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The study employs the Box-Jenkins Methodology to forecast South African gold sales. For a resource economy like South Africa where metals and minerals account for a high proportion of GDP and export earnings, the decline in gold sales is very disturbing. Box-Jenkins time series technique was used to perform time series analysis of monthly gold sales for the period January 2000 to June 2013 with the following steps: model identification, model estimation, diagnostic checking and forecasting. Furthermore, the prediction accuracy is tested using mean absolute percentage error (MAPE). From the analysis, a seasonal ARIMA(4,1,4)×(0,1,1) 12 was found to be the “best fit model” with an MAPE value of 11% indicating that the model is fit to be used to predict or forecast future gold sales for South Africa. In addition, the forecast values show that there will be a decrease in the overall gold sales for the first six months of 2014. It is hoped that the study will help the public and private sectors to understand the gold sales or output scenario and later plan the gold mining activities in South Africa. Furthermore, it is hoped that this research paper has demonstrated the significance of Box-Jenkins technique for this area of research and that they will be applied in the future.

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Risk governance & control: financial markets & institutions / Volume 7, Issue 1, Winter 2017

GOLD SALES FORECASTING:

THE BOX-JENKINS METHODOLOGY

Johannes Tshepiso Tsoku*, Nonofo Phukuntsi, Daniel Metsileng

* North West University, South Africa

Abstract

The study employs the Box-Jenkins Methodology to forecast South African gold sales. For a

resource economy like South Africa where metals and minerals account for a high proportion of

GDP and export earnings, the decline in gold sales is very disturbing. Box-Jenkins time series

technique was used to perform time series analysis of monthly gold sales for the period January

2000 to June 2013 with the following steps: model identification, model estimation, diagnostic

checking and forecasting. Furthermore, the prediction accuracy is tested using mean absolute

percentage error (MAPE). From the analysis, a seasonal ARIMA(4,1,4)×(0,1,1) was found to be the

“best fit model” with an MAPE value of 11% indicating that the model is fit to be used to predict

or forecast future gold sales for South Africa. In addition, the forecast values show that there will

be a decrease in the overall gold sales for the first six months of 2014. It is hoped that the study

will help the public and private sectors to understand the gold sales or output scenario and later

plan the gold mining activities in South Africa.

Furthermore, it is hoped that this research paper

has demonstrated the significance of Box-Jenkins technique for this area of research and that

they will be applied in the future.

Keywords: Gold Sales, ARIMA, Box-Jenkins, GDP, MAPE

JEL Classification : C38, L52

DOI : 10.22495/rgcv7i1art7

1. INTRODUCTION

year. However, recent figures published by Statistics

South Africa show that South Africa has been

The Box-Jenkins methodology has gained more

popularity since their book publication in 1970. The

Box-Jenkins method which does not require

establishing assumptions on the interdependence of

variables could be used to test applicability on data

series undergoing dynamic fluctuation. More

significantly, this technique does not introduce too

much personal bias into the process of forecasting.

The Box-Jenkins technique is considered as a suitable

forecasting tool when the components describing the

time series are fluctuating quite rapidly over time

(Bowerman and O’Connell, 1993; Wong et al., 2005).

At the same time, the Box-Jenkins method is a

reliable and convenient tool among numerous

common time series skills. Therefore, this research

paper adopted the Box-Jenkins methodology to

construct a forecasting model for South Africa gold

sales. The technique is based on the idea that a time

series in which successive values are highly

dependent can be regarded as being generated from

a series of independent shocks. Analysing such series

leads to the class of Autoregressive Integrated

Moving Average (ARIMA) models. An autoregressive

(AR) process is fundamentally a regression equation

slipping down the table from the world’s top

producer less than a decade ago to sixth position.

According to the Mineweb (2013), China is

currently leading, followed by Australia, the USA,

Russia and Peru in that order. In 1970, South Africa

produced almost 80% of global gold production now

it manages only around 6%, which is a very big fall

(Mineweb, 2013). There has been a noticeable decline

in gold production (extraction) and mining

contribution to South Africa’s Gross Domestic

Product (GDP). In terms of employment, the mining

industry reported an annual decrease of over 6%

from December 2008 to December 2009 (StatsSA,

2013). South Africa’s mineral industry is export -

oriented, due to the small domestic market for most

commodities.

In another report by Statistics South Africa

(2013), annual mineral sales was estimated to have

decreased by 8.5% in May 2013 and the largest

negative growth rates were recorded for gold with a

value of -42.6%, i.e. from May 2012 to May 2013, gold

sales decreased by 42.6% as illustrated in Table 1.

