Stochastic Modelling of Time Series

Abstract

In practice, hydrologists often deal with a limited amount of recorded data (i.e., a sample) while analyzing a hydrologic time series. This sample consists of a limited number of realizations of the population of same hydrologic process. When a hydrologic time series is characterized with statistical and probabilistic parameters, it represents a probability of occurrence of one of its possible stages. This probabilistic occurrence of the hydrologic time series is considered as one realization. All possible realizations of the hydrologic process constitute a population. The concept of terms sample and population has already been explained in Chapter 2. The main intent of the most hydrologic studies is to understand and quantitatively describe the population as well as the process that generates it based on a limited number of samples. Also, future predictions and/or simulations about the hydrologic time series can be made by applying statistical tools and techniques using probabilistic or stochastic models based on the historical data. When a hydrologic time series is analyzed in this manner, the technique is known as ‘stochastic modelling’ of time series and the parameters described with statistic and probabilistic terms are called ‘stochastic parameters’.