Seasonally Adjusting a Time Series

If you watch any news shows or read any papers related to business you often hear phrases like, "Seasonally adjusted housing starts", "Seasonally adjusted employment" etc. What this means is the seasonal variation has been removed from the data leaving only the underlying trend and interventions. This makes month to month and year to year comparisons easier. Trends and interventions become much clearer and easier to model with seasonal variation out of the way. Many of our forecasting models will work better using seasonally adjusted data.

In this course we are going to use the ratio to centered moving average approach to calculate and remove the seasonal variation in a data set.

For monthly data The seasonal index for month j (j=1,,12) is calculated as follows,

Indexj=1jnjSij,

Where,

j is the month of the year,

nj is the number of the j-th month in the series

Sij is the i-th raw seasonal index for month j

St=Yt/CMAt

CMAt is the centered moving average at time t

This looks much worse than it really is.

Data File: Mallorca Data

Question: Use the file US-YVR

Calculate the ratio to centered moving average seasonal indices

3 decimal places. Enter as .123 or 1.12

1--Jan--.922

2--Feb--

3--Mar--

4--Apr--

5--May--

6--June--

7--Jul--

8--Aug--

9--Sep--

10--Oct--

11--Nov--

12--Dec--.907

Air Passenger Volume to Palma de Mallorca 101 1 PE pur 3 dva Jan 34 F.84 Wir 348.411 1 2 PE cl44 14. 1994 1991 1904 1904 1994 194 1 ELIGE IM MI w 10 514 - Dy4 Nr.4 3/4 119,014 1,345,11 1.450.001 , Sa 4632 WA 194.183 097 ded. 11 HAM 1924 1 11 1994 12 13 195 14* Neil LOTIE M 11 19 var w Ft 1. 5 1.12 4,13,1 1/94 18 154.254 J-45 40 18 SA EPS FE BIPPE SYYE sect! Srdis SEED 6 UYS 1995 16 10 Nr.9 199511 1546.53 1.44.99 12 411.11 de wel 1 . Jesse F V4 Api 190 19 IW WW PEET FE SEBS 91 w w al 12 W? JE Jere JE Maps Sp. Ik Nar4 1,181/ 1,11/4 . 1.9111 . 2.334.37 229.00 145 wel 6 Neser == 14 11 19 1994 190 www 1 1961 16 1901 IW 46391 ACS das 11 F49 13 1403471 . 112495 3 LA . RIEGS WI Wil wil Art Naya ? 1 81-J 9 1.199.344 2.02.13 JW ol 1901 324299 14 5 CUP SIZE Mare NCC 01 toh Sur JE 10 100 10 104 A TER YET TYCZ 111111 43218148 321,32 del.. 124.982 16 2.147.751 ID 407,411 11 111/14 13 (29,441 2 su 2) M LOH GUC . LLLL w H 21% Yes 1162913 w J II - 23 2 HII Hand 190 23 745,393 less 4 .401221 44-45 Weita TE 2.300.311 113 art 41 114 119 dels 11 SFP 8 . W 106 YE WILLE 2015 22 2015 39 ww 19 391 2011 2015 200 w w 23 22 TE 1,741,721 VILL FIT 115 w 11 V 11 JE 132 19 Maret 12 134 War. 14 11 Julai 21 12 519,411 14 ? 296200 2 -14 M-PI PREK Why HURT 32704,70 3.170414 F w SF 7 9,728.101 . ICEHE 2445/12 HE TEE TER SESTE I ER S 136 OH 13:44 132 - B 133 194 11 Mar 29 TE 11 2003 1 1: 2.1 191493 31175 ! 235 1393 Baby LISLIP 13,141546 1211017 . 25 w 3995 2015 2015 2015 2015 145 Yerli 15 13 140 P45 141 5-15 143 OHS LATITE 1 14,370 VETT TWEETS It rel.14 1912.16 12 818338 5 1 131 14 143 144 142 I 166 8,5 11 44 13 46 40 A1 S! .81 159 155: 1591 .= | LESI 10 1.2152 11 613.7 19 1 2 2114 S1 TE ww Es ES ! TE 021, le 2.93 www Ivar Sentry 2.RO T4 1991 last 1940 1940 More 1995 A 1988 Nas 40 1955 1555 1555 U 1393 55 1558 1998 the 1990 las 1940 1990 Nar 1900 Apr 1986 1993 Nas 41 1553 . Jus NS 1553 BEST RF WY e 10 1.912,7 11 17071 TIM 41 247,519 3 MIASI . 