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ARMA and GARCH models for silver, nickel and copper price returns

Hansson, Mats LU ; Andersson, Ola LU and Holmberg, Olle LU (2015) STAH11 20142
Department of Statistics
Abstract
This thesis compares Auto Regressive Moving Average (ARMA) and Generalized Auto Regressive Conditional Heteroscedacity (GARCH) models for three metal commodities. ARMA models have an unconditionally non-random and constant variance, which typically serves well in effectively representing homoscedastic data. The GARCH models feature variable variance that is non-random when conditioning on the past. Thus these models are often used to represent heteroscedastic data. It is documented that financial data, including metal commodities frequently exhibit heteroscedacity. This thesis investigates if this heteroscedacity in the observed historical data is shown in the quality of its ARMA and GARCH fits. The data used for comparison involve three... (More)
This thesis compares Auto Regressive Moving Average (ARMA) and Generalized Auto Regressive Conditional Heteroscedacity (GARCH) models for three metal commodities. ARMA models have an unconditionally non-random and constant variance, which typically serves well in effectively representing homoscedastic data. The GARCH models feature variable variance that is non-random when conditioning on the past. Thus these models are often used to represent heteroscedastic data. It is documented that financial data, including metal commodities frequently exhibit heteroscedacity. This thesis investigates if this heteroscedacity in the observed historical data is shown in the quality of its ARMA and GARCH fits. The data used for comparison involve three time series of logarithmic price return for silver, nickel and copper. In the hypothesis it is assumed that GARCH is more efficient than ARMA. The efficient market hypothesis is also tested.

The logarithmic price returns are stationary which is confirmed by statistical tests. Thereby, it is appropriate to fit ARMA and GARCH models. The ARMA and GARCH models with the lowest Akaike’s Information Criterion (AIC) are selected from each series. The models forecasted values and running standard deviations are cross-validated with the observed historical data using three measures. These measures are Mean Absolute Scaled Error (MASE), symmetric Mean Absolute Percentage Error (sMAPE) and correct pairs of sign which all provide different assessment of magnitude of error in estimation of the observed historical records. The correct pairs of sign are then tested against the efficient market hypothesis.

The error in estimation for forecast values does not yield a difference between ARMA and GARCH models by MASE. For the running standard deviation, both measures MASE and sMAPE are applied. The GARCH model is then more efficient than ARMA. In this sense, the thesis confirms the increased efficiency of using GARCH models for metal commodities.

According to correct pairs of sign measure, nickel has no arbitrage opportunities for logarithmic price return. This is expected according to the efficient market hypothesis. However, the test indicates it is possible to predict correct sign of logarithmic price return for copper and silver, which indicates that the efficient market hypothesis does not always apply. (Less)
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author
Hansson, Mats LU ; Andersson, Ola LU and Holmberg, Olle LU
supervisor
organization
course
STAH11 20142
year
type
M2 - Bachelor Degree
subject
keywords
ARMA, GARCH, MASE, sMAPE, Heteroscedasticity, Stationarity, Ljung-Box test, McLeod-Li test, Running Standard Deviation, Forecast value.
language
English
id
5052225
date added to LUP
2015-03-02 09:21:49
date last changed
2015-03-02 09:21:49
@misc{5052225,
  abstract     = {This thesis compares Auto Regressive Moving Average (ARMA) and Generalized Auto Regressive Conditional Heteroscedacity (GARCH) models for three metal commodities. ARMA models have an unconditionally non-random and constant variance, which typically serves well in effectively representing homoscedastic data. The GARCH models feature variable variance that is non-random when conditioning on the past. Thus these models are often used to represent heteroscedastic data. It is documented that financial data, including metal commodities frequently exhibit heteroscedacity. This thesis investigates if this heteroscedacity in the observed historical data is shown in the quality of its ARMA and GARCH fits. The data used for comparison involve three time series of logarithmic price return for silver, nickel and copper. In the hypothesis it is assumed that GARCH is more efficient than ARMA. The efficient market hypothesis is also tested. 

The logarithmic price returns are stationary which is confirmed by statistical tests. Thereby, it is appropriate to fit ARMA and GARCH models. The ARMA and GARCH models with the lowest Akaike’s Information Criterion (AIC) are selected from each series. The models forecasted values and running standard deviations are cross-validated with the observed historical data using three measures. These measures are Mean Absolute Scaled Error (MASE), symmetric Mean Absolute Percentage Error (sMAPE) and correct pairs of sign which all provide different assessment of magnitude of error in estimation of the observed historical records. The correct pairs of sign are then tested against the efficient market hypothesis.

The error in estimation for forecast values does not yield a difference between ARMA and GARCH models by MASE. For the running standard deviation, both measures MASE and sMAPE are applied. The GARCH model is then more efficient than ARMA. In this sense, the thesis confirms the increased efficiency of using GARCH models for metal commodities. 

According to correct pairs of sign measure, nickel has no arbitrage opportunities for logarithmic price return. This is expected according to the efficient market hypothesis. However, the test indicates it is possible to predict correct sign of logarithmic price return for copper and silver, which indicates that the efficient market hypothesis does not always apply.},
  author       = {Hansson, Mats and Andersson, Ola and Holmberg, Olle},
  keyword      = {ARMA,GARCH,MASE,sMAPE,Heteroscedasticity,Stationarity,Ljung-Box test,McLeod-Li test,Running Standard Deviation,Forecast value.},
  language     = {eng},
  note         = {Student Paper},
  title        = {ARMA and GARCH models for silver, nickel and copper price returns},
  year         = {2015},
}