# Kalman Filter Trading Strategy – Rules, Python Backtest, Setup, Results

Just as traders use technical indicators to attempt to predict the future direction of an asset, quantitative analysts also utilize various statistical and mathematical models to forecast the future values of assets, with one of these models being the Kalman Filter. What is the Kalman Filter trading strategy?

The Kalman Filter is a mathematical algorithm used for estimating and forecasting the underlying trends or values of financial variables based on observed market data. It helps filter out noise and provide more accurate estimates of asset prices, returns, volatility, and other financial metrics. something this filter tries to do.

In this article, we will look at the Kalman Filter and show you how to calculate it and backtest a trading strategy using it.

## What is the Kalman Filter?

Imagine you’re trying to keep track of the position of a moving object, like a car. You have some sensors, like a GPS and a speedometer, that give you measurements of the car’s position and speed, but these measurements aren’t perfect – they might have some errors.

The Kalman filter is like a smart tool that helps you combine these imperfect measurements with your best estimate of the car’s position and speed. At least that’s the idea behind the filter. It takes into account both the measurements and your predictions to give you a more accurate and smooth estimate of where the car actually is and how fast it’s going. Keep reading and we’ll find out if the Kalman Filter lives up to its expectations.

## How to calculate the Kalman Filter?

The calculation of the Kalman filter is composed of 4 steps (we will continue to use the example of the car):

Prediction: First, you use your previous estimate of the car’s position and speed to predict where you think the car will be next. This prediction takes into account things like its current speed and direction.

Measurement: Then, you get new measurements from your sensors – the GPS and speedometer. These measurements might have errors, but they still give you some information about where the car could be.

Correction: The Kalman filter aims to figure out how much to trust your prediction and how much to trust the measurements. It calculates a weighted average between your prediction and the measurements, giving more weight to the one that’s more reliable. This way, if the measurements are really accurate, it leans more towards them. But if they’re not so accurate, it relies more on your prediction.

Update: After combining the prediction and measurements, you get a new and improved estimate of the car’s position and speed. This new estimate becomes the basis for the next round of predictions and corrections as the car continues to move.

We won’t go into detail about how to calculate it mathematically, given that it is a long process that involves many formulas. Instead, we are going to jump right into developing and backtesting a trading strategy with it.

The trading strategy we are going to backtest is relatively simple:

• We buy when the 5-day simple moving average of the asset crosses under the Kalman filter.
• We sell when the 5-day simple moving average of the asset crosses above the Kalman filter.

The strategy is mean reversion reversion in nature. Here is how the 5-day SMA and Kalman filter look on a chart:

We found that using the 5-day SMA performed best (using just the closing price). Note that if we make the SMA slower, the performance decreases.

## Kalman Filter strategy – backtest

We backtested the strategy using the ETF version of the S&P 500, SPY, since its inception, using Python. The data is adjusted for dividends.

Here is the equity curve:

Here are some performance metrics and statistics about the Kalman Filter strategy:

• CAGR is 6.33% (buy and hold 9.76%)
• Time spent in the market is 35.38%
• Risk-adjusted return is 17.80% (CAGR divided by time spent in the market)
• Maximum drawdown is -41.35% (-55.19%)

The strategy does relatively well, given that it is invested only â…“ of the time.

## Kalman Filter strategy – conclusion

To sum up, today, you learned what the Kalman filter is, and we developed a trading strategy with it.

Although it does not perform spectacularly, the returns are okay and it would probably do much better if we paired it up with another indicator. Finally, although the Kalman Filter may seem complex and difficult to understand, implementing it in your trading system can step up your algorithms.