INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND APPLIED MATHEMATICS.
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Combined Model of Markov Switching and Asymmetry of Generalized Seasonal Autoregressive Moving Average Conditional Heteroscedasticity for Early Detection of Financial Crisis in Hong Kong Sugiyanto.
Sri Subanti.
Isnandar Slamet.
Etik Zukhronah.
Irwan Susanto.
Winita Sulandari.
Nabila Churin Aprilia AbstractAiThe financial crisis in Hong Kong occurred in 1997 To prevent a crisis or reduce the impact of a crisis, action is needed through early detection of the crisis using export indicator.
The combination of Markov Switching and Asymmetric Generalized Seasonal Autoregressive Moving Average Conditional Heteroscedasticity (MS-AGSARMACH) models explains the crisis well.
The results show that the MSAGSARMACH.
,1,.
model can explain past and future crises Index TermsAiFinancial Crisis.
Early Detection.
Export.
MSAGSARMACH
I NTRODUCTION
HE development of Hong Kong to become one of the major countries began when Hong Kong became the worldAos financial center, and is considered the most influential country in the world.
In fact, according to the Global Financial Centers Index in 2014 .
Hong Kong is the third most important financial center in the world after New York and London.
In addition, the Hong Kong currency is the 8th most traded currency worldwide .
In addition to Hong KongAos prowess in its economic field.
Hong Kong has also experienced financial crises several times.
One of the causes of Hong KongAos economic downturn was the Asian financial crisis in 1997.
At the height of the Asian crisis in 1998.
Hong KongAos gross domestic product (GDP) shrank by around five percent, property prices fell by 50% .
Unemployment reached six percent .
In addition.
Hong Kong also experienced a crisis in 2008 which resulted in real GDP to 2.
5% from 6.
4% in 2007 .
A way is needed to detect financial crises that occur based on historical data from financial indicators so that the government is able to prevent crises or prepare appropriate policies to minimize the impact of crises.
One of the indicators that can be used to detect the crisis is the export indicator .
in the International Monetary Fund (IMF) .
When a crisis occurs, the export indicator will fluctuate highly .
Therefore the volatility model is very appropriate to be used to explain crises.
Engle has used the autoregressive conditional heteroscedasticity (ARCH) model to explain inflation in England from 1958 to 1977 .
Bollerslev Sugiyanto.
Subanti.
Slamet.
Zukhronah.
Susanto.
Sulandari.
Aprilia are with the Universitas Sebelas Maret.
Ir.
Sutami Street 36A.
Surakarta, 57125.
Indonesia.
e-mail: sugiyanto61@staff.
Manuscript received July 18, 2023.
accepted September 14, 2023.
used the generalized autoregressive conditional heteroscedasticity (GARCH) model to improve the ARCH.
model using gross national product (GNP) data from 1948 to 1983 .
If there is an element of asymmetry in the GARCH model, then Nelson uses the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model to overcome this .
An ARMA model that contains a seasonal element is known as SARMA.
If the data contains seasonal elements, there are heteroscedasticity and asymmetry effects, then the AGSARMACH model is very appropriate to use.
However, the AGSARMACH model has not considered shifts in volatility.
The shift in volatility can be explained through the Markov switching model.
Hamilton and Sumsel have combined the Markov switching model and autoregressive conditional heteroscedasticity (MS-ARCH) to explain the shift in volatility in New York stock prices from July 1962 to December 1987, the results are very good .
Sugiyanto et al.
also combined the two models to explain the crisis in Indonesia using real output and domestic credit/GDP indicators but different crisis thresholds presented by Hamilton and South Sumatra, the results were also very good .
According to Ford et al.
a smoothed probability value of more than 0.
5 describes a condition of high volatility, and conversely, a smoothed probability value of less than 0.
5 describes a condition of low volatility .
According to Hermo-sillo and Hesse, a smoothed probability value of less than 0.
4 is said to be low volatility, between 0.
4 and 0.
6 is said to be moderate volatility, and more than 0.
6 is said to be high volatility .
In conditions of high volatility, crises tend to occur.
Something that has not been answered in other studies is determining the crisis threshold.
In this study, the crisis threshold is determined by the lowest value of the smoothed probability in the MSAGSARMACH model when past crises occur.
Using this crisis threshold, we predict whether or not Hong Kong will be in financial crisis based on export indicator in 2021.
II.
M ETHOD
The data used is monthly Hong Kong export data for the period January 1990 to December 2020 taken from the International Monetary Fund (IMF) website.
The analysis used in this research was carried out with the help of R Studio The steps in this research begin with designing INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND APPLIED MATHEMATICS.
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the data so that it is stationary to obtain the ARMA model.
Detecting seasonal patterns to get the SARMA model, detecting heteroscedasticity to get the SARMACH model, and detecting asymmetry to build the AGSARMACH model.
The use of the Markov Switching model begins with determining the conditions corresponding to the export indicator.
Volatility shifts are described using a transition matrix.
The transition matrix is used to determine the smoothed probabilities.
The smallest value of the smoothed probability from the MSAGSARMAC model, when a crisis occurs, is used as the A smoothed probability value greater than the threshold represents a crisis.
