As part of a forecasting project, I would like to forecast future
periods based on historic timeseries of data. The data in the sample
attached is sales data from different products: the data is seasonal.
The objective is to forecast 9 periods ahead based on historic data,
basically to complete the data for 2003. The history of data is fairly
limited.

 Already I have worked through a few forecasting methods both in
theory as well as spreadsheet implementations. These include single,
double exponential smoothing and Holt-Winters. I have used the
formula's and background mainly from this page:

 http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm

 My objective and question I would like to get answered is twofold: 

  - Firstly to collect a set of arguments, a review if you like, of
what the pro's and con's of the different methods are specifically for
the set of data provided. I have already read through a general
classification of the different methods as described here:

 http://www.nyu.edu/its/pubs/connect/archives/96fall/yaffeesmooth.html

 but I am looking for a little bit more specific on the data provided.
An important criterium is that the review is understandable for
non-math educated.

  - Secondly I am seeking a founded recommendation on the optimal
settings (alpha, beta, gamma and initial values) for the holz-winter
smoothing method based on the set of data provided.
 The HW formula's can be found here:

 http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc435.htm


The answer should not only include the settings but also the related
forecast timeseries of the next 13 periods belonging to those
settings. Ideally a spreadsheet so I can reproduce the results. Please
address in the recommendation following:
  What is the best setting for all 6 products ? What would be the
ideal setting for each individual of the 6 products. Does it make a
difference if the 6 individual products are forecasted versus the sum
of the 4, what is more accurate ?


Sample data starts here:

		Product A	Product B	Product C
2000	1	131,354		112,752		198,366
	2	188,935		165,473		208,376
	3	202,453		176,231		208,265
	4	188,859		159,369		208,851
	5	161,065		121,484		204,284
	6	166,700		129,079		209,007
	7	160,094		118,146		205,493
	8	170,038		133,994		210,737
	9	187,966		156,692		222,392
	10	213,999		183,012		224,084
	11	223,759		193,645		221,593
	12	207,936		182,237		228,416
	13	154,805		136,922		219,348
2001	1	136,522		117,879		204,231
	2	190,700		164,765		210,034
	3	203,874		174,087		207,318
	4	188,693		148,168		208,501
	5	166,130		127,458		213,469
	6	175,948		126,840		206,164
	7	163,940		120,625		208,399
	8	160,434		125,320		204,949
	9	197,224		161,775		217,333
	10	232,414		196,154		231,852
	11	228,638		192,550		213,990
	12	230,756		196,007		228,657
	13	160,654		135,903		211,281
2002	1	148,455		123,501		206,761
	2	202,038		172,497		201,169
	3	209,522		171,344		202,196
	4	180,051		135,488		192,942
	5	178,589		135,986		196,790
	6	179,649		131,272		213,377
	7	174,772		125,608		200,446
	8	173,384		126,417		205,346
	9	199,096		155,394		209,602
	10	226,374		186,883		221,842
	11	226,766		193,218		211,542
	12	215,986		184,514		223,362
	13	160,358		138,143		204,869
2003	1	140,614		116,126		198,528
	2	199,498		164,169		196,086
	3	217,120		179,266		194,864	
	4	198,974		158,629		195,282

	Product D	Product E	Product F
2000	1	32,464	4,364		7,594
	2	36,011	6,028		7,519
	3	32,846	9,267		8,138
	4	33,627	11,009		8,666
	5	33,221	21,148		9,223
	6	34,543	18,859		8,258
	7	31,569	21,396		10,267
	8	33,686	16,362		9,274
	9	35,101	11,756		8,611
	10	36,407	7,418		10,115
	11	34,448	4,525		10,699
	12	35,522	4,508		8,691
	13	29,229	4,580		6,908
2001	1	34,522	5,327		6,714
	2	35,940	6,353		9,137
	3	39,637	10,700		8,779
	4	36,436	17,895		8,391
	5	35,799	17,415		8,884
	6	35,010	26,067		9,746
	7	31,273	22,421		9,978
	8	30,148	17,332		8,226
	9	33,090	12,666		8,314
	10	37,217	7,636		10,712
	11	34,004	7,356		11,716
	12	35,909	5,908		10,928
	13	32,949	4,159		9,992
2002	1	35,394	7,527		7,363
	2	36,696	7,772		8,067
	3	36,443	10,764		7,929
	4	34,911	19,868		7,308
	5	36,420	16,494		8,624
	6	36,959	23,641		8,789
	7	33,899	24,467		9,040
	8	33,902	22,652		8,899
	9	34,246	14,749		8,758
	10	40,693	8,963		7,899
	11	37,677	5,052		10,001
	12	37,383	5,416		9,246
	13	34,038	1,889		7,824
2003	1	39,945	6,095		5,859
	2	40,731	6,572		7,633
	3	37,621	11,814		7,158
	4	37,411	15,813		6,920

 If you would like to have the data in a spreadsheet to save retyping
etc. please contact me, so I can sent it.

Choosing a specific forecasting method is not really a precise
science.  As well as different methods there are other ways of
tweaking things, such as taking logarithms of the data, forecasting
that and then converting it back afterwards.  Admittedly some are
better than others for certain things, but it does not always work out
that way.  Maybe you should look for software that includes an expert
selection device e.g. http://www.forecastpro.com/

For your specific data set being seasonal, you should consider
seasonal decomposition, multiple regression, ARIMA + Box Jenkins
methodology as well as Holt-Winters smoothing.  The software package
Minitab will do all of these, I would recommend you have a look at it.

As for optimisation (Minitab will do it for double exponential
smoothing but not for HW) well, you need to consider the mathematical
approach.  I have written an optimiser for both double and HW
smoothing in Java and the biggest problem was working out the concept.
 I found that Tabu search can be applied for the double exponential
smoothing method although my computer ran out of memory when I tried
it for the Holt Winters as well.  I did however come up with an
optimiser that essentially performs the same operation but it cannot
store the data, it just works it out on the fly.

There are other mathematical techniques aside from Tabu search to
apply, however, you must think about them on the 4 dimensional level
with the HW technique.  You should look at simulated annealing, this
may give you some ideas on optimisation as well.

Also see this book ISBN: 0-471-53233-9