# Questions tagged [mean-reversion]

A mean reverting process is a process that, over time, tends to drift toward its long-term mean.

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### How to estimate the Mean reversion

I am looking for some insights and worked-out example on how exactly should I estimate the Mean reversion parameter of the One factor Hull White model This link suggests to fit some regression ...
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### What factors determine performance of mean-reversion strategy? What is the role of volatility?

I assume that P&L of mean-reversion strategy should depend on several factors. One important factor is optimal timing (optimal entry/exit points to open/close positions). This is quite intuitive. ...
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### Is it possible to discretize OU with a more general AR(p) / ARMA (p,q) models?

The discrete analogue of an OU process is a simple AR(1) model. More general AR(p) or ARMA(p,q) models can also be regarded as discrete analogues of an OU process? If so, which coefficients describe ...
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### What are best models to predict mean-reverting processes?

Surprisingly to me, I could not find any paper in the literature that discusses methods to predict a mean-reverting process. What are the best models to predict mean-reverting processes? Would also ...
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### Is there any advantage of constructing generalized (group) pairs trading strategy over ordinary pairs trading strategy?

Ordinary pairs trading is when we find asset (e.g., stock) $A$ and $B$ which prices are cointegrated. On the other hand, generalized (grouped) pairs trading strategy implies that we find cointegration ...
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### Mean reversion factor logic

I have a hard time understanding the caveats of mean reversion factor logic. Let's imagine a mean reverting process: $$dx_t = θ(μ−x_t)dt+e_t​$$ Where θ is the "mean reversion" coefficient, ...
1 vote
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### How find optimal entry/exit thresholds for a mean-reverting process?

Suppose we have $\{X_{t}\}$ mean-reverting process. The goal is to find optimal entry and exit thresholds which can maximize P&L of the trading strategy. I have 2 "empirical" approaches ...
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### Why does AR(1) model with a small coefficient exhibit faster mean-reversion than one with a greater coefficient (when |$\beta$|<1)? [closed]

Suppose we have two mean-reverting AR(1) models, given by $$X_{t}=\beta X_{t-1}+\epsilon_t,$$ where $|\beta|<1$. How fast series reverts to its mean is determined by the coefficient $\beta$. As far ...
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### Modeling mean-reversion for different volatility regimes

Motivation: Half-life (HL) period shows how long it takes for a mean-reverting process to return halfway to its mean after a deviation. Most commonly, an Ornstein–Uhlenbeck (OU) process is applied to ...
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### Interpretation and intuition behind half-life of a mean reverting process

I am struggling to understand the intuition and use of half-life period of a mean reverting process. According to definition, half-life period shows how long it takes for a time series to return ...
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### What is the common accepted/ best performed method to classify trends and mean-reversion for fixed peroid?

I have knew some strategies only work on trends peroid, and other only works on mean-reversion peroid. But I didn't find how to classify trends and mean-reversion. I wonder the best performed/verified ...
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I am slightly confused as to whether I should use price spread or ratio for mean reversion in pair trading. I have seen some work on testing stationarity for the price spread and then use the price ...
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### portfolio weights based on past returns

In the academic paper Industries and Stock Return Reversals by Hameed and Mian (JFQA,2015) (see picture below), the authors describe a trading strategy based on reversal, which essentially buys past ...
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### Setting up kalman filter on basket of multiple securities which are cointegrated

I want to use mean reversion trading strategy. I am able to find 3 stocks which are cointegrated on closing prices at daily level. Im curious on what's the trading strategy using kalman filter. I can ...
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### Determine Dependent Variable Product

Let's say I have three products that are correlated (e.g. AAPL, MSFT, and AMZN). I would like to construct a spread between these products and trade the mean-reverting spread. Specifically, sell the ...
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### Linear Regression Cointegration Strategy

When doing linear regression to figure out the hedge ratio for the cointegration relationship what does it mean if the residuals are stationary but end up looking like the price time series of y? How ...
1 vote
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### Converting Annual Vol to Instantaneous Vol with Mean Reversion [closed]

Options Pricing and Mean Reversion In the question above, in the accepted answer, the writer claims: "For instance with a 100% mean reversion a 20% historical annual standard deviation would ...
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### Generalizing a hidden semi-Markov model for trading

Taken from Wikipedia: A hidden semi-Markov model (HSMM) is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov rather than Markov. ...
319 views

### Why aren't the optimal entry/exit thresholds for OU pairs trading relatively invariant to shifts in the OU mean?

The optimal entry/exit thresholds for mean reversion trading (assuming an underlying Ornstein-Uhlenbeck (OU) process) is derived in the paper "Optimal Mean Reversion Trading with Transaction ...
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### StatArb : Fourier transform to find the perfect factor?

