The BLOCKSEASON or BLOCKSEASONAL statement is used to specify a seasonal component that has a special block structure. The seasonal is called a block seasonal of block size m and number of blocks k if its season length, s, can be factored as and its seasonal effects have a block form—that is, the first m seasonal effects are all equal to some number , the next m effects are all equal to some number , and so on.
This type of seasonal structure can be appropriate in some cases; for example, consider a series that is recorded on an hourly
basis. Further assume that, in this particular case, the houroftheday effect and the dayoftheweek effect are additive.
In this situation the houroftheweek seasonality, having a season length of 168, can be modeled as a sum of two components.
The houroftheday effect is modeled using a simple seasonal of season length 24, while the dayoftheweek is modeled as
a block seasonal component that has the days of the week as blocks. This dayoftheweek block seasonal component has seven
blocks, each of size 24.
A block seasonal specification requires, at the minimum, the block size m and the number of blocks in the seasonal k. These are specified using the BLOCKSIZE= and NBLOCKS= option, respectively. In addition, you might need to specify the position
of the first observation of the series by using the OFFSET= option if it is not at the beginning of one of the blocks. In
the example just considered, this corresponds to a situation where the first series measurement is not at the start of the
day. Suppose that the first measurement of the series corresponds to the hour between 6:00 and 7:00 a.m., which is the seventh
hour within that day or at the seventh position within that block. This is specified as OFFSET=7.
The other options in this statement are very similar to the options in the SEASON statement; for example, a block seasonal
can also be of one of the two types, DUMMY and TRIG. There can be more than one block seasonal component in the model, each
specified using a separate BLOCKSEASON statement. No two block seasonals in the model can have the same NBLOCKS= and BLOCKSIZE=
specifications. The following example illustrates the use of the BLOCKSEASON statement to specify the additive, houroftheweek
seasonal model:
season length=24 type=trig;
blockseason nblocks=7 blocksize=24;

BLOCKSIZE=integer

specifies the block size, m. This is a required option in this statement. The block size can be any integer larger than or equal to two. Typical examples
of block sizes are 24, corresponding to the hours of the day when a day is being used as a block in hourly data, or 60, corresponding
to the minutes in an hour when an hour is being used as a block in data recorded by minutes, etc.

NBLOCKS=integer

specifies the number of blocks, k. This is a required option in this statement. The number of blocks can be any integer greater than or equal to two.

NOEST

fixes the value of the disturbance variance parameter to the value specified in the VARIANCE=
option.

OFFSET=integer

specifies the position of the first measurement within the block, if the first measurement is not at the start of a block.
The OFFSET= value must be between one and the block size. The default value is one. The first measurement refers to the start
of the estimation span and the forecast span. If these spans differ, their starting measurements must be separated by an integer
multiple of the block size.

PLOT=FILTER
PLOT=SMOOTH
PLOT=F_ANNUAL
PLOT=S_ANNUAL
PLOT=( <plot request> …<plot request> )

requests plots of the season component. When you specify only one plot request, you can omit the parentheses around the plot request. You can use the FILTER and SMOOTH
options to plot the filtered and smoothed estimates of the season component . You can use the F_ANNUAL and S_ANNUAL options to get the plots of "annual" variation in the filtered and smoothed estimates
of . The annual plots are useful to see the change in the contribution of a particular month over the span of years. Here "month"
and "year" are generic terms that change appropriately with the interval type being used to label the observations and the
season length. For example, for monthly data with a season length of 12, the usual meaning applies, while for daily data with
a season length of 7, the days of the week serve as months and the weeks serve as years. The first period in each block is
plotted over the years.

PRINT=FILTER
PRINT=SMOOTH
PRINT=( <FILTER> <SMOOTH> )

requests the printing of the filtered or smoothed estimate of the block seasonal component .

TYPE=DUMMY  TRIG

specifies the type of the block seasonal component. The default type is DUMMY.

VARIANCE=value

specifies an initial value for the disturbance variance, , in the equation at the start of the parameter estimation process. Any nonnegative value, including zero, is an acceptable starting
value.