This was the largest negative growth rate observed

for gold sales in 2013.

where a variable is related to its own previous values

instead of to a set of independent variables

(Chatfield, 2000).

The gold mining sector played a substantial role

as a basis industry in the evolution of South African

industry. The gold mining industry has been the

dominant foreign exchange earner for the country

over the past century. More recent statistics indicate

that gold export earnings in 1980 accounted for over

50% of South Africa’s merchandise exports in that

Table 1. Year-on-year percentage change in gold

sales at current prices

Date % change

December 2012 -16.1

January 2013 12.4

February 2013 -9.1

March 2013 3.3

April 2013 -13.6

May 2013 -42.6

54

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Risk governance & control: financial markets & institutions / Volume 7, Issue 1, Winter 2017

There is a general decline in the gold sales over

Khan

(2013)

applied

Box- Jenkins’

ARIMA

the years and this could have long negative results in

approach for building forecasting model using the

the future. According to an article in the Mineweb

gold price sample (in US$ per Ounce). The results

(2013),

showed that ARIMA(0,1,1) is the most appropriate

“Mo re recent statistics indicate that gold export

model to be used for forecasting the gold price. Patel

earnings in 1980 accounted for over 50% of South

(2013) investigated the role of gold as a strategic

Africa’s merchandise exports in that year. However,

prophecy against inflation and exchange rate and

recent figures published

by Statistics South Africa

found that gold can act as a hedge against inflation

show that South Africa has been slipping down the

and exchange rate in two different ways. Firstly, gold

table from the world’s top producer less than a decade

price act as an internal hedge against inflation of the

ago to sixth position”.

country. This means, that if inflation increases, gold

The following could be listed as contributing

price would also increase. Secondly, gold price also

factors: sudden changes in gold demand levels, price-

acts as an external hedge. This means if exchange

cutting manoeuvres of the competition, strikes, large

rate decrease, price of gold will increase. Ranson

swings of the economy, interest rates, inflation rates

(2005) examined the role of gold and oil as predictor

and seasonality. A decline in gold sales has affected

of inflation. He found that gold price is more reliable

many

related

sectors

and

contributed

negatively

barometer of the inflation than oil price because the

towards South Africa's annual GDP. The forecasting

effect

on

official

inflation

statistics

is

reliably

of gold sales is essential to help in calculating the

indicated by how far policy actions have allowed the

volume of mining production which affects GDP and

price of gold to rise.

its components. The main objective of this study is

to apply a Box- Jenkins’ ARIMA model approach to

model South Africa’s monthly gold sales and to use

3. METHODOLOGY

the identified ARIMA model to forecast future South

African gold sales and the other objective is to

compare the year-on-year percentage change findings

with the Statistics South Africa gold findings.

The paper is set out as follows. Section 2

discusses some of literature relating to our study.

Section 3 briefly outlines the methodological

framework. Section 4 presents the results and

discussions. Concluding remarks is given in section

5.

The study present uses a monthly general gold

production data for the period January 2000 to June

2013. The Box-Jenkins methodology employed in

this study is based on the analysis of pattern

changes in the past history of the observations

and it uses a four-phase approach (Box, Jenkins and

Reinsel, 1994). Namely: tentative model

identification, model estimation, diagnostic checking

and forecasting.

2. LITERATURE REVIEW

3.1. Tentative Model Identification

Ping, Miswan and Ahmad (2013) carried out a study

on forecasting the prices of Kijang Emas, the official

Malaysian gold bullion. Their study employed two

methods, which are Box-Jenkins ARIMA and

Generalized Autoregressive Conditional

Heteroskedasticity (GARCH). Using Akaike’s

information criterion (AIC) as the goodness of fit

measure and mean absolute percentage error (MAPE)

as the forecasting performance measure, they found

that the gold prices data can be characterized by

GARCH (1,1) model. Their conclusion was based on

the fact that GARCH (1,1) had both a lower SIC and

MAPE value than ARIMA (1,1,1) in forecasting its

future values.

Mahipan, Chutiman and Kumphon (2013)

applied both Box-Jenkins and Artificial Neural

Network methods to prediction the rate of

unemployment in Thailand. In their paper, they

determined the stationary and seasonality of the data

and the Augmented Dickey-Fuller test.

(ADF) and autocorrelation (ACF) were used

A plot of the original data should be run as the initial

point in determining the most appropriate model.

Stationarity tests can be performed to determine if

differencing is necessary. Besides looking at the

graphical presentation of the time series values over

time to determine stationary or non-stationary,

the sample ACF also gives visibility to the data. Non-

stationary data displaying trend behaviour can be

transformed through regular differencing. In this

study more focus is based on first and second

regular differencing.

