Trends are the most powerful force in the markets.

Buy low and sell higher and higher.

There are many ways to model trends, but they all come down to the same idea.

From a time series perspective, that idea is that price changes are correlated with price changes in past periods—also known as lags.

And what tool do we have to measure the correlation of price changes with price changes in past periods?

Autocorrelation.

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A super simple way to find a trend

Traders and analysts use autocorrelation to predict future market movements by measuring the similarity between a time series and its lagged version.

Autocorrelation involves collecting historical price data, selecting a time lag, and calculating the autocorrelation coefficient.

This coefficient, which ranges from -1 to 1, indicates whether trends will continue or reverse.

Positive values suggest a continuing trend, while negative values indicate potential market reversals.

Professionals use autocorrelation to enhance technical analysis, combining it with other indicators like moving averages. It's particularly valuable in momentum-driven or volatile markets, where understanding trends can lead to profitable trades.

Advanced techniques like partial autocorrelation and spectral analysis provide deeper insights, while resources such as textbooks and online courses offer further learning opportunities.

Let's see how it works with Python.

Imports and set up

We will import the libraries needed to fetch financial data and perform time series analysis.

The first import is yfinance, which allows us to download historical market data. The second import is statsmodels.graphics.tsaplots, which provides functions to plot autocorrelation functions.

1import yfinance as yf
2from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
3
4
5prices = yf.download("ES=F", start="2022-01-01", interval="1mo")
6returns = prices.Close.pct_change().dropna()

Visualize the autocorrelation and partial autocorrelation of returns

We will create plots to visualize the autocorrelation and partial autocorrelation of the returns. These plots help us understand the relationship between the returns at different time lags.

1plot_acf(returns, lags=12);

The result is a plot that looks like this.

The `plot_acf` function generates a plot of the autocorrelation function for the returns.

The plot shows how the returns are correlated with their own past values at different lags, up to 12 months.

Each vertical bar represents the correlation at a specific lag, and the shaded area indicates the confidence interval.

If a bar extends beyond the shaded area, it suggests a statistically significant correlation at that lag.

This helps in identifying any patterns or dependencies in the return series.

Let's generate a plot of partial autocorrelation.

1plot_pacf(returns, lags=12);

The result is a plot that looks like this.

The `plot_pacf` function generates a plot of the partial autocorrelation function for the returns.

This plot shows the direct correlation between the returns and their lagged values, excluding the influence of intermediate lags.

Like the autocorrelation plot, the partial autocorrelation plot includes bars for each lag and shaded confidence intervals.

By examining these plots, we can identify significant autoregressive patterns that might be useful for modeling and forecasting future returns.

Your next steps

Try experimenting with different ticker symbols to analyze other financial instruments. Change the start date or interval to explore how different time frames affect the autocorrelation patterns. You can also extend the lag length to see if longer periods reveal more insights into the data's behavior.