tradeflow 1.2.0

A package to simulate autocorrelated time series of signs

As stated in the book Trades, Quotes and Prices: Financial Markets Under the Microscope by Bouchaud et al. [1, Chapter 10]:

"The signs of arriving market orders have long-range autocorrelations."

tradeflow is a Python package for fitting and simulating autocorrelated time series of signs.

Features

• Fit autoregressive (AR) models to time series of signs:
  • Automatic model order selection using the Partial Autocorrelation Function (PACF)
  • Parameter estimation methods: Yule-Walker equations, Maximum Likelihood Estimation, and Burg's method
• Simulate autocorrelated sign sequences from fitted models
• Summarize simulations by comparing original and simulated time series:
  • Plot the Autocorrelation Function (ACF) and the Partial Autocorrelation Function (PACF)
  • Compute the proportion of buy signs ($+1$)
  • Compute descriptive statistics on consecutive sign runs (mean, standard deviation, percentiles)
• Perform statistical tests:
  • Augmented Dickey-Fuller (ADF) test for time series stationarity
  • Breusch-Godfrey test for residual autocorrelation

Usage

Fit an autoregressive model to a time series of signs (e.g., [1, 1, -1, -1, 1, -1, 1, 1, 1, 1, ...]):

from tradeflow import AR

ar_model = AR(signs=signs, max_order=50, order_selection_method='pacf')
ar_model.fit(method="yule_walker", check_stationarity=True, check_residuals_not_autocorrelated=True)

Simulate an autocorrelated time series of signs from the fitted AR model:

ar_model.simulate(size=10_000)
# [1, -1, 1, 1, 1, 1, -1, -1, 1, 1, ...]

Compare the ACF and PACF of the original and simulated time series:

ar_model.simulation_summary(plot_acf=True, plot_pacf=False)

Installation

tradeflow can be installed with pip:

pip install tradeflow

Documentation

Read the full documentation here.

Background

This package is inspired by the book Trades, Quotes and Prices: Financial Markets Under the Microscope by Bouchaud et al. [1, Chapters 10 and 13].

The book discusses the highly persistent nature of the sequence of binary variables $\epsilon_t$ that describe the direction of market orders. That is, buy orders ($\epsilon_t = +1$) tend to follow other buy orders, and sell orders ($\epsilon_t = -1$) tend to follow other sell orders, often for very long periods.

We assume that the time series of signs $\epsilon_t$ is well modelled by a discrete autoregressive process of order $p > 0$. In this framework, the best predictor of the next market order sign (just before it occurs) is a linear combination of the past signs:

\hat{\epsilon}_t = \sum_{k=1}^{p} \mathbb{K}(k) \epsilon_{t-k}

Here, $\mathbb{K}(k)$ can be inferred from the sign autocorrelation function using the Yule-Walker equations. $p$ determines how many past signs are used ($\forall \ell > p, \mathbb{K}(\ell) \approx 0$).

As a result, the probability that the next sign is $\epsilon_t$ is:

\mathbb{P}_{t-1}(\epsilon_t) = \frac{1 + \epsilon_t \hat{\epsilon}_t}{2}

References

[1] Bouchaud J-P, Bonart J, Donier J, Gould M. Trades, Quotes and Prices: Financial Markets Under the Microscope. Cambridge University Press; 2018.