This paper deals with the development of the gold and silver prices from January 2001 until January 2015 and introduces the ARMA-model from Box & Jenkins for (weakly) stationary stochastic processes and the GARCH-model from Bollerslev to model heteroscedastic time series. The results, which were obtained with the help of the statistics package R, are presented in section 5 and 6 respectively. Besides, a forecast of the prices for both assets is made in section 7, the limitations of the research are presented in section 8 and section 9 concludes with a summary of the findings.
It is widely known in the financial world that both equities, silver and gold have a long history of serving as a hedge against inflation, political risk and currency exchange risk, which provide economic and physical safety for the investors during times of political and economic crises as well as equity market crashes. This phenomenon could be observed in the 2008 financial crisis, where other mineral prices fell, but only the gold price increased by 6%. Moreover, researchers also show that gold and dollar seem to be negatively related, as in times, when the dollar was weak the price for gold increases. Hence, gold was found to be uncorrelated with other types of assets, which leads to advantages for an investor in an era of globalization.
As gold and silver assets seem to play an important role for investors, it is of great necessity to monitor its prices and the volatility of the time series. The autoregressive moving average models (ARMA) and the generalized autoregressive heteroscedasticity (GARCH) models became popular for academics and practitioners and led to a fundamental change to the approach of examining financial data. The ARMA models have been further extended and an efficient modelling of the volatility of the prices with GARCH models was further inspected by many researchers.
Inhaltsverzeichnis (Table of Contents)
- Introduction
- Data
- Methodology
- Properties of an ARMA model
- Properties of a GARCH model
- Data Analysis...
- Examining gold close data..
- Gold log-returns..
- ACF and PACF of the gold log-returns........
- Applying ARMA-models on gold log-returns
- Testing the residuals of the gold log – returns
- Normality assumption of the residuals of the gold log - returns
- Heteroscedasticity of the gold log - returns.
- Using GARCH to model the time series of the gold log - returns ....
- Testing for skewed t-distribution of the residuals in a GARCH - model.
- Examining the silver close data.
- Silver log-returns & ACF/PACF of the silver return data.
- Testing ARMA models on the silver log-returns..
- Independence assumption of the residuals of the silver log-return data.
- Normality assumption of the residuals of the silver log-return data
- Heteroscedasticity of the residuals of the silver log-return data.
- Examining GARCH - models on the silver log-return data.
- Testing skewed t-distribution and independence assumption of residuals of the silver log - return data
- Forecasting gold and silver returns
- Drawbacks of the research..
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
The paper aims to analyze the development of gold and silver close prices from 2001 to 2015. The analysis utilizes the ARMA model, introduced by Box and Jenkins, and the GARCH model, introduced by Bollerslev, to examine the properties of the time series and determine which model best fits the data.
- Analysis of gold and silver close prices from 2001 to 2015
- Application of ARMA and GARCH models to time series data
- Assessment of model fit and performance
- Exploration of the properties of gold and silver time series
- Forecasting of gold and silver returns
Zusammenfassung der Kapitel (Chapter Summaries)
The introductory chapter discusses the role of gold and silver as hedges against inflation, political risk, and currency exchange risk. It highlights the importance of monitoring the prices and volatility of these assets and introduces the ARMA and GARCH models as tools for analyzing financial data.
Chapter 2 presents the data used in the analysis, which consists of daily close prices of gold and silver from January 3rd, 2001 to January 23rd, 2015. The chapter provides a visual representation of the data and discusses the trends observed in the prices of both assets.
Chapter 3 outlines the methodological approach, explaining the properties of the ARMA and GARCH models. It describes how these models are used to analyze the auto-correlation and volatility clustering present in real-time series data.
Chapters 5 and 6 present the results of the data analysis. Chapter 5 focuses on the examination of gold close data, exploring gold log-returns, applying ARMA models, and analyzing the residuals. Chapter 6 continues with the examination of silver close data, following a similar approach to the analysis of gold data.
Schlüsselwörter (Keywords)
The main keywords and focus topics of this paper include: gold, silver, close prices, ARMA model, GARCH model, time series analysis, volatility, heteroscedasticity, forecasting.
- Quote paper
- Van Anh Hoang (Author), 2016, Application of ARMA and GARCH models to the daily gold and silver exchange prices in US dollar, Munich, GRIN Verlag, https://www.grin.com/document/319861
