Most data scientist working business-related time series are primarily working with non-continuous, or discrete, time-based processes. Operationally, it might be useful for businesses to know, or to be able to quantify when a time series will be at a peak or trough in the future. The goal is to capture the trend and periodic patterns and to forecast the signal for >1 sample in the future. The link to the example notebook is available in Tensorflow Formulation section of this post.
Trend, Periodicity, and Noise
In most business-related applications, the time series have a non-constant mean and variance over time, or they can be said to be non-stationary. This is contrasted to stationary signals and systems used in the analysis of electrical circuits, audio engineering, and communication systems. The direction in which the mean value changes indicates the trend of the time series. The variation of the noise could be a function of some random process. The noise can potentially increase or decrease as a function of time.
There is a granularity time limit to the which periodic, or recurring, patterns can be captured. In digital signal processing, the Nyquist’s rate is the minimum sampling period required to capture a pattern that reoccurs with period N. Essentially, the sampling rate needs to be less than half of one cycle of the recurring pattern. For example, let us say there is a feature in the data that measures the number of sales every 6 hours. The most granular pattern that can be captured will be one that reoccurs every 12 hours.