Month-month seasonal adjustment using weekly data for VAR model forecasting

[lizzy28]

Hi SAS forecasting experts,

This time I came across the problem of using weekly data in a VAR model for forecasting. I have two-year weekly sales and marketing campaign data (RAQ) and want to use VAR to run forecast. However, the sales always have spikes at the end of month. As the data is weekly, the end of month can be the fourth week of a month or (the beginning of) the fifth week. So, my question is: how to do such month-month seasonal adjustment using weekly data in order to use the seasonally adjusted data in the VAR model?

The sample data is attached. Both the sales and the campaign activities are in logarithm form.

Thank you!

week	year	lsales	lcampaign
0	2013	9.511629	10.94447
1	2013	9.73074	11.19503
2	2013	9.820323	11.26294
3	2013	9.888374	11.30585
4	2013	10.02167	11.24355
5	2013	9.699779	11.14156
6	2013	9.985759	11.21244
7	2013	10.14345	11.28749
8	2013	10.35993	11.2146
9	2013	9.789815	11.09255
10	2013	9.98516	11.09909
11	2013	10.05651	11.18147
12	2013	10.36945	11.18582
13	2013	9.878631	11.0726
14	2013	9.971707	11.05936
15	2013	10.0575	11.08756
16	2013	10.20233	11.14399
17	2013	10.14624	11.02723
18	2013	9.879041	10.97432
19	2013	10.00406	11.02241
20	2013	10.25857	11.1648
21	2013	10.42955	11.14669
22	2013	9.923535	11.04971
23	2013	10.04329	11.06462
24	2013	10.13321	11.11524
25	2013	10.39035	11.20462
26	2013	10.05617	11.14541
27	2013	10.06216	11.11842
28	2013	10.08168	11.21829
29	2013	10.19347	11.32347
30	2013	10.2509	11.29164
31	2013	10.021	11.26334
32	2013	10.04863	11.25205
33	2013	10.12415	11.26457
34	2013	10.42899	11.28143
35	2013	9.972874	11.12966
36	2013	9.811756	11.10172
37	2013	9.864227	11.10297
38	2013	10.0174	11.06164
39	2013	9.921278	11.02241
40	2013	9.79568	11.00686
41	2013	9.940253	11.05972
42	2013	10.05595	11.11215
43	2013	10.11131	11.04937
44	2013	9.603395	10.9504
45	2013	9.723523	11.00896
46	2013	9.863915	11.05559
47	2013	10.20814	11.08708
48	2013	9.721606	10.91369
49	2013	9.669788	10.92228
50	2013	9.873131	10.93519
51	2013	9.990811	11.00627
52	2013	9.651366	10.49255
0	2014	9.381432	10.50381
1	2014	9.392162	11.03046
2	2014	9.713174	11.07163
3	2014	9.809342	11.12891
4	2014	9.986955	11.10241
5	2014	9.488502	11.0561
6	2014	9.833226	11.19188
7	2014	10.16574	11.24522
8	2014	10.4304	11.23107
9	2014	9.709357	11.12648
10	2014	9.98815	11.13966
11	2014	10.07631	11.19915
12	2014	10.21841	11.26174
13	2014	10.09005	11.09156
14	2014	9.982576	11.03743
15	2014	10.05959	11.12678
16	2014	10.14471	11.16423
17	2014	10.2376	11.08667
18	2014	9.961143	11.03373
19	2014	10.05651	11.13076
20	2014	10.17329	11.17912
21	2014	10.3772	11.13428
22	2014	9.946595	11.02451
23	2014	10.01864	11.04596
24	2014	10.09448	11.07414
25	2014	10.27215	11.15696
26	2014	10.21365	11.11531
27	2014	10.19388	11.16723
28	2014	10.08997	11.1838
29	2014	10.05651	11.17566
30	2014	10.19096	11.1527
31	2014	9.795457	11.072
32	2014	9.921769	11.09712
33	2014	10.07786	11.21036
34	2014	10.41085	11.3168
35	2014	10.05199	11.20929
36	2014	9.903837	11.1398
37	2014	9.965711	11.15681
38	2014	10.09237	11.18805
39	2014	10.07933	11.15161
40	2014	9.766636	11.13017
41	2014	9.85692	11.15869
42	2014	9.906732	11.16284
43	2014	10.16908	11.17224
44	2014	9.640368	11.14215
45	2014	9.805875	11.21039
46	2014	9.870758	11.32554
47	2014	10.12579	11.27662
48	2014	9.86277	11.19193
49	2014	9.844268	11.13488
50	2014	10.06373	11.17643
51	2014	10.07643	11.15661
52	2014	10.1118	10.81565

[alexchien]

You can consider creating a dummy variable to capture the end-of-month effect. Since you are using the log scale of the dependent variables, the dummy variable will basically provide the multiplicative lift of the base.