In General it does not make sense to overfit your data on purpose. The problem is that it is difficult to make sure that the patterns also appear in the part which is not included in your data. You have to affirm that there are pattern in the data. One possibility of doing so is the concept of stationarity.
What you describe reminds me of stationarity and ergodicity. From a contextual side/ business side you assume that your time series follows certain patterns. These patterns are called stationarity or ergodicity.
A stationary process is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Therefore parameters such as mean and variance also do not change over time.
An ergodic process is a process relating to or denoting systems or processes with the property that, given sufficient time, they include or impinge on all points in a given space and can be represented statistically by a reasonably large selection of points.
Now you want to make sure that it really follows these certain patterns. You can do this, e.g. with Unit root test (like Dickey-Fuller) or Stationarity test (like KPSS).
Definition Unit root test:
$H_0:$ There is a unit root.
$H_1:$ There is no unit root. This implies in most cases stationarity.
Definition Stationarity test:
$H_0:$ There is stationarity.
$H_1:$ There is no stationarity.
What is the difference between a stationary test and a unit root test?
It the time-series really follows these patterns forecasting and predicting will be "easier from a statistical point of view", for example you can apply econometric models for forecasting like ARIMA or TBATS. My answer relates to univariate and also multivariate time series if you have cross-sectional data stationarity and unit roots are not common concepts.