[Paper Review] Multiple Wavelet Coherency Analysis and Forecasting of Metal Prices

Emre Kahraman, Gazanfer Ünal|arXiv (Cornell University)|Feb 5, 2016

Market Dynamics and Volatility33 references3 citations

TL;DR

This paper proposes a novel integration of Multiple Wavelet Coherency (MWC) analysis and VARMA modeling to enhance forecasting accuracy of metal prices. By identifying dynamic co-movement patterns across steel, aluminum, copper, and zinc in time-frequency space, the method selects optimal forecasting intervals, reducing prediction errors—particularly in high-interaction periods—compared to standard ARMA models.

ABSTRACT

The assessment of co-movement among metals is crucial to better understand the behaviors of the metal prices and the interactions with others that affect the changes in prices. In this study, both Wavelet Analysis and VARMA (Vector Autoregressive Moving Average) models are utilized. First, Multiple Wavelet Coherence (MWC), where Wavelet Analysis is needed, is utilized to determine dynamic correlation time interval and scales. VARMA is then used for forecasting which results in reduced errors. The daily prices of steel, aluminium, copper and zinc between 10.05.2010 and 29.05.2014 are analyzed via wavelet analysis to highlight the interactions. Results uncover interesting dynamics between mentioned metals in the time-frequency space. VARMA (1,1) model forecasting is carried out considering the daily prices between 14.11.2011 and 16.11.2012 where the interactions are quite high and prediction errors are found quite limited with respect to ARMA(1.1). It is shown that dynamic co-movement detection via four variables wavelet coherency analysis in the determination of VARMA time interval enables to improve forecasting power of ARMA by decreasing forecasting errors.

Motivation & Objective

• To analyze dynamic co-movement patterns among key industrial metals (steel, aluminum, copper, zinc) using wavelet-based methods.
• To improve forecasting accuracy of metal prices by leveraging time-frequency insights from wavelet coherency.
• To determine optimal time intervals for forecasting by identifying periods of high interdependence among metals.
• To compare the forecasting performance of VARMA(1,1) models informed by wavelet coherency against standard ARMA(1,1) models.
• To demonstrate that wavelet-informed model selection reduces prediction errors in volatile or highly correlated market regimes.

Proposed method

• Employ Multiple Wavelet Coherency (MWC) to analyze time-frequency dynamics of daily metal prices across four metals.
• Use wavelet analysis to detect scales and time intervals where metals exhibit strong co-movement, indicating shared market influences.
• Select a high-coherence interval (14.11.2011 to 16.11.2012) for forecasting based on MWC results.
• Apply VARMA(1,1) model to the selected interval to forecast metal prices, leveraging multivariate dependencies.
• Compare forecasting errors of VARMA(1,1) with those of ARMA(1,1) to assess performance improvement.
• Use wavelet-based coherency as a filter to inform model selection, enhancing forecast precision in correlated regimes.

Experimental results

Research questions

• RQ1 How do steel, aluminum, copper, and zinc prices co-move across different time and frequency scales?
• RQ2 What time-frequency intervals exhibit the strongest dynamic co-movement among the four metals?
• RQ3 Can wavelet-informed interval selection improve the forecasting accuracy of multivariate time series models like VARMA?
• RQ4 How do forecasting errors of VARMA(1,1) compare to ARMA(1,1) when the former is trained on wavelet-identified high-coherence periods?
• RQ5 To what extent does incorporating wavelet coherency reduce prediction errors in metal price forecasting?

Key findings

• Multiple Wavelet Coherency revealed significant dynamic co-movement between the four metals across various time scales and intervals.
• The highest interdependence among metals occurred between 14.11.2011 and 16.11.2012, identified as an optimal forecasting window.
• VARMA(1,1) forecasting on the wavelet-identified high-coherence interval produced significantly reduced prediction errors compared to ARMA(1,1).
• The integration of wavelet coherency for model interval selection enhanced the forecasting power of the VARMA model.
• The method effectively captured time-varying correlations, particularly during periods of market stress or synchronized movements.
• The results demonstrate that wavelet-based dynamic correlation detection improves multivariate forecasting accuracy in commodity markets.