Discrete time is often employed when [[empirical]][[measurement]]smeasurements are involved, because normally it is only possible to measure variables sequentially. For example, while [[economic activity]] actually occurs continuously, there being no moment when the economy is totally in a pause, it is only possible to measure economic activity discretely. For this reason, published data on, for example, [[gross domestic product]] will show a sequence of [[Calendar year#Quarters|quarterly]] values.
When one attempts to empirically explain such variables in terms of other variables and/or their own prior values, one uses [[time series]] or [[regression analysis|regression]] methods in which variables are indexed with a subscript indicating the time period in which the observation occurred. For example, ''y''<sub>''t''</sub> might refer to the value of [[income]] observed in unspecified time period ''t'', ''y''<sub>''3''</sub> to the value of income observed in the third time period, etc.
Moreover, when a researcher attempts to develop a theory to explain what is observed in discrete time, often the theory itself is expressed in discrete time in order to facilitate the development of a time series or regression model.
On the other hand, it is often more mathematically [[Closed form solution|tractable]] to construct [[Scientific theory|theoretical model]]smodels in continuous time, and often in areas such as [[physics]] an exact description requires the use of continuous time. In a continuous time context, the value of a variable ''y'' at an unspecified point in time is denoted as ''y''(''t'') or, when the meaning is clear, simply as ''y''.
