Models in Irrigation andWater Management - Practices of Irrigation and On-farm Water Management - page 385

- the theoretical basis of the model, and
- the numerical implementation of model
Stochastic Model
Stochastic means random . A stochastic process is one whose behavior is non-
deterministic, that is, the system's subsequent state is determined both by the
process's predictable actions and by a random element. However, any kind of pro-
cess, which is analyzable in terms of probability, deserved the name stochastic
process. A model that relies on stochastic process (theory of probabilities) to predict
the new/future values is termed as stochastic model.
For example, a stochastic model of stock prices includes in its ontology a sample
space, random variables, the mean and variance of stock prices, various regression
coefficients.
10.2.2.8 Time Series Model
A time series is a sequence of data points, measured typically at successive times
spaced at uniform/equal time intervals. Time series analysis accounts for the fact
that data points taken over time may have internal structure (such as trend or sea-
sonal variation, autocorrelation) that should be accounted for. Time series model is
that type of model which uses known past events to forecast future events. Time
series analysis is used for many applications such as yield projections, resource
depletion/degradation (e.g., groundwater table), demand forecasting, utility studies.
Time series model may be of two types: deterministic and stochastic time series
model.
Deterministic Time Series Model
If the process is such that the future values are exactly determined by some mathe-
matical function, and once have identified this function we can exactly predict future
values of the time series, then the underlying process is said to be a deterministic
time series model.
Stochastic Time Series Model
If the process is such that a future value of the process must be regarded as a random
variable and identifying the underlying process only enables to identify the proba-
bility distribution of this random variable, then the underlying process is said to be
a stochastic time series model.
10.2.2.9 Logical Model
The logical model is a generalized formal structure in the rules of information
science.