# Neural network stock market predictions in further future (>1day) approach an exponential behavior

I want to predict the trend of a specific stock using neural networks in PyTorch. I followed a guide¹ to learn about the basic structures of a program of that type. This guide, however, only works on single-day predictions based on the stock values of x past day (lookback).

My aim was to see if the predictions could be made further into the future, so past single-day prediction. Therefore, I modified the program to make recursive predictions, based on previously predicted values by the neural network. Essentially I started off by making a one-day prediction, appended the value into the lookback array from which the previous prediction was made, and made a new prediction for the second day, using the predicted value from day one and the given values from the previous days.

The program itself runs fine, however the predicted values seem to approach a certain value. Graphing the predicted values shows an exponential graph (see image below).

I am looking for either explanations of why this behavior is observed and/or proposals for a better algorithm of predicting values into the future past one day. It is highly possible that I made some obvious logical mistake, as this is all new territory for me.

NOTE

I am working with datasets provided by AlphaVantage. The stock dataset used in the example is the AMZN stock.

Code

import os
import numpy as np
import pandas as pd
import matplotlib.pyplot as plot
from sklearn.preprocessing import MinMaxScaler
import torch
import torch.nn as nn
import math
import time
import datetime

# ALGORITHM FOR FUTURE PREDICTIONS (this is where the issue lies)
def forward_future(model, mse, past, length):
results = np.zeros(length)
approach = past

for i in range(length):
pred_y = model(approach)
approach = torch.cat((approach, pred_y.unsqueeze(2)), dim=1)
#approach = torch.from_numpy(np.append(approach[:, 1:, :].detach().numpy(), pred_y.detach().numpy()[np.newaxis, :, :], axis=1)).type(torch.Tensor)
results[i] = pred_y

return results

# CONSTS
PATH_FILES = os.path.join(os.path.dirname(os.path.abspath(__file__)), "stockdata/raw")
FILE  = "stock_AMZN.csv"
PATH = os.path.join(PATH_FILES, FILE)
lookback = 20

# DATA PROCESSING
df = pd.read_csv(PATH, lineterminator="|", usecols=["timestamp", "open", "high", "low", "close", "volume"]).sort_values("timestamp")[1:]

dates = df.loc[:, "timestamp"].to_numpy()

p_HIGH = df.loc[:, "high"].to_numpy()
p_LOW = df.loc[:, "low"].to_numpy()
p_MID = (p_HIGH + p_LOW) / 2.0

scaler = MinMaxScaler(feature_range=(-1, 1))
p_MID = scaler.fit_transform(pd.Series(p_MID).values.reshape(-1, 1))

# PREPARING DATA
def split(price, lookback):
d_RAW = price
d_CLEAN = []

for i in range(len(d_RAW) - lookback):
d_CLEAN.append(d_RAW[i: i + lookback])

d_CLEAN = np.array(d_CLEAN)
s_TRAIN_size = d_CLEAN.shape[0]

s_TRAIN_x = d_CLEAN[:s_TRAIN_size,:-1:]
s_TRAIN_y = d_CLEAN[:s_TRAIN_size, -1,:]

s_PRED = s_TRAIN_x[-1]
s_PRED = s_PRED[np.newaxis, :, :]

return [s_TRAIN_x, s_TRAIN_y, s_PRED]

s_TRAIN_x, s_TRAIN_y, s_PRED = split(p_MID, lookback)

s_TRAIN_x = torch.from_numpy(s_TRAIN_x).type(torch.Tensor)
s_TRAIN_y = torch.from_numpy(s_TRAIN_y).type(torch.Tensor)

s_PRED = torch.from_numpy(s_PRED).type(torch.Tensor)

# DEFINITION OF THE NEURAL NETWORK
dim_INPUT = 1
dim_HIDDEN = 32
dim_OUTPUT = 1
lay_NUM = 2
epo_NUM = 100

class GRU(nn.Module):
def __init__(self, dim_INPUT, dim_HIDDEN, lay_NUM, dim_OUTPUT):
super(GRU, self).__init__()
self.dim_HIDDEN = dim_HIDDEN
self.lay_NUM = lay_NUM

self.gru = nn.GRU(dim_INPUT, dim_HIDDEN, lay_NUM, batch_first = True)
self.fc = nn.Linear(dim_HIDDEN, dim_OUTPUT)
def forward(self, x):
out, (hn) = self.gru(x, (h0.detach()))
out = self.fc(out[:, -1, :])
return out

model = GRU(dim_INPUT = dim_INPUT, dim_HIDDEN = dim_HIDDEN, dim_OUTPUT = dim_OUTPUT, lay_NUM = lay_NUM)
criterion = torch.nn.MSELoss(reduction = "mean")
optimiser = torch.optim.Adam(model.parameters(), lr = 0.01)

