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Sequence

As explained in Time Series Forecasting Using Foundation Models

Time-series data are observations indexed by time, often representing measurements collected sequentially.

Time-series data are sequential observations whose order carries meaning. A transformer converts the raw series into tokens, learns multidimensional embeddings, and adds positional encoding so repeated values remain distinguishable and future information does not leak into the past. section 1.2.1

Important implementation characteristics include:

  • Tokens may represent individual values or windows of values. section 1.2.1
  • Fixed sinusoidal positional encoding uses sine and cosine at different frequencies, matching the embedding dimensions. section 1.2.1
  • Domain diversity exposes forecasting models to different trends and seasonalities, while minimally processed data preserves noise and outliers. section 3.2.1

Temporal patterns

Hourly traffic can show daily and weekly seasonality, while daily weather can show yearly seasonality. These patterns illustrate why ordering and domain coverage matter. section 3.2.1

Figure 1.3 Visualizing the result of feeding a time series through an embedding layer. First, the input is tokenized, and an embedding is learned. The result is the abstract representation of the input made by the model.
A diagram of a person

Visualizes tokenization, learned embeddings, and the abstract representation passed onward. section 1.2.1

How Time Series Forecasting Using Foundation Models covers it

How deep it goes
Explains tokenization, embeddings, and positional encoding, but stops short of detailed forecasting procedures.
Examples
Uses hourly traffic with daily and weekly cycles and daily weather with yearly seasonality.
What it assumes
Assumes familiarity with sequential observations while teaching tokenization, embeddings, and positional encoding from their input role.
What you can do after
Evaluate how ordering, tokenization, positional information, and domain diversity affect time-series model inputs.
How it connects
Connects time-series data with transformers, embeddings, positional encoding, forecasting, trends, and seasonality.

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This explainer was generated by Manning's knowledge graph from the text of Time Series Forecasting Using Foundation Models. The section links point to the parts of the book it draws on.