Mean Reversion in Time Series: What to Expecet and How to Find it

Mean Reversion in Time Series: What to Expecet and How to Find it

15 mins read

Mean reversion is one of the most commonly used statistical concepts in finance, where it’s known as regression to the mean. It describes the way that long-term averages tend to be pulled toward the center by short-term variations around that average. Lets see how the mean reverting process will work.

This process can be observed in time series data, whether it’s stock market returns or baseball player batting averages, so knowing how to find mean reversion can help you make more educated investment decisions and predictions about all kinds of phenomena.

What is Mean Reversion?

Mean-reversion or mean-reverting equation is a theory used in finance that suggests that asset price volatility and historical returns eventually return to their long-term averages, or average levels across data sets.
This average level can occur in a variety of situations. B. Economic growth, stock volatility, stock price/earnings ratio (P/E), or industry average return.


What is mean reversion? Simply put, it is the tendency of a time series to revert back to its mean value. This can be thought of as a pulling force that helps keep the time series in check. Mean reversion is a powerful concept that is widely used in financial analysis and trading.

In this blog post, we will discuss what mean reversion is, what causes it, and how you can identify it in time series data.

We will also touch on some real-world examples of how you might use this information in your own work. What Causes Mean Reversion? The cause of mean reversion is usually one or more periods where the time series behaves unusually.

For example, if there was a sudden spike in an otherwise steadily rising trend line then that could potentially lead to an exaggerated dip before returning to its original trajectory. Mean Reversion python how to do it.

The effects of these anomalous periods may not always be so dramatic but they are often enough to bring about at least some degree of mean reversion over time.How Do You Identify Mean Reversion?

The principle of mean reversion

Mean reversion is the principle that states that prices and returns eventually move back towards the mean or average.

This principle is based on the belief that markets are efficient and that prices are constantly adjusting to new information.

While mean reversion is a powerful tool, it’s not always easy to find. Here are a few tips for finding mean reversion opportunities using three simple steps: create an interval for the price of interest (e.g., $200-250), identify periods where there were large deviations from the price of interest and 3) examine these periods for trends that might suggest reversals (e.g., when selling volume exceeds buying volume).

For example, if you are interested in detecting possible mean reversion points within Bitcoin’s recent price trend, then you could set your interval as $2k-3k (to account for Bitcoin’s volatility).

You would then see that after a period of prolonged declines with little relief ($2k-1k), prices have been trending upward since early November 2018.

Since late December 2018, prices have reached nearly the highest levels observed since July 2014 at $4k+.

Note that this does not necessarily mean a reversal has occurred; instead, we should take notice of higher selling volumes versus buying volumes.

The time series plot below shows how volume was relatively high during most price drops but lower during increases in value.

If we keep this trend in mind and continue to monitor changes in these values over time, we may be able to detect whether Bitcoin will continue its bullish momentum or revert back to its previous state – another good reason to start learning about time series analysis!

Mean Reversion Model

Mean-reversion techniques operate under the premise that an asset’s price has an underlying, stable trend and that prices vary erratically around this trend. As a result, values that deviate significantly from the trend have a tendency to change course and return to the trend. That example, if the value is abnormally high, we anticipate it to decline, and if it is unusually low, we anticipate it to increase.

Time-series analysis raises a number of fundamental queries, including:

How can we simulate trends? How can we forecast a time series’ future value using its historical values? How can seasonality be modelled? How can we select the best time-series model? And how do we account for variations in time series variance throughout the course of time? In this reading, we address each of these concerns.
If all three of the following three criteria are met, a time series is covariance stationary:

The time series’ anticipated value must, first and foremost, be constant and finite throughout.

Second, the time series’ variance needs to be steady and limited throughout.

Third, the time series’ covariance with itself across a predetermined number of previous periods.

Outline of the procedure

Mean reversion is the tendency of a time series to revert back to its mean over time. This can be caused by a variety of factors, including seasonal cycles, economic cycles, and random fluctuations.

You can test for mean reversion using a variety of statistical tests, including the Augmented Dickey-Fuller test, the Phillips-Perron test, and the KPSS test.

If you find evidence of mean reversion, you can then try to trade on it by buying when the price is below the mean and selling when it is above the mean.