The initial work on stationarity testing came

from Dickey and Fuller (1979), who conceptualised

the technique as “testing for a unit root”. This is a

formal test employed in this study to check for

stationarity in the time series data. Within the

framework of the Box-Jenkins methodology, there is

an overall model which can be decomposed into

three basic models. The ARIMA can be decomposed

into an AR, Moving Average (MA) and Autoregressive

Moving Average (ARMA) model.

respectively. The ADF test for stationary showed that

the series had a unit root implying that the original

3.2. Model Estimation

series was non-stationary. The data became

stationary after first order difference. Examination of

the correlogram indicated that Seasonal ARIMA

model was appropriate. The Box-Jenkins

methodology proved more efficient to estimate the

This phase involves estimation of the parameters of

the models identified (specified) in the first phase.

The least squares approach is employed in model

estimation.

rate of unemployment in Thailand. MAPE was used to

show that SARIMA, SARIMA(0,1,1) provided

satisfactory representation of the unemployment rate

data.

3.3. Diagnostic Checking

Diagnostic testing in the Box-Jenkins methodology

essentially involves the statistical properties of the

55

0 1

�

∑

𝑛 𝑦

k

ˆ

l

n − l

2

�

Risk governance & control: financial markets & institutions / Volume 7, Issue 1, Winter 2017

error terms (normality assumption, weak white noise

Holt’s forecast model and a combination

of Box-

assumption) as well as common testing procedures

Jenkins and Holt’s in regression, by providing lowest

on the estimates. As mentioned earlier, ε t is expected

to follow a white noise process. Graphical procedure

mean MAPE (Warant, 2006). There are many simple

measures of prediction accuracy, for instance the

and formal testing procedure can be used to test

mean squared error (MSE), mean absolute error (MAE)

adequacy of the model. In the graphical procedure a

and

mean

squared

deviation

(MSD).

However

the

plot

of

the

residuals

is

examined

to

check

for

most appropriate simple error measure for this study

outliers. To check the overall acceptability of the

is the MAPE given by the following equation:

overall model, the Ljung-Box (1978) test can be used

as follows:

H : Model is adequate versus H : Model is

inadequate

𝑀𝐴𝑃𝐸 = 1 𝑛 | 𝑦 𝑡 − 𝑓 � | (2)

𝑖=1 𝑡

This test statistic can be used to compare the

Test statistic:

accuracy of forecasts based on two entirely different

series (Hanke and Wichern, 2005). According to Lewis

Q * = n ' ( n ' + 2) ' 1 r 2 ( a )

l = 1

(1)

(1982), the level of accuracy for the MAPE test is

divided into four stages as shown in Table 2. Each

level of accuracy gives the percentage of the accuracy

of predicted value compared to the original time

where

𝑛 1 = 𝑛 − 𝑑 ,

n

is

the

number

of

series value (Muda and Hoon, 2012).

observations and d is the degree of non-seasonal

differencing used to transform the original time

Table 2. Level of accuracy for MAPE test

series values into stationary. The 𝑟 � (�̂�) is the square

of the autocorrelation of the residuals at lag l

(Bowerman, O ’Connell and Koehler, 2005). If the p -

value is greater than significant level α or

MAPE value

MAPE ≤ 10%

10% < MAPE ≤ 20%

Level of accuracy

Very accurate

Accurate

equivalently 𝑄 ∗ is less than chi-square distribution,

20% < MAPE ≤ 50%

Medium

the null hypothesis cannot be rejected concluding

50% ≤ MAPE

Less accurate

that the model is adequate. According to Verbeek

(2004), if a model is rejected at this stage; the model-

building cycle has to be repeated.

4.

RESULTS AND DISCUSSION

3.4. Forecasting

This section of the study carries out the four Box-

Jenkins technique’s steps to analyse the gold sales

The

final

and

most

important

stage

of

the

Box-

data.

Jenkins process is forecasting. There are two broad

types of forecasts: one step ahead forecasts are

4.1. Step 1: Model Identification

generated for the next observation only whereas

multi-step ahead forecasts are generated for

1,2,3,…..,s steps ahead. Many researchers suggest

that Box- Jenkins’ ARIMA is the most accurate

forecasting model. ARIMA wins over other models;

The first step in developing a Box-Jenkins model is to

determine if the series is stationary and if there is

any observed pattern. The data is plotted as shown in

Figure 1 below.

Figure 1. Original Plot o f Gold Sales

(a) Gold series plot

(b) ACF plot of the original data

56

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