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):
        h0 = torch.zeros(self.lay_NUM, x.size(0), self.dim_HIDDEN).requires_grad_()
        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 %snMSE: %s"%(str(t), str(loss.item())))
    hist[t] = loss.item()

    optimiser.zero_grad()
    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