A strong indicator that a stock is following the normal distribution is that there are few outliers or extreme observations on either end of the distribution curve. One way to identify this pattern is with a Pareto chart, which plots an observation’s rank against its frequency.

The majority of points should cluster around the median value (inclusive) and not show any significant deviation from it.

For example, here’s a sample pareto chart from Yahoo Finance for Intel Corporation (INTC). As you can see, the data shows that about 80% of Intel’s daily closing prices are within $0.50 of $37.89 — the median point on the x-axis — and most values fall between $35 and $40.

There is little variance from these two intervals, so we might conclude that INTC follows a normal distribution


One example of mean reversion is the stock market. Over time, the stock market has a tendency to move back towards the mean, or average, level.

Another example is interest rates. When rates are low, there is often an expectation that they will eventually rise back up.

A third example is home prices. After a period of rapid appreciation, prices will often soften and return closer to their long-term average levels.

Mean reversion can also be seen in economic data such as gross domestic product (GDP).

In general, any time series that exhibits periods of extreme values followed by periods of more moderate values is likely exhibiting some degree of mean reversion.

Examples include fluctuations in unemployment rates, changes in consumer confidence, changes in jobless claims, fluctuations in export prices and many others. To see if a time series is exhibiting mean reversion, you need to compare the recent values with past ones and look for signs of coming back towards what would be considered normal for that series.

For instance, looking at unemployment rates you might notice that monthly rates have been steadily increasing from five percent over the last year until it reached six percent this month.

The next few months may not show similar increases, which could suggest that we’re seeing mean reversion rather than just continued trend upwards.

Technical Indicators using Mean Reversion:

Technical Indicators are also thrive on this basic mean reversion time strategy which they use it to make good prediction while trading.

  1. Moving Average
  2. RSI
  3. Bollinger Bands

Moving Average:

A moving average is a technical indicator that is frequently used with time series data to lessen transient data variation and smooth out short-term oscillations.

Simple Moving Average, Exponential Moving Average, and Weighted Moving Average are the three most widely used types of moving averages for the analysis of market data.

Simply said, the moving average, also known as rolling average, is the mean or average of the specified data field across a specific range of subsequent periods.

The mean of the data is calculated by subtracting the oldest value and adding the most recent when new data becomes available. The name “Moving Average” comes from the fact that the mean or average is essentially moving along with the data.

RSI ( Relative Strength Index ):

A momentum oscillator called the relative strength index can detect overbought and oversold market circumstances.

It oscillates between 0 and 100, and values below a particular value—typically 30, which denotes oversold conditions—indicate overbought ones. Values beyond a given value, such as 70, denote overbought conditions.

Its calculation typically takes a look back period of 14 days, however this can be adjusted to meet the characteristics of a certain asset or trading strategy.

The following steps are involved in RSI calculation:

Average Gain is equal to (prior average gain multiplied by 13 plus current gain)/14.
First average gain equals the 14-day rolling average of gains

Average Loss is equal to (prior average loss times 13 plus current loss) / 14.
First average loss equals the 14-day total of losses divided by 14.

Bollinger Bands :

The Bollinger Band is a three-part oscillator that is based on volatility or standard deviation. The other two bands are predetermined distances from the moving average, typically two standard deviations apart from the middle band, which is a moving average.

You can also surf ‘How to test for mean reversion in excel’ which is a big topic to cover and it will give you a out line of Bollinger bands.

The distance between the bands varies along with the volatility of stock prices. The gap increases in highly volatile market conditions, whereas it decreases in low volatility situations.

The following computations are involved with Bollinger bands:

Moving average or middle band: 20 day moving average
Upper Band: Middle Band plus two times the 20-day moving average
Lower Band: Two times the 20-day moving standard deviation of the middle band


Mean reversion is a powerful tool that can help you make better investment decisions. By understanding what it is and how to find it, you can improve your chances of success. Just remember that mean reversion is not always reliable, so be sure to do your own research before making any decisions.

I hope this post was helpful! If you found anything confusing or want more information on anything, let me know in the comments below. Mean reverting formula is used in many quant firm.

If there are other topics related to finance that you would like me to write about, let me know as well! And if you enjoyed reading this blog post, don’t forget to share it with your friends using the buttons below.

Also feel free to connect with me on social media for more insights into finance and investing! You can find me on Twitter at @sagewhiz.

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