This is the first part of our two-part work. Here, we, motivated by a pract
ical problem of prediction for dry-and-hot winds, start to develop a theory
of systems analysis which can be used to analyze data, when the set of ava
ilable data is small compared to the cases considered in statistics. As a t
est of applications, in the second part of our work, the practical predicti
on on dry-and-hot winds is given based on actual data and the prediction re
sults are compared with the actual situations appeared after the time the f
inal data values were collected and used in the prediction calculation.