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**performs Bayesian seasonal adjustment modeling**

**CALL TSBAYSEA(***trend, season, series, adjust, abic, data*

*<,order, sorder, rigid, npred, opt, cntl, print>***);**

*data*- specifies a
*T*×1 (or 1 ×*T*) data vector. *order*- specifies the order of trend differencing.
The default is
*order*=2. *sorder*- specifies the order of seasonal differencing.
The default is
*sorder*=1. *rigid*- specifies the rigidity of the seasonal pattern.
The default is
*rigid*=1. *npred*- specifies the length of the forecast
beyond the available observations.
The default is
*npred*=0. *opt*- specifies the options vector.

*opt*[1]- specifies the number of seasonal periods (
*speriod*). By default,*opt*[1]=12.

*opt*[2]- specifies the year when the series starts (
*year*). If*opt*[2]=0, there will be no trading day adjustment. By default,*opt*[2]=0.

*opt*[3]- specifies the month when the series starts (
*month*). If*opt*[2]=0, this option is ignored. By default,*opt*[3]=1.

*opt*[4]- specifies the upper limit value for
outlier determination (
*rlim*). Outliers are considered as missing values. If this value is less than or equal to 0, TSBAYSEA assumes that the input data does not contain outliers. The default is*rlim*=0. See the "Missing Values" section.

*opt*[5]- refers to the number of time periods
processed at one time (
*span*). The default is*opt*[5]=4.

*opt*[6]- specifies the number of time
periods to be shifted (
*shift*). By default,*opt*[6]=1.

*opt*[7]- controls the transformation of
the original series (
*logt*). If*opt*[7]=1, log transformation is requested. No transformation (*opt*[7]=0) is the default.

*cntl*- specifies control values for the TSBAYSEA subroutine.
These values will be automatically set.
Be careful if you change these values.

*cntl*[1]- controls the adaptivity of the trading
day adjustment component (
*wtrd*). The default is*cntl*[1]=1.0.

*cntl*[2]- controls the sum of seasonal components
within a period (
*zersum*). The larger the value of*cntl*[2], the closer to zero this sum is. By default,*cntl*[2]=1.0.

*cntl*[3]- controls the leap year effect (
*delta*). The default is*cntl*[3]=7.0.

*cntl*[4]- specifies the prior variance of
the initial trend (
*alpha*). The default is*cntl*[4]=0.01.

*cntl*[5]- specifies the prior variance of the
initial seasonal component (
*beta*). The default is*cntl*[5]=0.01. [.03in]

*cntl*[6]- specifies the prior variance of the initial
sum of seasonal components (
*gamma*). The default is*cntl*[6]=0.01.

*print*- requests the power spectrum and the estimated
and forecast values of time series components.
If
*print*=2, the spectra of irregular, differenced trend and seasonal series are printed, together with estimates and forecast values. If*print*=1, only the estimates and forecast values of time series components are printed.

If*print*=0, printed output is suppressed. The default is*print*=0.

*trend*- refers to the estimate and forecast of the trend component.
*season*- refers to the estimate and forecast of the seasonal component.
*series*- refers to the smoothed and forecast values of the time series.
*adjust*- refers to the seasonally adjusted series.
*abic*- refers to the value of ABIC from the final estimates.

Bayesian seasonal adjustments are performed with the TSBAYSEA subroutine. The smoothness of the trend and seasonal components is controlled by the prior distribution. The Akaike Bayesian Information Criterion (ABIC) is defined to compare with alternative models. The basic TSBAYSEA procedure processes the block of data in which the length is SPAN*SPERIOD, while the first block of data consists of length (2*SPAN-1)*SPERIOD. The block of data is shifted successively by SHIFT*SPERIOD.

The TSBAYSEA call decomposes the series

To analyze the monthly data with rigidity 0.5, you can specify

call tsbaysea(trend,season,series,adj,abic) data=z order=2 sorder=1 rigid=0.5 npred=10 print=2;or

call tsbaysea(trend,season,series,adj,abic,z,2,1,0.5,10,,,2);The TREND, SEASON, and SERIES components contain 10-period-ahead forecast values as well as the smoothed estimates. The detailed result is also printed since the PRINT=2 option is specified.

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