Analysis of Gold Price Movements Through a Financial Forecasting
Model Approach
RR ERLINA1, AYI AHADIAT1, RIALDI AZHAR2, FAJRIN SATRIA DWI KESUMAH1,
TOTO GUNARTO3
1Department of Management, University of Lampung, Bandar Lampung, INDONESIA
2Department of Accounting, University of Lampung, Bandar Lampung, INDONESIA
3Department of Economics Development, University of Lampung, Bandar Lampung, INDONESIA
Abstract: - The resilience of gold to situations full of risk has been proven over a long period of time.
Forecasting the movement of gold which is in a safe range is done to prove that gold is still stable. The purpose
of this study is to obtain the best model, estimate the parameters, and predict the daily gold price change in the
last two years. The AR-GARCH(1.1) model is proven to be able to form the best forecasting model so that
future gold resistance can be known with a low error rate. This model can be reliably applied to predict gold
prices over the next 30 days. This may prompt investors to consider investing in or out of gold.
Key-Words: - Gold Prices, GARCH, Investment, Secure Investment, Financial Forecasting, Risk Investment.
Received: April 18, 2023. Revised: July 18, 2023. Accepted: July 24, 2023. Published: August 4, 2023.
1 Introduction
Investment is an activity that is invested or financed
with the expectation of profit or return in the future.
One form of investment is to use gold, [1].
Furthermore, several people are interested in
investing in gold, because the price of gold is quite
affordable, and investing in gold is also very easy to
do and flexible, [2]. Gold is included in the low-risk
investment class because price movements tend to
follow the inflation rate, usually, gold prices will
increase, [3]. In addition, gold is one of the most
sought-after investment instruments by the public,
[4]. Gold is also even used to store wealth for a long
time, [5]. Gold is currently one of the rare
commodities and is becoming a raw material that is
increasingly difficult to mine, [6]. Investing in gold
is also often used as a safe haven or as a hedge
against inflation, [7]. Gold prices are volatile and
gold price movements are very common, because of
the power of supply and demand where when
demand is high the price will rise and when supply
is high the price will fall indirectly, [8].
In addition, gold prices continue to change from
time to time, and the projected future gold price
movements can be monitored using forecasting, [9].
By forecasting, it will provide a basis for investors
in planning and making decisions to increase profits
and prevent losses, [10]. In general, the relationship
between return and risk is linear, [11]. These
principles are important for investors before making
investment deals, [12]. Several methods can be used
for forecasting, one of which is the Generalized
Autoregressive Conditional Heteroscedasticity
(GARCH) model. In addition, some previous studies
have used GARCH's econometric model to estimate
variance volatility and calculate the maximum loss
percentage from the return of a given portfolio. In
Indonesia, [13], found that investors should make
investment decisions in equity instruments by
monitoring daily volatility movements and trends.
In addition, a study conducted by, [14], used the
GARCH model to measure conditional variance to
forecast daily share prices for one of Indonesia's
stock prices.
2 Statistical Model
2.1 Stationary Satisfaction
To satisfy the requirements of the GARCH(p,q)
model, the first condition that must be met is that
the data set is considered stationary. Statistically, a
measurement consists of checking the data record,
and if the variation of the dataset is not stable
around zero, it is considered non-stationary, [15].
[16], added that tests steady state by computing the
autocorrelation function (ACF) and partial
autocorrelation (PACF). Non-stationary datasets can
be identified by the slow motion of any lag.
Furthermore, Dickey and Fuller 1979 introduced the
Augmented Dickey-Fuller (ADF) test to
mathematically verify the presence of stationarity.
The Augmented Dickey Fuller Test (ADF) is a
statistical test for testing the null hypothesis that the
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Rr Erlina, Ayi Ahadiat, Rialdi Azhar,
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time series is nonstationary and has a root of 1. The
ADF test is considered a type of unit root test used
to determine the stationarity of time series in
econometrics and time series analysis. The
"extended" part of the name refers to the fact that
the test includes an additional term in the regression
equation compared to the original Dickey-Fuller
test, making it easier to detect roots of 1. The results
of the test can be used to decide whether to
differentiate the time series data or apply a
transformation to stationary data for further
analysis. The hypothesis for the ADF test can be
expressed as follows.
(1)
The hypothesis is defined as.
H0:
> 2.57 = non-stationary
H0:
< 2.57 = stationary
Since most financial data series are non-
stationary in both mean and variance,
transformation to stationary data must be done by
applying differentiation methods, [16].
2.2 Differencing
In 1980, Granger and Joyeux introduced a
differentiation method to transform a nonstationary
time series data set into a stationary data set to
stabilize the mean and volatility. The formula is:
a(B) = (1-B)d (2)
where B is defined as a backward operator; d is the
number of derivatives. a(B) is called an integration
filter of order d. The GARCH stable mean and
volatility model can be applied if the stationary
dataset is satisfied. However, only after confirming
that the model introduced in this study was not
affected by autoregressive conditional
heteroscedasticity (ARCH) effects, [16].
