Error can be additive or multiplicative.

Trend can be None, additive or Multiplicative.

Seasonality can be None, additive or multiplicative.

  1. Additive

    1. Changes stay constant over time

  2. Multiplicative

    1. Changes grow with the trend

  3. Types of models in ETS

    1. AAN: Additive Error, Additive Trend, No Seasonality.
    2. AAA: Additive Error, Additive Trend, Additive Seasonality.
    3. MAM: Multiplicative Error, Additive Trend, Multiplicative Seasonality.
    4. ANN: Additive Error, No Trend, Multiplicative Seasonality.

  4. Prophet divides the time series data into 3 parts

    1. Trends

    2. Seasonality

    3. Holiday or Events

    4. Formula of prophet

      $$ \text{Forecast = Trend + Seasonality + Holiday + Error} $$

    5. Parameters

      1. growth
        1. Controls the type of trend
        2. Default = “linear”
        3. Options:
          1. linear → straight line trend
          2. logistic →
      2. changepoints
        1. Prophet automatically detects moments when the trend changes (like a sharp increase/drop)
        2. You can add your own if you know what event happened.
      3. seasonality_mode
        1. Determines if seasonal pattern are constant or growth over time.
        2. Options
          1. Additive
          2. Multiplicative
      4. seasonality_prior_scale
        1. Controls how flexible the seasonality can be
        2. Higher = Prophet can twist the seasonal curve more.
      5. changepoint_prior_scale
        1. Controls how much Prophet is allowed to detect trend changes.
        2. Low value = smooth curve
        3. High value = very flexible trend
        4. Tune this if Prophet is too smooth or too jumpy.
      6. holidays
        1. You can pass a list of custom holidays or events.
        2. Prophet will learn how these days affect your data.
        3. Example: Diwali, Black Friday, Product Launches.
      7. weekly_seasonality, yearly_seasonality, daily_seasonality
        1. Set to True or False to include/exclude seasonal effect.