587
2003 "Sep" 155.8  9.2 139.5    2 178.4 18.2 524 2.2192035  33 0 0  -3.883444  .6931472 2.9014215        18   5.038587
2004 "Jan" 170.3 10.1 158.9  3.4 186.1 19.2 528 2.3125355  34 0 1 -3.1455896 1.2237754   2.95491      18.8   1.038587
2004 "Mar" 175.4 10.2 165.1  3.9 189.6   19 530 2.3223877  35 0 1   -3.86483 1.3609766  2.944439      18.8 -.16141304
2004 "Apr"   175 10.7 163.3  5.2 191.3 18.2 531 2.3702438  36 0 1  -3.433105 1.6486586 2.9014215      18.3   -.761413
2004 "May" 171.7 11.1 157.6  5.8 191.3 17.8 532  2.406945  37 0 0  -3.476863  1.757858 2.8791986      17.9   -.361413
2004 "Jun" 168.9 11.3 151.2    6 193.3 17.8 533  2.424803  38 0 0   -3.62675 1.7917595 2.8791986 17.724998  .03858696
2004 "Jul" 163.4 11.6 141.1  6.3 194.3 17.5 534  2.451005  39 0 0  -3.488896 1.8405496  2.862201    17.325 -.26141304
2004 "Aug" 163.9 11.3 139.1  6.3 198.3 16.5 535  2.424803  40 0 0 -4.0449123 1.8405496 2.8033605    16.025   -.961413
2004 "Sep" 172.9 10.9 152.5  9.4   201 12.7 536  2.388763  41 0 0  -4.137705 2.2407098  2.541602     14.25  -3.761413
2004 "Oct" 174.9 12.2 154.7 10.8 202.6 13.6 537  2.501436  42 0 0  -2.436627 2.3795462   2.61007    13.275    .938587
2004 "Nov"   180 12.8 162.2 12.8 204.5 12.9 538  2.549445  43 0 0   -3.03135  2.549445 2.5572274        13   -.661413
2004 "Dec" 184.3 13.7 168.4 14.1 206.4 13.3 539  2.617396  44 0 0  -2.668978  2.646175  2.587764     12.85  .43858695
2005 "Jan" 194.1   14 183.5 15.5   209 12.3 540 2.6390574  45 0 1  -3.188218   2.74084  2.509599    12.675   -.961413
2005 "Feb" 200.4 14.2 190.7 15.5 213.8 12.7 541  2.653242  46 0 1 -3.2442346   2.74084  2.541602     12.45  .43858695
2005 "Mar"   201 14.9 191.1   17 214.7 12.3 542  2.701361  47 0 1 -2.7063806  2.833213  2.509599    12.325   -.361413
2005 "Apr"   198 15.3 185.7 17.8 215.1 12.4 543  2.727853  48 0 1 -2.9378796 2.8791986 2.5176964     12.25  .13858695
2005 "May"   195 15.5 179.3 18.6 216.7 12.1 544   2.74084  49 0 0  -3.087767 2.9231615 2.4932055     12.15 -.26141304
2005 "Jun" 189.3 15.9 168.7 19.6 217.8 12.1 545  2.766319  50 0 0 -2.8499124   2.97553 2.4932055      12.1  .03858696
2005 "Jul" 188.4 15.6 165.3 19.3 220.4   12 546  2.747271  51 0 0 -3.4997995  2.960105  2.484907      12.1 -.06141304
2005 "Aug"   189 15.4 165.1 18.7 222.2 12.1 547 2.7343676  52 0 0  -3.392592 2.9285235 2.4932055        13  .13858695
2005 "Sep" 200.1 15.8 176.3 15.6 233.1   16 548   2.76001  53 0 0 -2.7792556  2.747271  2.772589    14.825   3.938587
2005 "Oct" 202.5 15.9 179.6 16.1 234.4 15.7 549  2.766319  54 0 0 -3.0291426  2.778819  2.753661    15.775 -.26141304
2005 "Nov" 209.1 16.2 188.9 16.5   237 15.9 550  2.785011  55 0 0  -2.797418 2.8033605  2.766319      15.8  .23858696