# TRAINING
hist = np.zeros(epo_NUM)
t_initial = time.time()

for t in range(epo_NUM):
pred_TRAIN_y = model(s_TRAIN_x)
print(pred_TRAIN_y)

loss = criterion(pred_TRAIN_y, s_TRAIN_y)
print("Epoch %s\nMSE: %s"%(str(t), str(loss.item())))
hist[t] = loss.item()

loss.backward()
optimiser.step()

t_delta = time.time() - t_initial
print("Training Time: {}".format(t_delta))

# CALL TO MAKE FUTURE PREDICTIONS
prediction_size = 30
predictions = forward_future(model, hist[-1], s_PRED, prediction_size)

prediction_plot_x = range(len(p_MID) - prediction_size, len(p_MID))

# PREPARATION FOR PLOTTING
vfunc = np.vectorize(lambda x: round(x, 3))
p_MID = scaler.inverse_transform(p_MID)
predictions = scaler.inverse_transform(predictions[:, np.newaxis])

# PLOTTING
fig, (ax1, ax2) = plot.subplots(2)

ax1.plot(range(len(p_MID)), p_MID, color="blue", label="True")
ax1.plot(prediction_plot_x, predictions, color="green", label="Predictions")
plot.sca(ax1)
plot.xticks(range(len(p_MID)), dates, rotation="vertical")
plot.setp(ax1.get_xticklabels()[::1], visible=False)
ax1.grid(False)
ax1.legend()

ax2.plot(range(epo_NUM), hist)
ax2.set_ylabel("Loss")
ax2.set_xlabel("Epochs")
ax2.grid()
plot.show()


References

¹ Stock Price Prediction with PyTorch, Medium, https://medium.com/swlh/stock-price-prediction-with-pytorch-37f52ae84632

Disclaimer: I'm not at all expert in predicting stock market.

The error between the actual and the true evolution might simply be caused by the fact that the model is reproducing a pattern it observed in the past data: if in the past a small plateau was more often followed by a progressive decrease, then it makes sense to predict a decrease. This might include some level of overfitting, for example if the model relies on some very specific indication (e.g. "the value has oscillated between 3143.6 and 2159.7 during 9 days") to make its prediction.

More generally at a semantic level I'm not surprised that this doesn't work very well: I would be very skeptical of any attempt to predict a stock market value based solely on the past performance of this value. A stock market value doesn't only depend on its past evolution, it depends on many external factors such as the general economic context, the market of the company, its strategy, and various other general news that can affect the value. Doing this is like trying to predict somebody's life expectancy knowing only their age: sure there's a good chance that they will still be alive the next day, but no long term prediction can be made without taking into account their health, lifestyle, wealth, environment, etc. There's no magic, a ML model needs reliable indicators in order to make reliable predictions.

• I appreciate the answer! While I am aware that a prediction of a stock price based solely on historical data is extremely primitive and inaccurate, the project I am working on is set out to test exactly that. We tried to see how well the trend of a stock can be predicted only by its numerical data. While what you're saying makes sense, it does not quite explain the near perfect exponential function that is formed by the results, which is the part I am confused about. I am hereby assuming that this is not the standard behavior it was taught during the training process of the neural network. Apr 21 at 21:56
• @bezunyl maybe it would be interesting to try training the model while slightly changing the date where the split between training/test data is. this would show how much the model is affected by a small difference. Apr 22 at 8:31
• That is what I initially did while following the cited guide. The results of which were fairly interesting, especially when working with the AMZN stock, which, due to COVID-19, experienced a large boom in the last year. When excluding the last ~1.5 years from the training set, the predictions are made heavily below the real value, as the "boom" was an unforeseeable event. With my self-designed algorithm, however, the predictions just adapt other weird exponential-like behaviors when I change the split between training and test data. Apr 22 at 12:32

I've seen this behavior when using a CNN model trained on less than 50 epochs. Assuming training time is not the issue, try predicting several days out (as a vector of sequential future prices). This exercise alone will reveal any bugs in your script, as it will become apparent the output is completely wrong.

Looking at your code, in your training forward() function, I'm suspicious of h0 = torch.zeros() - basically you are feeding the network zeros as input, no wonder it outputs values that are smaller and smaller. Layer zeroing usually happens once outside of the forward() function, not every iteration.