=Paper=
{{Paper
|id=Vol-2667/paper13
|storemode=property
|title=Forecasting the foreign exchange market using the modified G (ARCH) model
|pdfUrl=https://ceur-ws.org/Vol-2667/paper13.pdf
|volume=Vol-2667
|authors=Nikita Sviatov,Alexander Blagov
}}
==Forecasting the foreign exchange market using the modified G (ARCH) model ==
https://ceur-ws.org/Vol-2667/paper13.pdf
Forecasting the foreign exchange market using
the modified G (ARCH) model
Nikita Sviatov Alexander Blagov
Samara National Research University Samara National Research University
Samara, Russia Samara, Russia
nikitasviatov@gmail.com alexander.blagov@gmail.com
Abstract—The article provides a comparative analysis of where 𝑒𝑡 is deviation of the actual value from the forecast in
existing models for forecasting prices in the foreign exchange the previous period, 𝛽 is coefficient before 𝑒𝑡 , 𝑢𝑡 is “White
market. The authors propose an improved modification of the noise” is residues that do not correlate with the remnants of
model that is most suitable for predicting the behaviour of the
the previous period, 𝑐 is constant.
EUR / USD currency pair. The calculation is performed by the
developed software tool that processes and analyses the entered Another well-known model is the autoregressive model
parameters of the time series. of conditional heteroskedasticity - (G) ARCH. The meaning
of this model is encrypted in its name. So, the ARCH model
Keywords—data analysis, time series analysis, auto-
uses past values of the series for forecasting
regression, foreign exchange market
(autoregression), which in turn is heterogeneous, which is
I. INTRODUCTION manifested in the variability of the variance of random error
Currently, there is great interest in the stock market, and (heteroskedasticity) [7] [8]. This model was proposed by
in particular in the foreign exchange market. Many Robert Engle in 1982 [9], it can be represented as the
researchers create algorithms and methods for its prediction following equation (2):
[1-4]. Therefore, it is of great interest to analyze existing
𝜎𝑡2 = 𝛼0 + 𝛼1 𝑟𝑡−1
2 2
+ ⋯ + 𝛼𝑖 𝑟𝑡−1 , (2)
approaches, as well as develop a model that has a number of 2
advantages over existing analogs. Given the increased where 𝜎𝑡 is volatility function, m𝛼𝑡 is base volatility, 𝑟𝑡−1 is
volume of data necessary for analysis, new, often non- squares of past asset returns, 𝛼𝑖 is model coefficients
classical approaches are required. These include problem showing the effect of past asset returns on the current value
solving using artificial intelligence. Currently, it is used in of volatility.
various fields of activity, including the financial sector. The The (G) ARCH model has a number of disadvantages,
authors set the task of finding the model most suitable for for example, the need to choose a large order of the model
predicting the behavior of the EUR / USD currency pair, as so that the results are better [10-11].
well as its improvement.
Let's try to compare the effectiveness of the ARMA and
Many authors conducted research on this topic and they G (ARCH) models[12-14] on the EUR / USD currency pair
got different results. For example, an interesting approach is (Figure 1).
described in the article on fractal time series analysis [1].
A number of articles describe works on expert short-
term forecasting of the foreign exchange market [2-4]. The
paper [3] presents research on the fundamental analysis of
world currency markets. The article [5] describes the
campaigns used in predicting changes in time series
parameters.
II. ANALYSIS OF EXISTING MODELS
Consider the currently most popular models for
forecasting prices in the foreign exchange market. The
Fig. 1. The graph of the behavior of a currency pair over a time interval
model of autoregression is moving average (ARMA) is one with a highlight of the start date of the study.
of the mathematical models used to analyze the forecasting
of stationary time series in statistics. The ARMA model
generalizes two simpler time series models: the
autoregressive (AR) model and the moving average (MA)
model [4]. As a rule, ARMA models, although they have a
more complex structure, in comparison with AR and MA
models, are characterized by fewer parameters. ARMA
models also have a number of other properties that
determine their practical attractiveness [6].
The predicted value is determined as the following linear
function (1)
Fig.2. The graph of the behavior of a currency pair over a time interval
𝑌𝑡 = 𝑐 + 𝑒𝑡 + 𝛽𝑒𝑡−1 + 𝑢𝑡 , (1) with the highlighting of the end date of the study.
Copyright © 2020 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0)
Data Science
At the beginning of the study period on November 19, Table 2 shows the result of the work of the data of the
2019, the currency pair was at around 1.08301. At the end modified model (with daily expert intervention) in
of this period, 1.2138 (Figure 2). comparison with the base model G (ARCH).
