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.

链接地址：https://towardsdatascience.com/deep-autoregressive-models-41b21c8a140c