There is another possibility. You can call the program TRAMO/SEATS from MATLAB using this interface:

http://www.mathworks.com/matlabcentral/fileexchange/27523-ts-matlab

TRAMO/SEATS also do seasonal adjustment, but using a different method.

On the other hand, which frequency have your time series? You know that X-11 (and TRAMO/SEATS) only works with monthly or quarterly data, do you?

Thanks Ignacio;

I will have a look at the TRAMO/SEATS. I have weekly data.

Actually I don´t need the X-11. What I want to do, is to estimate the amplitude of the annual cycle of the ocean sea surface temperature allowing to temporal changes in the seasonal cycle.

The way I use to do it is by a harmonic analysis but this methodology implies that the amplitude of the seasonal cycle is fixed. I read a paper where they use the X-11 to find the temporal changes of the amplitude but I don´t know how to apply that in Matlab.

Thanks again for your help

Carlos Teixeira

The X-11 programs are available free of charge from the US Bureau of Census. http://www.census.gov/srd/www/x12a/. However, the method does not handle weekly data so you would have to fudge the data a little. The method is fairly complicated even without the adjustments for lengths of months, Easter effects etc. which are not relevant in your case.

You could try to emulate a similar method--I imagine you would assume an additive series. The method is based on moving averages, firstly over a whole year to eliminate seasonal effects (only roughly because a trend affects the result). By subtracting the averages we have a trend series which may be smoothed by a moving average to give a smoother trend which may be subtracted from the original to give a purely seasonal series.

All these processes are imprecise when the trend is not linear and the seasonality is changing. Also each step loses points from the ends of the series. These are crudely estimated later.

The X-11 method uses various diagnostics from the above process to find the best length of moving average. It also tries to adjust for outliers. Then it applies the process twice more with new lengths of moving average.

In your case you obviously need a 52 point moving average at the first step centred with a two point MA afterwards. But there is a slight problem--if your data uses calendar weeks then there will be a drift by one week over a six year period. You might have to fudge this somehow.