For this study period, a forecast was made using both Applying the modification of the G model (ARCH), the
ARMA and G (ARCH) models. Table 1 shows the results of accuracy of the calculations increased by almost 4%. For the
these models. foreign exchange market, this is a good indicator.
TABLE I. THE RESULTS OF THE MODELS ARMA AND G (ARCH) FOR 42 A modified model with adjustments 2 times a day gives
DAYS an even more accurate result (Table 3).
Parameters ARMA Model Model G TABLE III. THE RESULTS OF THE MODIFIED G (ARCH) MODEL
(ARCH) (EXPERT INTERVENTION 2 TIMES A DAY) FOR 42 DAYS
Mean 0.0000209 0.0000299
Standard error 0.0000427 0.0000402 Parameters ARMA Model Model G
(ARCH)
Standard deviation 0.0005642 0.0005222 Mean 0.0000302 0.0000299
Scope 0.0037821 0.003922 Standard error 0.0000340 0.0000402
Minimum -0.001625 -0.001832 Standard deviation 0.0005219 0.0005222
Maximum 0.002577 0.002677 Scope 0.003988 0.003922
Sum 0.00211404761 0.002542333 Minimum -0.001920 -0.001832
Amount of days 42 42 Maximum 0.00276 0.002677
Sum 0.0027653 0.002542333
According to the results of the models shown in table we
Amount of days 84 42
can see that the G (ARCH) model for this currency pair
turned out to be more accurate. In this model, the standard
In this case, the model prediction accuracy increased by
error has decreased, and there is also a more accurate total
amount. 7% relative to the base model G (ARCH).
The authors implemented modifications to the An obvious factor is a significant increase in the
G (ARCH) model, which showed the best result complexity of this model. Optimization of the modified
model is possible due to the replacement of the expert’s
III. DEVELOPMENT OF G (ARCH) MODEL work with elements of artificial intelligence. As an artificial
MODIFICATION AND THE RESULTS intelligence, we are developing a neural network that will
select this CF, instead of a human. A neural network will be
The model was modified on the basis of an empirical able to more objectively consider factors and the same
approach related to the fact that the value of a currency sample will be an order of magnitude higher.
depends on many factors (events of a different nature taking
place in the world) that the expert can somehow evaluate. Using a neural network, we plan to increase the accuracy
of predictions to at least 10% relative to the base method.
Such an assessment can be made at each step of the
model, making certain adjustments to it (3). These changes IV. CONCLUSION
can be made, for example, daily, so that the next day a more
The paper presents popular time series forecasting
accurate result is obtained. The result of such a model will
models. The authors developed an improved modification of
depend not only on mathematical calculations, but also on
the (G) ARCH model, which showed the best result for
the experience of the person who implements it.
predicting the EUR / USD currency pair. To assess the
𝜎𝑡2 = 𝛼0 + (𝛼1 + 𝑛₁)𝑟𝑡−1
2 2
+ ⋯ + (𝛼𝑖 +𝑛𝑖 )𝑟𝑡−1 (3) performance of the models, a comparative analysis of the
forecast data with the real one was carried out. The results
where 𝑛𝑖 is a parameter whose value the expert sets showed some advantage in the accuracy of forecasting an
depending on events that, in his opinion, could affect the improved model over existing analogues. This is very
value of the currency. important, because this result allows us to evaluate the
benefits of using additional parameters in classical models.
TABLE II. THE RESULTS OF THE MODIFIED G (ARCH) MODEL (WITH
DAILY EXPERT INTERVENTION) FOR 42 DAYS
Additional parameters are expert, but potentially they can be
obtained analytically using various tools, for example,
Parameters ARMA Model Model G neural networks. The authors plan further work to improve
(ARCH)
models for forecasting the behavior of the foreign exchange
Mean 0.0000301 0.0000299
market. As a result, we can say that our neural network will
Standard error 0.0000350 0.0000402
predict the currency price, otherwise than usual, since we
Standard deviation 0.0005111 0.0005222 will not train it on simple mathematical equations, but also
Scope 0.003977 0.003922 take into account the opinions of a person who is versed in
this area and will be able to adjust the model based on his
Minimum -0.001944 -0.001832
experience, and not just numbers, we believe this is the
Maximum 0.00277 0.002677 uniqueness of this development.We use not just
Sum 0.0026562 0.002542333 mathematics, but also human experience. Which can help
find those factors that the neural network cannot see.
Amount of days 42 42
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 55
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