2005 "Dec" 214.8 16.5 197.4 17.2   239 15.8 551 2.8033605  56 0 0 -2.7534344 2.8449094   2.76001    15.675 -.06141304
2006 "Jan" 226.6 16.7 216.4 17.9 240.8 15.3 552  2.815409  57 0 1  -2.809451  2.884801  2.727853    14.975  -.4614131
2006 "Feb" 234.5 17.1 228.7 19.9 242.6 13.5 553 2.8390784  58 0 1 -2.5715966   2.99072   2.60269    13.925  -1.761413
2006 "Mar" 234.4 16.6 227.7 19.2 243.6 13.4 554  2.809403  59 0 1  -3.421484   2.95491  2.595255      13.4 -.06141304
2006 "Apr"   229 16.1   220 18.5 243.7 13.3 555  2.778819  60 0 1  -3.426535 2.9177706  2.587764    13.275 -.06141304
2006 "May" 225.8 15.8 211.8 18.1 245.1 13.1 556   2.76001  61 0 0  -3.231587  2.895912  2.572612    13.075 -.16141304
2006 "Jun" 218.2 15.3 198.3 17.5 245.8 12.8 557  2.727853  62 0 0  -3.424379  2.862201  2.549445    12.825 -.26141304
2006 "Jul" 216.6 14.9 193.7 17.2 248.2 12.6 558  2.701361  63 0 0  -3.329431 2.8449094  2.533697    12.625 -.16141304
2006 "Aug" 211.8   12 184.2 11.6   250 12.5 559  2.484907  64 0 0  -5.828353  2.451005  2.525729        12 -.06141304
2006 "Sep" 223.5 11.6   199 12.9 257.3 10.4 560  2.451005  65 0 0 -3.4805095 2.5572274 2.3418057     10.85  -2.061413
2006 "Oct" 224.7   11 200.9 12.2 257.7 10.1 561  2.397895  66 0 0  -3.679432  2.501436 2.3125355     10.05 -.26141304
2006 "Nov" 230.9 10.5 210.3 11.3 259.6  9.5 562 2.3513753  67 0 0 -3.5906124  2.424803 2.2512918  9.700001 -.56141305
2006 "Dec" 236.6 10.1 218.3 10.6 261.9  9.6 563 2.3125355  68 0 0  -3.495664  2.360854  2.261763       9.5  .13858695
2007 "Jan" 248.4  9.6 237.4  9.7 263.5  9.4 564  2.261763  69 0 1  -3.594586  2.272126 2.2407098       9.4 -.16141304
2007 "Feb"   256  9.2 249.4  9.1 265.3  9.3 565 2.2192035  70 0 1 -3.4996374 2.2082744 2.2300143     9.275 -.06141304
2007 "Mar" 254.6  8.6 246.5  8.3 265.8  9.1 566 2.1517622  71 0 1 -3.6985595 2.1162555 2.2082744  9.150001 -.16141304
2007 "Apr" 249.2  8.4 237.3  7.9 265.8  9.1 567 2.1282318  72 0 1   -3.30974 2.0668628 2.2082744  9.025001  .03858696
2007 "May" 243.7  7.9   227  7.2 266.7  8.8 568 2.0668628  73 0 0  -3.596404  1.974081 2.1747518  8.825001 -.26141304
2007 "Jun" 234.9  7.7 211.8  6.8 266.9  8.6 569 2.0412204  74 0 0  -3.301455 1.9169226 2.1517622      8.55 -.16141304
2007 "Jul" 232.6  7.4 206.6  6.7 268.6  8.2 570   2.00148  75 0 0 -3.3881185 1.9021075  2.104134     8.225   -.361413
2007 "Aug" 227.1  7.2 196.3  6.6 269.7  7.9 571  1.974081  76 0 0  -3.280911 1.8870697 2.0668628     7.975 -.26141304
2007 "Sep" 239.3  7.1 212.3  6.7 276.7  7.5 572 1.9600948  77 0 0  -3.167575 1.9021075  2.014903     7.925   -.361413
2007 "Oct"   241  7.2   214  6.5 278.2    8 573  1.974081  78 0 0  -2.948109 1.8718022 2.0794415     8.025    .538587
