Comparative Analysis of Advanced Time Series Forecasting Techniques: Evaluating the Accuracy of ARIMA, Prophet, and Deep Learning Models for Predicting Inflation Rates, Exchange Rates, and Key Financial Indicators

Abstract

This paper presents a rigorous comparative analysis of advanced time series forecasting techniques, specifically focusing on the application of ARIMA, Prophet, and deep learning models to the prediction of key financial indicators, including inflation rates and exchange rates. The study seeks to address the growing demand for accurate and reliable forecasting methods in financial markets, where precise predictions are crucial for informed decision-making. By systematically evaluating the performance of these models, this research contributes to the ongoing discourse on the efficacy of traditional versus modern forecasting approaches in the context of financial time series data.

The analysis begins with an exploration of the theoretical foundations and mathematical formulations underlying each model. ARIMA, a widely used statistical method, is known for its capacity to model linear relationships in time series data by capturing autoregressive, differencing, and moving average components. Prophet, developed by Facebook, is a relatively recent addition to the forecasting landscape, designed to handle seasonality, holidays, and trends with a focus on ease of use and interpretability. The deep learning models, on the other hand, represent a paradigm shift, employing neural networks to capture complex, nonlinear relationships in time series data. These models, including Long Short-Term Memory (LSTM) and Convolutional Neural Networks (CNNs), have demonstrated significant potential in various domains but require extensive computational resources and expertise.

In this study, we implement these models on a comprehensive dataset comprising historical inflation rates, exchange rates, and other critical financial metrics. The dataset is pre-processed to ensure consistency and to account for missing values, outliers, and non-stationarities, which are common challenges in financial time series analysis. Each model is trained and tested using a rolling window approach, allowing for the evaluation of forecast accuracy over multiple time horizons. The models are assessed based on several performance metrics, including Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE), providing a multifaceted view of their predictive capabilities.

The findings reveal distinct strengths and weaknesses across the models. ARIMA, while robust in capturing linear trends and seasonality, exhibits limitations in handling non-linear patterns and sudden shifts in the data, which are often encountered in financial markets. Prophet, with its flexible handling of seasonality and trend components, shows promise, particularly in cases where domain knowledge can be leveraged to improve model specification. However, its performance is sensitive to the choice of hyperparameters and may require extensive tuning for optimal results. The deep learning models, particularly LSTM, excel in capturing complex, non-linear relationships and demonstrate superior performance in scenarios with high volatility and noise. However, their computational demands and susceptibility to overfitting present challenges, particularly in situations with limited data or when interpretability is a priority.

The study also delves into the computational efficiency of these models, an important consideration for real-time forecasting applications. ARIMA, being relatively simple in its formulation, is computationally efficient and suitable for scenarios with limited computational resources. Prophet, while more computationally intensive than ARIMA, offers a reasonable trade-off between accuracy and efficiency, making it a viable option for many practical applications. The deep learning models, despite their superior accuracy in complex scenarios, require substantial computational resources and longer training times, which may limit their applicability in time-sensitive or resource-constrained environments.

Furthermore, the paper explores the models' ability to handle seasonality, trends, and noise, which are critical features of financial time series. ARIMA's reliance on differencing to achieve stationarity may lead to the loss of important information, particularly in series with complex seasonal patterns. Prophet's explicit modeling of seasonality and holidays provides an advantage in such cases, allowing for more accurate forecasts in the presence of recurrent patterns. The deep learning models, with their capacity to learn from large amounts of data, are particularly adept at handling noise and uncovering hidden patterns, making them well-suited for highly volatile financial time series.