causal-time-series 0.0.1

Python library for causal time series modeling

🧠 Causal Time Series (CTS)

Causal Time Series (CTS) is a Python library for modeling, simulating, and intervening in dynamic business systems using Dynamic DAGs and ODE-style causal updates.

It bridges causal inference, forecasting, and simulation, letting you answer “what if” questions such as:

“What if we increase marketing spend, lower price, or improve support response times — how does that affect revenue?”

---

🚀 Features

• 🕸️ Dynamic DAGs — define causal dependencies across time.
• ⚙️ Mechanism-based modeling — learn how each variable evolves.
• 💡 Interventions (Do operator) — simulate counterfactuals.
• 🔁 Forecasting & simulation — Euler-style integration through time.
• 🧮 Derived variables — define deterministic metrics (e.g., revenue = price × paying users).
• 📊 Pandas-first API — DataFrame in, DataFrame out.
• 🔍 Scikit-learn style — familiar fit(), forecast(), simulate(), plot() interface.

---

📦 Installation

pip install numpy pandas matplotlib scikit-learn

Then clone or copy this repository locally.

---

🧩 Example: Business Metrics Simulation

This demo models a subscription-based business with feedback between growth, churn, and monetization.

📊 Variables

Variable	Type	Description
marketing_spend	Lever	Daily advertising investment
new_users	Flow	New users acquired
churned_users	Flow	Users leaving the platform
active_users	Stock	Current engaged user base
support_tickets	State	Customer support volume
price	Lever	Subscription price
paying_users	State	Users converting to paid plans
revenue	Derived	price × paying_users
arpu	Derived	revenue / active_users

---

🧭 Quickstart

import pandas as pd
from cts import CausalDAG, CTSModel, Do
from cts.utils import business_dataset

# 1️⃣ Load synthetic data
df = business_dataset()

# 2️⃣ Define the causal DAG (no explicit revenue node)
dag = CausalDAG(
    nodes=['M','P','N','C','S','A','Pay'],
    edges=[
        ('M','M'), ('P','P'),           # persistence for levers
        ('M','N'),                      # marketing -> new users
        ('A','S'), ('S','C'),           # active -> tickets -> churn
        ('N','A'), ('C','A'),           # new adds, churn removes
        ('P','Pay'), ('A','Pay'),       # price & active -> paying users
        ('Pay','Pay'), ('S','S')        # persistence
    ],
    lag=1,
    rename={
        "M":"marketing_spend","P":"price","N":"new_users",
        "C":"churned_users","S":"support_tickets",
        "A":"active_users","Pay":"paying_users"
    }
)

# 3️⃣ Derived variables
derived = {
    "revenue": lambda s: s["price"] * s["paying_users"],
    "arpu": lambda s: s["revenue"] / (s["active_users"] + 1e-6)
}

# 4️⃣ Fit causal model
cts = CTSModel(dag, backend="ridge", derived=derived).fit(df)

cts.constraints = {
    "price": "nonnegative",
    "marketing_spend": "nonnegative",
    "paying_users": "nonnegative",
    "active_users": "nonnegative",
    "churned_users": "nonnegative"
}

# 5️⃣ Forecast baseline
forecast = cts.forecast(h=30)

# 6️⃣ Counterfactual: increase marketing
cf = cts.simulate(
    h=60,
    intervention=Do(shift={"marketing_spend": +50}, from_time=df.index[-1])
)

# 7️⃣ Visualize
cts.plot(df, forecast, cf, cols=["marketing_spend","price","paying_users","churned_users","revenue"])

---

🧠 Core Concepts

🕸️ Dynamic DAGs

Each edge expresses a temporal causal relationship:

X_{t−1} → Y_t

Variables evolve in time through their causal parents.

⚙️ Differential formulation

CTS learns: [ ΔX_t = f(\text{Parents}_{t−1}) + ε_t ] for each node, using Ridge regression by default (can be extended to Neural ODEs).

🧮 Derived Variables

Derived columns are deterministic functions of other state variables:

derived = {
    "revenue": lambda s: s["price"] * s["paying_users"],
    "arpu": lambda s: s["revenue"] / (s["active_users"] + 1e-6)
}

They are recomputed automatically after each forecast or simulation step.

🧩 Interventions

Simulate causal “what-if” changes:

# Increase marketing spend
Do(shift={'marketing_spend': +100}, from_time='2023-06-01')

# Fix a variable to constant value
Do(set={'price': 8.0}, from_time='2023-07-01')

---

📁 Repository Structure

cts/
  __init__.py
  dag.py
  core.py
  intervene.py
  models/
    __init__.py
    ridge_delta.py
  utils/
    __init__.py
    datasets.py
examples/
  demo_business.ipynb
main.py
README.md

---

👩‍💻 License

MIT License © 2025 Nick Gavriil

---

“Don’t just forecast the future — understand how your actions create it.”