Page 49 - Proceeding The 2nd International Seminar of Science and Technology : Accelerating Sustainable Innovation Towards Society 5.0

The 2 International Seminar of Science and Technology
nd
“Accelerating Sustainable innovation towards Society 5.0”
ISST 2022 FST UT 2022
Universitas Terbuka
random variable at time t, ω = regression coefficient in the i-order AR
i
process, i = 1, 2, ..., p, p = orde AR, ∅ = regression coefficient on MA
i
process of order i, i = 1, 2, ..., q, q = orde MA, å = error value at time
t
t, t = time, d = orde differencing.
− − = ∅ + ∑ ( −1 − −1− ) + ∑ ∅ − (3)
1

0
=1
=1
2.2 Autoregressive Conditional Heteroscedastic Model (ARCH)
The Autoregressive Conditional Heteroscedasticity (ARCH) model is
an autoregressive model that occurs in a state of non-constant
variance. This model shows the instability of variance in the time
series model so that it can be used as an alternative for calculating
and modelling data [6]. The basic concept of the ARCH model is the
variance of the squared residuals from several past periods. The
ARCH model with order p denoted ARCH(p) is expressed in two
equations, namely the average equation and the variance equation (4)
and (5) [6], where = dependent variable at time t, = independent

variable at time t, = constant, =multiple regression coefficient,

1
0
= residual.

= â + â + å (4)

1
0

ó 2 = á + á å 2 −1 (5)
1

2.3 Generalized Autoregressive Conditional
Heteroscedasticity Model (GARCH)
The ARCH-GARCH model was developed primarily to address the
issue of volatility in economic and business data, particularly in the
financial sector. This causes the previous forecasting models to be
less able to approach the actual conditions. This volatility is reflected
in the residual variance that does not meet the assumption of
homoscedasticity [10].
This model was developed as a generalization of the volatility model
and in this model, the variance consists of three components [10].
GARCH is one approach to modelling time series with error conditions
varying according to time (heteroscedasticity). GARCH is considered
to provide simpler results because it uses fewer parameters, thereby

28 ISST 2022 – FST Universitas Terbuka, Indonesia
International Seminar of Science and Technology “Accelerating Sustainable
Towards Society 5.0