1,02 . 3.3.1995 . 0. T22W,312 ESSE Open ESSI IL SV) 101 SV 441 1 RY -- ORP 3 MIUI DONE DOTE 10 1911 We 1599 $ 2,355, 1 1999 in 11 1998 11 . 13 1500 12 2 2001 1 wc, 2000 2 . Nar0 2001 3 ING, . .. . 1,349 71 Marc 2000 2 LUND Java 2000 w 2000 ? 3.A 3000 a 3160 0 % 3000 11 3 " Two 12 512 lui TA 134, RHI 2X20 Nara . 2001 3 . .. 2001 . 1.STLIT May 1 > .WS Jen! 2001 20 91 Nga 30 V 19. CHE ! in 25 45 w 11 wa 2001 12 SING 1, 11 12 2001 a 1 213 58 KHZ 2002 .16.25 59 Narad 162 3 1.131.13 LP 2002 Meso 2002 $ 1,351,325 TO Jes re 18 de sre A 12 1-Y 1012 15. ERP 1992 WENDE '' 1 * * 10 : 191 101 69 Air Passenger Volume to Palma de Mallorca 101 1 PE pur 3 dva Jan 34 F.84 Wir 348.411 1 2 PE cl44 14. 1994 1991 1904 1904 1994 194 1 ELIGE IM MI w 10 514 - Dy4 Nr.4 3/4 119,014 1,345,11 1.450.001 , Sa 4632 WA 194.183 097 ded. 11 HAM 1924 1 11 1994 12 13 195 14* Neil LOTIE M 11 19 var w Ft 1. 5 1.12 4,13,1 1/94 18 154.254 J-45 40 18 SA EPS FE BIPPE SYYE sect! Srdis SEED 6 UYS 1995 16 10 Nr.9 199511 1546.53 1.44.99 12 411.11 de wel 1 . Jesse F V4 Api 190 19 IW WW PEET FE SEBS 91 w w al 12 W? JE Jere JE Maps Sp. Ik Nar4 1,181/ 1,11/4 . 1.9111 . 2.334.37 229.00 145 wel 6 Neser == 14 11 19 1994 190 www 1 1961 16 1901 IW 46391 ACS das 11 F49 13 1403471 . 112495 3 LA . RIEGS WI Wil wil Art Naya ? 1 81-J 9 1.199.344 2.02.13 JW ol 1901 324299 14 5 CUP SIZE Mare NCC 01 toh Sur JE 10 100 10 104 A TER YET TYCZ 111111 43218148 321,32 del.. 124.982 16 2.147.751 ID 407,411 11 111/14 13 (29,441 2 su 2) M LOH GUC . LLLL w H 21% Yes 1162913 w J II - 23 2 HII Hand 190 23 745,393 less 4 .401221 44-45 Weita TE 2.300.311 113 art 41 114 119 dels 11 SFP 8 . W 106 YE WILLE 2015 22 2015 39 ww 19 391 2011 2015 200 w w 23 22 TE 1,741,721 VILL FIT 115 w 11 V 11 JE 132 19 Maret 12 134 War. 14 11 Julai 21 12 519,411 14 ? 296200 2 -14 M-PI PREK Why HURT 32704,70 3.170414 F w SF 7 9,728.101 . ICEHE 2445/12 HE TEE TER SESTE I ER S 136 OH 13:44 132 - B 133 194 11 Mar 29 TE 11 2003 1 1: 2.1 191493 31175 ! 235 1393 Baby LISLIP 13,141546 1211017 . 25 w 3995 2015 2015 2015 2015 145 Yerli 15 13 140 P45 141 5-15 143 OHS LATITE 1 14,370 VETT TWEETS It rel.14 1912.16 12 818338 5 1 131 14 143 144 142 I 166 8,5 11 44 13 46 40 A1 S! .81 159 155: 1591 .= | LESI 10 1.2152 11 613.7 19 1 2 2114 S1 TE ww Es ES ! TE 021, le 2.93 www Ivar Sentry 2.RO T4 1991 last 1940 1940 More 1995 A 1988 Nas 40 1955 1555 1555 U 1393 55 1558 1998 the 1990 las 1940 1990 Nar 1900 Apr 1986 1993 Nas 41 1553 . Jus NS 1553 BEST RF WY e 10 1.912,7 11 17071 TIM 41 247,519 3 MIASI . 1,02 . 3.3.1995 . 0. T22W,312 ESSE Open ESSI IL SV) 101 SV 441 1 RY -- ORP 3 MIUI DONE DOTE 10 1911 We 1599 $ 2,355, 1 1999 in 11 1998 11 . 13 1500 12 2 2001 1 wc, 2000 2 . Nar0 2001 3 ING, . .. . 1,349 71 Marc 2000 2 LUND Java 2000 w 2000 ? 3.A 3000 a 3160 0 % 3000 11 3 " Two 12 512 lui TA 134, RHI 2X20 Nara . 2001 3 . .. 2001 . 1.STLIT May 1 > .WS Jen! 2001 20 91 Nga 30 V 19. CHE ! in 25 45 w 11 wa 2001 12 SING 1, 11 12 2001 a 1 213 58 KHZ 2002 .16.25 59 Narad 162 3 1.131.13 LP 2002 Meso 2002 $ 1,351,325 TO Jes re 18 de sre A 12 1-Y 1012 15. ERP 1992 WENDE '' 1 * * 10 : 191 101 69