We have a basic mean reverting strategy. Given a bench of assets, we are looking for the best linear combination of them such as the resulting normalized time series would be noisy at high frequencies ...
1 vote
91 views

### How to predict a portfolio's reversion?

Sorry if this has been asked before. I've been baffled by a question I'm facing. Assuming I know there are some certain demands for some stocks in near future, and I put them in a basket as a ...
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### Trading based on the log return series

A common strategy in trading is to use a bollinger band system. Simply put, we bet on reversion to the mean and take the opposite trade to the current movement under the assumption a move is overdone. ...
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116 views

### Mean Reversion without Bollinger Band

What are the ways one can trade mean reversion apart from using Bollinger Bands?
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### Dumb question : under the assumption of the normal distribution and using log return stationarity

Under the assumption of the normal distribution, I'm trying to create a single stock mean reversion strategy. I took the log returns because they are stationary, I standardized them and used the ...
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### Why do I need fancy methods to calculate half-life of mean reversion?

I am investigating ways to calculate the mean reversion half life of a mean reverting series. I am encountering things like the Ornstein – Uhlenbeck Process and various types of regression to estimate ...
1 vote
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### Correlation between fundamental and market data

I got hold of a data set which contains fundamental data like analyst recommendations/revisions (consensus only) and I am trying to come up with an idea of how this could be used as a trading signal ...
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### Why is my mean-reversion half-life completely wrong?

I am using a couple of resources (here and here) to calculate the mean reversion half-life of a time series. This method of calculating it is also presented in Ernest Chan's Algorithmic Trading on ...
2k views

### How to incorporate momentum in Ornstein Uhlenbeck to capture overshooting in financial markets?

In modelling asset prices, it is a good idea to model it using a fair value or target price concept. Recently Carr & Prado explored this idea to find optimal stop loss/take profit levels when the ...
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### How to derive a pricing PDE for an asset that follows a mean-reverting process?

I want to derive a Black-Scholes type partial differential equation to price options on an asset that follows a mean-reverting process (Schwartz model). My attempt follows the methodology of deriving ...
839 views

I'm excited to ask my first question here! I'll try to describe the mean-reversion strategy with some background, then explain what I couldn't understand. The strategy is described in Earnest Chan's ...
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### The distribution of mean reversion time from the OU process

I was reading the paper Statistical Arbitrage in the US Equity Market and I couldn't understand the figure that plots the histogram of the empirical distribution of characteristic time to mean ...
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### Cointegration stationary test yields different results if the pairs are swapped

I've been backtesting on a spread mean reversion strategy on certain stock pairs. I observe the stationarity via scatterplot and plotting a histogram. Then I verify it using Augmented Dickey Fuller ...
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### Can one successfully daytrade 0dte options based on RSI?

I've been doing that manually for 2 months successfully (40% ROI) with SPX 0-1 DTE (Days To Expiration) options, both puts and calls. I might be just lucky so I purchased some data to do backtesting ...
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### pairs trading algorithm with returns

I'm having a difficulty grasping how to write a pair algorithm using returns instead of prices. With price differences, I have the mean difference over a long time period. When the current price ...
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### What the most general but precise description one can make about mean-reversion and momentum strategies?

Is there anything about this metaphor of momentum and mean-reversion in markets that is more subtle, more general. What factors are amenable to the interpretation? Are people almost always referring ...
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236 views

### What is a good way to think about and estimate VIX half life?

Would it make sense to run an AR(1) regression to estimate a beta and then estimate the half life as -ln(2)/beta?
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### Negative values in CIR model

I'm having difficulty understanding the well known property of the CIR model that it can't go below zero. Wikipedia says that this is because the random shock on the rate will grow very small as r ...
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### Mean-reverting backtest between index and components [closed]

I am a beginner with ETF replication: I have to make a code to make the value of my assets go back to the average of the index Eurostoxx 50 with a subset of components. I am not sure how to implement ...
277 views