Time series forecasting is crucial for a myriad of applications. It’s essential for predicting stock market trends, product demand, or weather forecasts, where accurate predictions are vital for strategic decision-making. Over time, numerous modeling techniques have been developed to address the complexities of time series data. Notably, linear regression and XGBoost have emerged as prevalent methods.

Linear regression, a straightforward yet powerful technique, is extensively utilized in time series prediction. Conversely, XGBoost, an advanced ensemble learning algorithm, is celebrated for its superior predictive capabilities.

This article explores time series prediction by leveraging the advantages of both linear regression and XGBoost. We aim to devise a composite model that combines linear regression’s simplicity with XGBoost’s predictive efficiency, offering precise, reliable, and interpretable predictions for time series data.

**Introduction to XGBoost Regression**

Consider the analogy of solving a sophisticated puzzle, where each piece represents a solution fragment. XGBoost operates similarly to a team of specialists, each proficient in a specific piece type, collaborating to piece the puzzle together. The essence of the algorithm is to enhance or ‘boost’ a model’s performance. It begins with a fundamental model, such as a decision tree, and incrementally refines it.

XGBoost meticulously focuses on its errors, prioritizing correcting previously misinterpreted segments. It employs multiple experts (decision trees) rather than a single specialist to address the entire challenge. Each contributes their perspective on solving the puzzle, collectively deciding on the ultimate solution.

XGBoost extensively trains with numerous practice puzzles (training data) to refine its experts. It learns from errors and progressively improves, continuously evaluating its performance and making necessary adjustments. This process allows each specialist to reassess and enhance their contribution to the puzzle.

The culmination of all expert insights typically yields a significantly improved outcome than any expert could achieve alone.

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**Introduction to Linear Regression**

Linear regression is an uncomplicated yet potent method utilized in statistics and machine learning to decipher and forecast the interrelations between two variables. Let’s simplify this concept.

Envision attempting to discern how one factor influences another. For instance, you might be curious about how the duration of your study sessions (which we’ll refer to as “X”) impacts your exam scores (which we’ll denote as “Y”). Linear regression aids in identifying a straight line that most accurately depicts this connection.

Linear regression seeks a straight line that most snugly fits the data points. This line is known as the line of best fit. The line of best fit is expressed through a straightforward equation: Y = mX + b.

In this formula, “Y” represents the outcome you wish to predict (exam scores), “X” is the predictor (study duration), “m” denotes the slope of the line (the variation in Y with X), and “b” is the intercept (the point where the line intersects the Y-axis). After determining the line of best fit, it can be utilized for making forecasts. For instance, knowing your planned study duration (X) allows you to estimate your probable exam score (Y) using the line.

Linear regression elucidates how accurately your line of best-fit forecasts actual results. It evaluates how closely the forecasted values align with the real data. The objective is to align the line closely with the data points.

**Creating the Model and Evaluating the Results**

This article aims to predict a specific time series by employing both models and then amalgamating their forecasts to contrast with the individual analyses. We will adopt the simple hit ratio (accuracy) metric for evaluation. The time series in focus is the COT values of the Japanese Yen.

The COT report, or commitments of traders report, is a weekly release by the U.S. CFTC that sheds light on the stances of various market participants, including commercial hedgers, large speculators, and small traders, in the futures and options markets. It offers essential insights into the sentiments and positions of these groups, assisting traders and investors in anticipating potential market trends and reversals. This report frequently scrutinizes commodity and financial futures markets for making well-informed trading decisions.

The ensuing chart displays the weekly values of the COT for the Japanese Yen. This time series exhibits a positive correlation with JPYUSD (and, thus, a negative correlation with USDJPY).

**The Net COT Value of the Japanese Yen**

The structure of this investigation is outlined as follows:

- Retrieve and load the COT JPY dataset from the specified source.
- Normalize the dataset to achieve stationarity by calculating the differences between data points.
- Partition the dataset into training and test groups, employing lagged variables as predictors. Independently apply the linear regression and XGBoost algorithms for fitting and forecasting.
- Integrate the predictions through simple averaging.
- Assess the performance of the three models.