2.2 ARCH-Effect Test
Note that when modelling time series of financial
data, the probability of heteroscedasticity is very
high, [17]. This means that the estimated parameters
of the forecast model can be less accurate. The
presence of the ARCH effect is examined by
computing the Lagrangian multiplier (LM) test,
[18]. If the probability value of the LM test is
significant from <0 p=0)>0), the variance is
estimated as the squared residual of the past data,
[16].
2.3 Mean and Variance Model
The average model of the AR (p) is defined to have
a delay number p, and the distributed diversification
and the dual dips of the number are represented as
the latest p and q, respectively. Equations 3 and 4
mathematically express the intended model.
(3) (4)
(4)
XAUSUDt is defined as the mean model of
AR(p) and
is a variance model for p and q order.
If the mean squared error (MSE) and mean squared
error (RMSE) associated with a statistical
descriptive model are relatively small, the model is
considered to have a good scale for prediction, [17].
3 Result and Discussion
3.1 Analysis of Data Distribution
This research is an observation of the last 2 years
with data qualifications that have been considered
well. The data used in this study is the daily gold
price, where gold is the underlying of various
currencies in circulation. Figure 1 shows the
distribution of data for more than 700 days, more
fully presented in the following graph.
Fig. 1: Data Distribution Graph
After observing the distribution of data from
gold, it is highly recommended to check the
stationarity of the time series data. Table 1 shows
that we performed the first differencing method on
705 data, where it is known that the standard
deviation is at a value of 17.86701.
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Table 1. Descriptive Data
Name of Variable
XAUUSD
Period(s) of Differencing
1
Mean of Working Series
0.264383
Standard Deviation
17.86701
Number of Observations
705
Observation(s) eliminated by
differencing
1
3.2 Stationary Data
Examination of the stationarity of the data continues
with the white noise test which is shown in Table 2.
At this stage, the initial indication that the data is
stationary is because of the distribution of
autocorrelation values around 0 which is a factor of
confidence in the gold data is stationary.
The next data stationarity check is using
indicators from the test ADF. Table 3 provides
information that the values of Pr > Q and Pr>LM are
significant with p-value <0.0001. This value
indicates that the golden data opportunity for further
deeper analysis can continue. More detailed results
from the ADF test are shown in Table 3.
Table 2. Autocorrelation Check for White Noise
To Lag
Chi-Square
DF
Pr > ChiSq
Autocorrelations
6
12.55
6
0.0508
0.044
-0.038
0.024
-0.062
-0.098
0.012
12
20.64
12
0.0560
-0.063
0.022
0.069
-0.022
0.004
0.040
18
30.75
18
0.0307
0.027
-0.012
-0.039
-0.010
-0.036
-0.101
24
38.44
24
0.0313
0.011
-0.042
-0.029
0.077
-0.043
0.006
Table 3. Augmented Dickey-Fuller Unit Root Tests
Type
Lags
Rho
Pr < Rho
Tau
Pr < Tau
F
Pr > F
Zero Mean
0
-672.600
0.0001
-25.36
<.0001
1
-728.467
0.0001
-19.08
<.0001
Single Mean
0
-672.736
0.0001
-25.35
<.0001
321.34
0.0010
1
-728.870
0.0001
-19.07
<.0001
181.92
0.0010
Trend
0
-674.501
0.0001
-25.39
<.0001
322.44
0.0010
1
-733.875
0.0001
-19.12
<.0001
182.84
0.0010
Fig. 2: Observation Graph and ACF After Differencing
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Furthermore, Figure 2 confirms that the data
mean after differencing has values around zero,
indicating the data set is now stationary. Also, from
the ACF graph, it can be visually confirmed the
rapid decline after lag 1 the data set has been
stationary.
3.3 ARCH Effect
The main problem with time series data is
heteroscedasticity, which makes the estimation
inaccurate. This problem can be solved by
appropriate methods, such as the GARCH model.
Investigation of whether there is heteroscedasticity
or not, in general, can use the ARCH-LM test. This
step must be confirmed before determining the best
model of GARCH(p,q). Table 4 shows that the
hypothesis can be rejected because the Portmanteau
test (Q) and LM which is calculated from the
squared residual have a very significant p-value (P <
0.0001). This shows that the ARCH effect for the
data can be applied to the GARCH(p,q) model in
forecasting.
