The Nature of Sequential and Time-Series Data
Unlike static data points, time-series and sequential data contain order-dependent patterns. The value of a data point is conditioned on the history of previous points, which requires models capable of maintaining temporal memory.
Sequential Data Properties
Sequential data appears in text sentences, audio clips, and time-series recordings. These sequences are characterized by temporal dependencies and variable lengths.
Autoregressive Properties
Sequences are autoregressive: future elements depend on past elements. In language, the meaning of a word depends on the preceding words. In finance, stock prices exhibit temporal momentum and mean reversion patterns.
Variable Lengths
Unlike images (which can be resized to a fixed grid), text sentences and audio clips naturally vary in length. Models must be flexible enough to ingest variable-length inputs without padding distortions.
Time-Series Components
Time-series data is a specific subset of sequential data measured at regular intervals, consisting of trend, seasonality, and stationarity features.
Trend, Seasonality, and Noise
Time-series data can be decomposed into: a long-term upward/downward movement (trend), periodic repeating patterns (seasonality, like energy usage peaks in summer), and random fluctuations (noise).
Stationary vs. Non-Stationary
A time series is stationary if its statistical properties (mean, variance) remain constant over time. Non-stationary data is difficult to model because patterns change. We convert non-stationary series using differencing: y'_t = y_t - y_{t-1}.