Silver and Palladium Price Dynamics: Analyzing Relationships and Forecasting with ARIMA and Prophet

This research focuses on the price linkages of silver and palladium and the efficiency of the ARIMA and Prophet models in the forecast of price movements. As these two valuable metals are increasingly used in major industries, an understanding of their price mechanism is very relevant for investors, analysts, and policymakers. It thus analyzes the short-run and long-run linkages between the prices of silver and palladium to identify to what extent these two metals share the same price patterns. We have used the historical price series to analyze this correlation over varying time horizons, and despite both metals recording some common price patterns, their relationship really fluctuates heavily in the near term due to market speculation, industrial demand, and various geopolitical events, while long-term correlations are more stable at the influence of broader economic and industrial trends. Besides, the study gauges the predictive performance of two widely used forecasting models: ARIMA and Prophet. An ARIMA model is a classical time series forecasting technique applied for modeling and predicting linear trends in price data. A Prophet model, which is more flexible and developed by Facebook, is assessed for handling seasonality, outliers, and missing data. The results indicated that ARIMA is relatively good at predictions in stable market conditions but can't work well during volatile periods. In contrast, Prophet has a better forecast capability in capturing both the short-run fluctuations and the long-run trends. This study therefore concludes that price correlation analysis coupled with advanced predictive modeling will lead to an improvement in forecasting accuracy and hence better decision-making in both silver and palladium markets.