Table 4. Tests for ARCH Disturbances Based on
Residuals
Order
Q
Pr > Q
LM
Pr>LM
1
642.3624
<.0001
610.5254
<0.0001
2
1189.1941
<.0001
610.9943
<0.0001
3
1652.3749
<.0001
611.0102
<0.0001
4
2045.5623
<.0001
611.0218
<0.0001
5
2391.0342
<.0001
611.7529
<0.0001
6
2710.7554
<.0001
612.8121
<0.0001
7
3001.0883
<.0001
613.0781
<0.0001
8
3272.3654
<.0001
613.5574
<0.0001
9
3518.8545
<.0001
613.8611
<0.0001
10
3736.3120
<.0001
613.9551
<0.0001
11
3929.6393
<.0001
614.0048
<0.0001
12
4104.8068
<.0001
614.0576
<0.0001
As the probability of the LM test is significant at
any order of lag, it confirmed that the differencing
data set of gold prices has the variance estimated as
the squared residual of the past data, so the study
can be carried out for the next steps.
3.4 Estimating the GARCH Model
Finally, based on the results of a series of data
analysis, the AR(1)–GARCH(1,1) model can
represent the best model. Table 5 shows that the
AR(1)–GARCH(1.1) model has an R-square value
of 0.96, in other words, 99% of the variables have
been explained by the model. Likewise, MSE =
318,73018 provides information that the model has
very good forecasting ability. In addition, in Table
5, MAE has a relatively very small statistic, namely
12.9366563, while the forecasting accuracy is very
good as a representation of a very small MAPE
value of 0.72095993.
Table 5. Statistical Estimation of GARCH
SSE
225023.507
Observations
706
MSE
318.73018
Uncond Var
323.859706
Log
Likelihood
-3008.7904
Total R-
Square
0.9699
SBC
6050.3789
AIC
6027.58082
MAE
12.9366563
AICC
6027.66654
MAPE
0.72095993
HQC
6036.39014
Normality Test
189.4688
Pr > ChiSq
<.0001
It then requires AR(1)–GARCH(1,1) modeling
from Table 6 that the parameter estimation for
AR(1) is very significant because the t value is 4.37
and P = 0.001, indicating alignment with zero with a
significance of P < 0.05. Thus, based on the results
of the AR(1)–GARCH(1,1) analysis, the model
estimation can be presented as follows.
Table 6. Parameter Estimates of The AR(1)–
GARCH(1,1)
Parameter Estimates
Variable
DF
Estimate
Std.
Error
t Value
Approx
Pr>|t|
Intercept
1
1518
242.7643
6.25
<.0001
AR1
1
-0.9975
0.002815
-354.34
<.0001
ARCH0
1
29.4120
10.5180
2.80
0.0052
ARCH1
1
0.1085
0.0248
4.37
<.0001
GARCH1
1
0.8007
0.0515
15.56
<.0001
Or can be explained by the model of AR(1) as the
equation of mean model as:
and the variance model of GARCH(1,1) is as
follows.
The mean model of AR(1) expresses that the
gold prices are affected negatively by its historical
data set at lag 1 of 0.9975; while the variance model
of GARCH(1,1) examines the gold prices variances
are affected by the volatility of its past data at lag 1.
The goal in finding the best model from
GARCH, in the end, is to get values that can predict
the future based on past data. Forecasting in the
financial sector is a future financial forecast for
companies, industries, and countries using historical
internal accounting and sales data, [19]. Future
research into the needs of providers and users of
firms and accurate forecasts is essential for
disseminating financial knowledge of possible
uncertainties, [13].
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Fig. 3: Graph of Forecasting for XAUUSD Prices
Figure 3 presents a graph of Forecasting for
XAUUSD Prices. Specifically, the forecasting
results of XAUUSD prices have experienced a not-
so-sharp decline for 30 days. The slow decline
shows that XAUUSD is a strong instrument, so the
movement is not extreme. However, the error range
that is also predicted shows a fairly large range. The
movement of XAUUSD is very likely to be
influenced by external factors, such as
macroeconomic conditions both domestically and
globally. The projected downtrend of gold prices
confirmed the study of, [20], which found that
during the economic crisis, almost all sectors have a
declining trend.
4 Conclusion
Forecasting is one way to predict how the future
will be, besides that it provides an opportunity to
take into account the bad risks that will occur, which
is then followed by the preparation of a handling
strategy. The results of the study show that the AR-
GARCH(1.1) model can provide the best model for
forecasting with 99% of constructs that can be
explained. The opportunity to predict errors is also
an advantage of this model.
Acknowledgment:
The authors would like to thank the Financial
Exchange for being willing to provide data in this
study. The authors would also like to thank the
University of Lampung because the form of
institutional funding has provided the opportunity
for research to run.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
Rr Erlina, Ayi Ahadiat carried out the concept of the
study.
Fajrin Satria Dwi Kesumah collected and run the
data analysis.
Fajrin Satria Dwi Kesumah , Rialdi Azhar organized
and wrote the article.
Toto Gunarto reviewed the article.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
The authors would also like to thank the University
of Lampung because the form of institutional
funding has provided the opportunity for research to
run.
Conflict of Interest
The authors have no conflict of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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