**Linear Regression Algorithm Implementation:**

import numpy as np

from sklearn.linear_model import LinearRegression

import matplotlib.pyplot as plt

import pandas as pddef preprocess_data(data, num_lags, split_ratio):

# Data preparation for model training

x, y = [], []

for i in range(len(data) – num_lags):

x.append(data[i:i + num_lags])

y.append(data[i + num_lags])

# Conversion to numpy arrays

x, y = np.array(x), np.array(y)

# Data division into training and testing subsets

split_idx = int(split_ratio * len(x))

x_train, y_train = x[:split_idx], y[:split_idx]

x_test, y_test = x[split_idx:], y[split_idx:]return x_train, y_train, x_test, y_test

data = np.reshape(pd.read_excel(‘COT_JPY.xlsx’).values, (-1))

data = np.diff(data)

x_train, y_train, x_test, y_test = preprocess_data(data, 80, 0.80)# Model instantiation

model = LinearRegression()

# Model fitting

model.fit(x_train, y_train)

# Prediction

y_pred_lr = model.predict(x_test)

# Accuracy calculation

hit_ratio_lr = np.sum(np.sign(y_pred_lr) == np.sign(y_test)) / len(y_test) * 100

print(‘Hit Ratio Linear Regression = ‘, hit_ratio_lr, ‘%’)

**XGBoost Algorithm Implementation:**

from xgboost import XGBRegressor

# Data reloading and preprocessing as before

data = np.reshape(pd.read_excel(‘COT_JPY.xlsx’).values, (-1))

data = np.diff(data)

x_train, y_train, x_test, y_test = preprocess_data(data, 80, 0.80)# Model instantiation

model = XGBRegressor(random_state=0, n_estimators=16, max_depth=16)

# Model fitting

model.fit(x_train, y_train)

# Prediction

y_pred_xgb = model.predict(x_test)

# Visualization

plt.plot(y_pred_lr[-100:], label=’Forecasted | LR’, linestyle=’–‘, marker=’.’, color=’red’)

plt.plot(y_pred_xgb[-100:], label=’Forecasted | XGBoost’, linestyle=’–‘, marker=’.’, color=’orange’)

plt.plot(y_test[-100:], label=’Actual Data’, marker=’.’, alpha=0.7, color=’blue’)

plt.legend()

plt.grid()

plt.axhline(y=0, color=’black’, linestyle=’–‘)

# Accuracy calculation

hit_ratio_xgb = np.sum(np.sign(y_pred_xgb) == np.sign(y_test)) / len(y_test) * 100

print(‘Hit Ratio XGBoost = ‘, hit_ratio_xgb, ‘%’)

**Averaged Forecasts Algorithm Implementation:**

averaged_predictions = (y_pred_xgb + y_pred_lr) / 2

hit_ratio_avg = np.sum(np.sign(averaged_predictions) == np.sign(y_test)) / len(y_test) * 100

print(‘Hit Ratio Averaged Forecasts = ‘, hit_ratio_avg, ‘%’)plt.plot(y_pred_lr[-100:], label=’Forecasted | LR’, linestyle=’–‘, marker=’.’, color=’red’, alpha=0.5)

plt.plot(y_pred_xgb[-100:], label=’Forecasted | XGBoost’, linestyle=’–‘, marker=’.’, color=’orange’, alpha=0.5)

plt.plot(averaged_predictions[-100:], label=’Forecasted | Averaged’, linewidth=2, marker=’.’, color=’black’)

plt.plot(y_test[-100:], label=’Actual Data’, marker=’.’, alpha=0.7, color=’blue’)

plt.legend()

plt.grid()

plt.axhline(y=0, color=’black’, linestyle=’–‘)

**Comparison of Outcomes:**

The outcomes for the models are as follows:

- Hit Ratio Linear Regression = 54.05%
- Hit Ratio XGBoost = 62.16%
- Hit Ratio Averaged Forecasts = 64.86%

The fusion of the two models yields enhanced precision. This strategy allows for exploiting model integration, underlining the adage that two systems outperform one individually.