2007 "Nov"   248  7.4 224.3  6.7 280.8  8.2 574   2.00148  79 0 0  -2.816384 1.9021075  2.104134     8.225  .23858696
2007 "Dec" 254.4  7.5 232.9  6.7 284.2  8.5 575  2.014903  80 0 0   -2.87853 1.9021075 2.1400661      8.55    .338587
2008 "Jan" 267.6  7.7 253.4  6.7 287.2    9 576 2.0412204  81 0 1  -2.746805 1.9021075 2.1972246         9    .538587
2008 "Feb" 276.4    8 266.2  6.7   292  9.5 577 2.0794415  82 0 1 -2.6089506 1.9021075 2.2512918      9.45    .538587
2008 "Mar" 275.5  8.2 263.6  6.9   292  9.8 578  2.104134  83 0 1  -2.664967 1.9315214 2.2823825     9.825    .338587
2008 "Apr" 269.5  8.1 252.6  6.4 292.9 10.2 579  2.091864  84 0 1  -2.927113  1.856298 2.3223877      10.1  .43858695
2008 "May"   263  7.9 240.7    6   294 10.2 580 2.0668628  85 0 0  -3.007647 1.7917595 2.3223877    10.325  .03858696
2008 "Jun" 254.9  8.5 225.5  6.5 295.5 10.7 581 2.1400661  86 0 0 -2.1943104 1.8718022 2.3702438     10.65    .538587
2008 "Jul"   253  8.7 220.3  6.6 298.3   11 582  2.163323  87 0 0  -2.531939 1.8870697  2.397895    10.975    .338587
2008 "Aug" 247.8  9.1 210.3  7.1 299.8 11.2 583 2.2082744  88 0 0 -2.2940845 1.9600948  2.415914      11.2  .23858696
2008 "Sep" 261.6  9.3 227.9  7.3 308.3 11.4 584 2.2300143  89 0 0 -2.4439716 1.9878744  2.433613      11.4  .23858696
2008 "Oct" 263.7  9.4 229.9  7.4 310.6 11.6 585 2.2407098  90 0 0 -2.5061176   2.00148  2.451005      11.6  .23858696
2008 "Nov" 271.8  9.6 241.3  7.6   314 11.8 586  2.261763  91 0 0 -2.3743927 2.0281482 2.4680996     11.75  .23858696
2008 "Dec" 279.7  9.9 251.7  8.1 318.4   12 587 2.2925348  92 0 0 -2.2365386  2.091864  2.484907      11.7  .23858696
2009 "Jan" 294.5 10.1 274.5  8.3 322.2 12.2 588 2.3125355  93 0 1  -2.292555 2.1162555  2.501436     11.35  .23858696
2009 "Feb" 303.1  9.7 289.5  8.7   322 10.8 589  2.272126  94 0 1  -2.854701  2.163323 2.3795462    10.875  -1.361413
2009 "Mar" 301.7  9.5 286.6  8.7 322.6 10.5 590 2.2512918  95 0 1  -2.653623  2.163323 2.3513753    10.525 -.26141304
2009 "Apr" 294.4  9.2 273.6  8.3 323.1 10.3 591 2.2192035  96 0 1  -2.740286 2.1162555 2.3321438      10.3 -.16141304
2009 "May" 285.9  8.7 258.6  7.4 323.7 10.1 592  2.163323  97 0 0  -2.933079   2.00148 2.3125355      10.1 -.16141304
2009 "Jun" 276.4  8.4 241.4  7.1 324.9  9.9 593 2.1282318  98 0 0 -2.7381306 1.9600948 2.2925348     9.775 -.16141304
2009 "Jul" 273.3    8 235.6  6.9 325.6  9.2 594 2.0794415  99 0 0  -2.830923 1.9315214 2.2192035      9.25   -.661413
2009 "Aug" 267.1  7.8 224.6  6.8 325.9  8.7 595 2.0541236 100 0 0 -2.6298454 1.9169226  2.163323     8.775  -.4614131
end
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