{% extends "backcast/base.html" %}
{% load humanize %}

{% block title %}Models · Backcast{% endblock %}

{% block content %}
<article class="prose">
  <h1>Models</h1>
  <p class="lede">
    {{ models|length|apnumber|capfirst }} models, from the benchmark itself to gradient-boosted trees. Each one turns a price history into a forecast
    path with an {{ level }}% interval, and none of them sees a price after the forecast date.
  </p>

  <dl class="model-list">
    {% for model in models %}
      <div>
        <dt><span class="model-name">{{ model.name }}</span> <span class="model-family">{{ model.family }}</span></dt>
        <dd>{{ model.summary }}</dd>
      </div>
    {% endfor %}
  </dl>

  <h2>Chronos-Bolt</h2>
  <p>
    Chronos-Bolt, Amazon's pretrained forecasting model, is an optional extra because it needs PyTorch. Install it
    with <code>uv sync --extra foundation</code> and it joins every backtest. It forecasts without being fitted to
    the stock: it learned from a large collection of other time series. It makes runs about three times as long.
  </p>

  <h2>Volatility</h2>
  <p>
    The volatility backtest forecasts how much the price will move over the next <var>h</var> trading days, in
    either direction: the variance of the <var>h</var>-day return. Naive here assumes the last month's volatility
    carries on.
  </p>
  <dl class="model-list">
    {% for model in volatility_models %}
      <div>
        <dt><span class="model-name">{{ model.name }}</span> <span class="model-family">{{ model.family }}</span></dt>
        <dd>{{ model.summary }}</dd>
      </div>
    {% endfor %}
  </dl>

  <h2>Adding a model</h2>
  <p>
    Subclass <code>Model</code> in <code>backcast/models.py</code>, return a <code>Forecast</code> with the median
    path and its quantiles from 10% to 90%, and add an instance to <code>MODELS</code>. The backtest, leaderboard and
    charts pick it up. Every forecast must be a positive price, with the quantiles in increasing order; working on
    log prices, as the models here do, guarantees both. A model that is slow to estimate can implement
    <code>fit</code> instead, which returns a forecaster that keeps its estimates between refits.
  </p>
<pre><code>class Average(Model):
    key, name, family = "average", "Historical average", "Baseline"
    summary = "Forecasts the average log price of the whole history."

    def forecast(self, y, h):
        log_y = np.log(y)
        median = np.full(h, np.exp(log_y.mean()))
        return Forecast(median, median * np.exp(Z * log_y.std(ddof=1)))  # Z: one row per forecast quantile</code></pre>
</article>
{% endblock %}