It really puzzled me when people talked about using CNN for stock market prediction. CNN is for processing images. How can CNN be used for predicting the stock market? Surely we need LSTM for that, because it is a time series?

The key here is to recognise that time series can be viewed in polar coordinate, like this: (Ref #2 and #3)

Stock charts are time series, which is basically the price of the stock across time. This is in Cartesian coordinate, i.e. X and Y coordinate. A point in X and Y coordinate can be converted into polar coordinate and vice versa, like this: (Ref #4)

This way, the line in the x and y chart (such as time series) can be converted into a Polar Coordinate chart, like above. The reason we are converting it to Polar Coordinate is to make it easier to detect patterns or anomalies (Ref #5).

To identify the temporal correlation in different time intervals we look at the cosine of sum between each pair of points (Ref #6 and #7), like this:

The above matrix of cosine is called the Gramian Matrix.

To make it easier to visualise, we convert the Gramian Matrix into an image, like below left: (Ref #3)

The image on the left is a Gramian Angular Summation Field (GASF). If the Gramian Matrix uses sin instead of cos, and the operative is minus instead of plus, then the image is called a Gramian Angular Difference Field (GADF), like above right. Together, GASF and GADF are called GAF (Gramian Angular Field).

So why do we use GAF? What are the advantages? The first advantage is that GAF preserves temporal dependency. Time increases from the top left corner of the GAF image to the bottom right corner. Each element of the Gramian Matrix is a superposition or difference of directions with respect to the time difference between 2 points. Therefore GAF contains temporal correlations.

Second, the main diagonal in the Gramian Matrix contains the values with no time difference between 2 points. Meaning that the main diagonal contains the actual angular values. Using this main diagonal we can construct the time series of the features learned by the neural network (Ref 6# and #7).

Different colour schemes are used when creating GAF chart, but the common one is from blue to green to yellow to red. Blue for -1, green for 0, yellow for 0.3 and red for 1, like this: (Ref 6)

Once the time series become images, we can process them using CNN. But how do we use CNN to predict the stock prices? The idea is to take time series of thousands stocks and indices from various time periods, convert them into GAF images, and label each image with the percentage up or down the next day, like below.

We then train a CNN to classify those GAF images to predict which series will be up or down the next day and by how much (a regression exercise).

Secondly, for each of the stock chart we produce various different indicators such as Bollinger Bands, Exponential Moving Average, Ichimoku Cloud, etc. like below (Ref 15), and convert all of them to GAF images.

We put all these overlays together with the stock/index, forming a 3D image (dimensions: x = time, y = values, z = indicators. We use the same labels, which is the percentage up or down the next day, to train a CNN network using those 3D images and those labels. Now, we don’t only use the stock prices to predict the next day movement, but also the indicators.

Of course, we can use the conventional LSTM to do the same task, without converting them to the Polar Coordinate. But the point of this article is to use CNN for stock prediction.

I’ll finish with 2 more points:

- Apart from GAF there are other method for converting time series into images, for example Markov Transition Field (MTF, Ref 9) and Reference Plot (RP, Ref 10). We can use MTF and RP images (both the prices and the indicators) to predict the next day prices.
- There are other methods for using CNN to predict stock prices without involving images. The stock prices (and their indicators) remain as time series. See Ref 11 first, then 12 and 13. The time series is cut at different points and converted into matrix, like below.

If you Google “using CNN for predicting stock prices”, the chances are it is this matrix method that you will find, rather than using images. Because this matrix method uses X and y (input variable and target variable) then we can also use other ML algorithm including classical algorithms such as Linear Regression, Decision Trees, Random Forest, Support Vector Machines and Extreme Gradient Boosting.

The third method is using CNN-LSTM. In this method the local perception and weight sharing of CNN is used to reduce the number of parameters in the data, before the data is processed by LSTM (Ref 14).

So there you go, there are 3 ways of using CNN for predicting stock prices. The first one is using images (GAF, MTF, RP, etc), the second one is converting the time series into X and y matrix and the third one is by putting CNN in front of LSTM.

**References:**

- Encoding time series as images, Louis de Vitry (link).
- Convolutional Neural Network for stock trading using techincal indicators, Kumar Chandar S (link)
- Imaging time series for classification of EMI discharge sources, Imene Mitiche, Gordon Morison, Alan Nesbitt, Michael Hughes-Narborough, Brian G. Stewart, Philip Boreha (link)
- Keisan online calculator (link)
- Sensor classification using Convolutional Neural Network by encoding multivariate time series as two dimensional colored images, Chao-Lung Yang, Zhi-Xuan Chen, Chen-Yi Yang (link)
- Spatially Encoding Temporal Correlations to Classify Temporal Data Using Convolutional Neural Networks, Zhiguang Wang, Tim Oates (link)
- Imaging Time-Series to Improve Classification and Imputation, ZhiguangWang and Tim Oates (link)
- How to encode Time-Series into Images for Financial Forecasting using Convolutional Neural Networks, Claudio Mazzoni (link)
- Advanced visualization techniques for time series analysis, Michaël Hoarau (link)
- Financial Market Prediction Using Recurrence Plot and Convolutional Neural Network, Tameru Hailesilassie (link)
- How to Develop Convolutional Neural Network Models for Time Series Forecasting, Jason Brownlee (link)
- Using CNN for financial time series prediction, Jason Brownlee (link)
- CNNPred: CNN-based stock market prediction using several data sources, Ehsan Hoseinzade, Saman Haratizadeh (link)
- A CNN-LSTM-Based Model to Forecast Stock Prices Wenjie Lu, Jiazheng Li, Yifan Li, Aijun Sun, Jingyang Wang (link)
- StockCharts.com (link)

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