R中的时间序列建模

Question

I have got a question about modeling time series in R. My data consist of the following matrix:

1   0.03333333 0.01111111 0.9555556
2   0.03810624 0.02309469 0.9387991
3   0.00000000 0.03846154 0.9615385
4   0.03776683 0.03119869 0.9310345
5   0.06606607 0.01201201 0.9219219
6   0.03900325 0.02058505 0.9404117
7   0.03125000 0.01562500 0.9531250
8   0.00000000 0.00000000 1.0000000
9   0.04927885 0.01802885 0.9326923
10  0.06106870 0.02290076 0.9160305
11  0.03846154 0.00000000 0.9615385
12  0.00000000 0.00000000 1.0000000
13  0.06028636 0.03843256 0.9012811
14  0.09646302 0.05144695 0.8520900
15  0.04444444 0.06666667 0.8888889

This matrix has in total 200 rows.

As you can see, in each situation the sum of each row is 1, that is because the values are the percentage of a whole. For example row 1 contains 3.33% of variable a, 1.11% of variable 2 and 95.5% of veriable 3. the first column indicates the year that the values are measured.

My goal is to make a prediction for the next 5 years, so from year 200 to 205.

I can do that by making three normal time series forecast. But for that forecast the total sum is never equal to 1, which is very important. Normally, I use techniques like arima and exponential smoothing.

Does somebody know a method to make a forecast for such a problem?

Answer 1

Well, I think that you need to make a statistical Normalization ; subtracting each estimated score from the estimated mean, then dividing the result by the estimated standard deviation. This would gurantee that your forecast values lie in the range [0-1].