Stock Return Forecasting Based on the ARIMA Model

Abstract "Stock price forecasting is extremely difficult—especially forecasting into the future." Many of you have certainly heard this famous quote attributed to Danish physicist Niels Bohr. Stock price forecasting is the central theme of this blog post. In this article, we will discuss the popular ARIMA forecasting model for predicting stock returns and demonstrate a step-by-step ARIMA modeling process using R programming. What Is a Time Series Forecasting Model? Forecasting involves using historical data points of a variable to predict its future values—or, alternatively, predicting how one variable changes given changes in another variable. Forecasting methods fall broadly into two categories: qualitative and quantitative. Time series forecasting belongs to the quantitative category, where statistical principles and concepts are applied to a variable’s historical data to forecast its future values. Some commonly used time series forecasting techniques include: • Autoregressive (AR) models • Moving average (MA) models • Seasonal regression models • Distributed lag models What Is the ARIMA Model? ARIMA stands for AutoRegressive Integrated Moving Average. ARIMA is also known as the Box-Jenkins method. Box and Jenkins proposed that non-stationary data can be transformed into stationary data through differencing of the series, denoted Yₜ. The general model for Yₜ is written as: Yₜ = ϕ₁Yₜ₋₁ + ϕ₂Yₜ₋₂ + … + ϕₚYₜ₋ₚ + εₜ + θ₁εₜ₋₁ + θ₂εₜ₋₂ + … + θ_qεₜ₋q where Yₜ represents the differenced time series value; φ and θ are unknown parameters; and ε denotes zero-mean, independent and identically distributed (i.i.d.) error terms. Here, Yₜ is expressed in terms of its own past values as well as the current and past values of the error term. The ARIMA model integrates three fundamental components: 1. Autoregression (AR): In autoregression, the value of a time series is regressed on its own lagged values. The parameter "p" in ARIMA indicates the number of lagged values used. 2. Differencing (I—for Integrated): This involves differencing the time series data to remove trends and convert a non-stationary series into a stationary one. It is represented by the parameter "d" in ARIMA. If d = 1, it computes the difference between consecutive observations; if d = 2, it computes the difference of the first-differenced series, and so on. 3. Moving Average (MA): The moving average component of ARIMA is captured by the parameter "q", representing the number of lagged error terms included. This model is referred to as an ARIMA model for Yₜ—or more specifically, ARIMA(p, d, q). We will construct our model following the steps outlined below. Step 1: Test and Ensure Stationarity To build a time series model using the Box-Jenkins methodology, the series must be stationary. A stationary time series exhibits no trend, and its mean and variance remain constant over time—making forecasting more reliable. Stationarity Test: We use the Augmented Dickey-Fuller (ADF) unit root test to assess stationarity. The p-value obtained from the ADF test must be less than 0.05 (or 5%) for the time series to be considered stationary.

LSTM + Mean Reversion: A New Exploration in AI-Based Stock Prediction

import pandas as pd import numpy as np from sklearn.preprocessing import MinMaxScaler from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Dense, LSTM, Dropout import matplotlib.pyplot as plt # Load data def load_data(file_path): # Load data using Parquet format data = pd.read_parquet(file_path) return data # Feature engineering def prepare_features(data): # Select relevant features features = data[['Open', 'High', 'Low', 'Close', 'Volume']] # Add technical indicators # Calculate RSI (Relative Strength Index) delta = features['Close'].diff() gain = delta.where(delta > 0, 0) loss = -delta.where(delta < 0, 0) avg_gain = gain.rolling(window=14).mean() avg_loss = loss.rolling(window=14).mean() rs = avg_gain / avg_loss features['RSI'] = 100 - (100 / (1 + rs)) # Calculate moving averages features['SMA20'] = features['Close'].rolling(window=20).mean() features['EMA20'] = features['Close'].ewm(span=20, adjust=False).mean() # Calculate Bollinger Bands features['MA20'] = features['Close'].rolling(window=20).mean() features['20dSTD'] = features['Close'].rolling(window=20).std() features['Upper_Band'] = features['MA20'] + (features['20dSTD'] * 2)

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