LOESS extrapolation seems pretty dicey to me. Results can vary widely depending on personal preference for the smoothing parameter.

Extrapolating a linear or exponential or power law or similar fit at least puts the weight of the entire dataset behind the extrapolation. One might even think of a theoretical reason to believe the extrapolation as one is finishing the graph. LOESS just puts the edge of the dataset behind the extrapolation, after effectively admitting one didn’t have a clue in advance as to the real shape of the interpolative fit one is resorting to LOESS to do.

Subject to even more concerns than most extrapolations, I’d say.

Sure, you can extrapolate, subject to concerns raised by any extrapolation.

In the other comment I showed how to get the extrapolated values. Using the first button in the second row, you pick two ranges, each two columns wide. The first has the input data, that is, the actual X and Y values to be used in the extrapolation. The second has the output X, that is, the X values at which you want to extrapolate Y, and blank cells for the output Y.

The result:

I have another question about the utility. According to my last two comments which
contain the necessary data I would like to know if a prediction is possible for the next two years. I found a similar comment from K. A. (Saturday, October 8, 2011, 3:39 am).
Unfortunately I did not understand your solution quite well. Maybe you could explain it to me once more (with the final table). Thank you in advance.

thank you very much. This is a very good solution for this problem.
Now it looks much better than before. Thanks again.

Do you have full dates for the multiple values in each year? What the utility does is compute a Y value for each input X value. Since each X value is repeated, the calculated Y value is also repeated. The many duplicates also caused problems with the regression algorithm within the LOESS program.

If I assume the 12 values for each year correspond in order to values on the first of each month (1/1/95, 2/1/95, etc.) I get a result which is much more typical of what I would have expected.