Pairs Trading with Nonlinear and Non-Gaussian State Space Models
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Quant Buffet native backtest IDEEdit and run Quant Buffet Python for Pairs Trading with Nonlinear and Non-Gaussian State Space Models in the browser. Results update live with equity, drawdown, and metrics charts. Allowed: backtest.data, backtest.engine, backtest.metrics, numpy, pandas. Define ASSETS and make_on_day(prices). Shortcut: Ctrl+Enter. API docs →
Quant Buffet syntax cheat sheet (copy / insert)
Paste these fragments into the editor. The sandbox rejects QuantConnect, os, and network libraries.
from __future__ import annotations
import numpy as np
import pandas as pd
from backtest.data import load_daily_prices
from backtest.engine import EngineConfig, PortfolioEngine
from backtest.metrics import compute_metricsASSETS = ["SPY", "QQQ", "TLT", "GLD", "BIL"]def make_on_day(prices: pd.DataFrame):
cols = [c for c in ASSETS if c in prices.columns]
sma = prices[cols].rolling(200, min_periods=200).mean()
state = {"last": None}
def on_day(engine: PortfolioEngine, dt: pd.Timestamp) -> None:
if sma.loc[dt].isna().all():
return
key = (dt.year, dt.month)
if state["last"] == key:
return
state["last"] = key
long = [
s for s in cols
if pd.notna(prices.at[dt, s]) and pd.notna(sma.at[dt, s])
and prices.at[dt, s] > sma.at[dt, s]
]
weights = {} if not long else {s: 1.0 / len(long) for s in long}
engine.set_target_weights(dt, weights)
ready = sma.dropna(how="all").index.min() if sma.notna().any().any() else None
return on_day, readyengine.set_target_weights(dt, {"SPY": 0.60, "BIL": 0.40})Live backtest performance
Accent = strategy · dashed grey = buy-and-hold benchmark
Export to your platform
Transform Quant Buffet lab code (ASSETS + make_on_day / PortfolioEngine) into native classes for a third-party IDE — then copy and paste.
# Generated from Quant Buffet → QuantConnect LEAN
# Strategy: Pairs Trading with Nonlinear and Non-Gaussian State Space Models
# Detected pattern: Mean reversion
# Source uses Quant Buffet lab APIs (ASSETS + make_on_day / PortfolioEngine).
# Review fees, data, and risk before live trading — educational export only.
from AlgorithmImports import *
class QuantBuffetExport(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2010, 1, 1)
self.SetCash(100000)
tickers = ["SPY", "TLT", "GLD", "BIL"]
self.symbols = []
for t in tickers:
if "-" in t: # crypto proxy e.g. BTC-USD
self.symbols.append(self.AddCrypto(t.replace("-USD", ""), Resolution.Daily).Symbol)
else:
self.symbols.append(self.AddEquity(t, Resolution.Daily).Symbol)
self.Schedule.On(
self.DateRules.MonthStart(self.symbols[0]),
self.TimeRules.AfterMarketOpen(self.symbols[0], 30),
self.Rebalance,
)
# Logic: Buy when return z-score < -1 over 20 days.
def Rebalance(self):
import numpy as np
picks = []
for symbol in self.symbols:
hist = self.History(symbol, 20 + 5, Resolution.Daily)
if hist.empty: continue
close = hist["close"]
if hasattr(close, "unstack"):
close = close.unstack(level=0).iloc[:, 0]
rets = close.pct_change().dropna()
if len(rets) < 20: continue
window = rets.iloc[-20:]
z = (window.iloc[-1] - window.mean()) / (window.std() or 1e-9)
if z < -1:
picks.append(symbol)
w = 1.0 / len(picks) if picks else 0.0
for symbol in self.symbols:
self.SetHoldings(symbol, w if symbol in picks else 0.0)
Exported code uses the platform’s native classes and libraries. Install dependencies in your third-party IDE, then run. Validate before live trading.
Academic paper
Teaser
Enter when short-horizon z-score is deeply negative; exit near zero. Universe: EWT, EWH. Parameters: lookback=20; entry_z=-1.0; exit_z=0.0; rebalance=daily. Rebalanced on the engine's template schedule with 5 bps commission and 2 bps slippage.
Strategy in a nutshell
This paper studies pairs trading using a nonlinear and non-Gaussian state-space model framework. We model the spread between the prices of two assets as an unobservable state variable and assume that it follows a mean-reverting process. This new model has two distinctive features: (1) The innovations to the spread is non-Gaussianity and heteroskedastic. (2) The mean reversion of the spread is nonlinear. We show how to use the filtered spread as the trading indicator to carry out statistical arbitrage. We also propose a new trading strategy and present a Monte Carlo based approach to select the optimal trading rule. As the first empirical application, we apply the new model and the new trading strategy to two examples: PEP vs KO and EWT vs EWH. The results show that the new approach can ach
Economic rationale
Short-horizon overreaction produces temporary dislocations that reverse toward a local mean. Related evidence from “Pairs Trading with Nonlinear and Non-Gaussian State Space Models”: This paper studies pairs trading using a nonlinear and non-Gaussian state-space model framework. We model the spread between the prices of two assets as an unobservable state variable and assume that it follows a mean-reverting process. This new model has two distinctive features: (1) The innovations to the spread is non-Gaussianity and heteroskedastic. (2) The mean reversion of the spread is nonlinear. We show how to use the filtered spread as the trading indicator to carry out statistical arbi