The model used is a model that can explain past crises, and then this model is used to detect future crises.
D ISCUSSION
The export data indicator plot can be seen in Fig.
Fig.
1: Plot Export Indicator The non-heteroscedasticity test uses the Lagrange Ae Multiplier for the residues of the GSARMACH.
The results show that the value of is 0.
757 which is smaller than N0,05.
= 7.
815 and the p-value is 0.
384 which is greater than so it can be concluded that there is no heteroscedasticity The next step that needs to be done is to test the asymmetric effect on the model.
Based on the hypothesis test shows that the model has an asymmetric effect.
The best asymmetry model is the AGSARMACH.
model because it has the smallest AIC value and is the only model where all parameters are significant.
The model AGSARMACH.
can be written as AtOe1
ln Et2 = Oe 4, 651 0, 062
EtOe1
AtOe1
0, 070
1, 804 ln EtOe1 et EtOe1 The test of asymmetric effect on the model is performed.
The result gives p-value equal to 0.
897 which is greater than the value, so it can be concluded that there is no asymmetric effect in the model.
Changes in volatility in the export indicator can be explained by combining the Markov Switching model with the volatility To model the change in volatility, a transition probability matrix can be formed.
Before forming the transition matrix, it is necessary to know the number of states that will be used in the model.
In this study, the number of suitable states is two, as can be seen in Fig.
State 1 states low Figure 1 shows that Hong KongAos export data tends to have an upward trend so that the data can be said to be nonstationary and contains seasonal elements.
For this reason, the data must be stationary and seasonality removed.
ee Fig.
Fig.
3: The Number of States That Match Fig.
2: Plot Stationary Export Indicator After the data is stationary and does not load seasonally, the SARMA model is built.
The SARMA model that has the smallest AIC is SARMA .
, .
, .
The normality test for model residues was carried out using the Kolmogorov-Smirnov test.
The results of the test show that the residuals of the SARMA model are normally The non-autocorrelation test for the residues of the SARMA model uses the Ljung-Box test.
The results of the test show that there is no residual correlation between The Lagrange-Multiplier test is used to perform a nonheteroscedasticity test.
The test results on the residues show that there is heteroscedasticity.
Therefore, the GSARMACH model was formed.
The best model is GSARMACH .
volatility and state 2 states high volatility.
After obtaining the optimal state of 2, the model that will be used to detect a crisis is the MSAGSARMACH.
,1,.
model with the transition probability pi j for i, j = 1, 2.
The transition probability matrix can be written as Based on the probability matrix P, information is obtained that the probability of surviving in state 1 from time t to t 1 is 972 while the probability of surviving in state 2 is 0.
The probability of a shift from state 1 to state 2 is 0.
028 and the probability of a shift from state 2 to state 1 is 0.
After constructing the MS-AGSARMACH.
,1,.
model, the next step is to construct a smoothed probability plot to see whether there is no crisis or crisis based on export indicator.
The smoothed probability plot can be seen in Fig.
Crisis detection can be performed using the smallest smoothed probability value from the MSAGSARMACH.
,1,.
model during a crisis period.
INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND APPLIED MATHEMATICS.
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TABLE i: Comparison of Predicted Value and Actual Smoothed Probability in 2020 Periods Fig.
4: Plot Smoothed EGSARIMACH.
,1,.
Probability Model
MS-
this case we need to define the treshold first by observing the smoothed probability at the time when the crisis occurred.
Therefore we calculate the smoothed probability for October 1997 to July 1998 and October 2009 to March 2009 and presented the results in Table I and Table II, respectively.
TABLE I: Smoothed Probability Value for October 1997 - July Periods October 1997 November 1997 December 1997 January 1998 February 1998 March 1998 April 1998 May 1998 June 1998 July 1998 Smoothed Probability Condition Crisis Crisis Crisis Crisis Crisis Crisis Crisis Crisis Crisis Crisis TABLE II: Smoothed Probability Value for October 2008 March 2009 Periods October 2008 November 2008 December 2008 January 2009 February 2009 March 2009 Smoothed Probability Condition No Crisis Crisis Crisis Crisis Crisis Crisis Based on Table I and Table II, we can see that 0.
is the smallest smoothed probability when the actual condition is crisis.
Therefore this value can be considered as the threshold of crisis condition.
Later, we predict crisis when the predicted smoothed probability is higher than the The next stage is to carry out early detection for test data, namely the period January 2020 to December 2020.
Based on the calculation using MS-AGSARMACH.
,1,.
we obtain smoothed probability values for January to July 2020 and present the results in Table i.
It shows the values are less than the threshold, so we can conclude that predicted conditions are stable, the same as the actual condition.
Thus.
MSAGSARMACH.
,1,.
is appropriate for predicting the financial crisis .
esting dat.
in Hong Kong.
Jan 2020 Feb 2020 March 2020 April 2020 May 2020 June 2020 July 2020 August 2020 September 2020 October 2020 November 2020 December 2020 Prediction Smoothed Probability Condition Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Actual Smoothed Probability Condition Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Based on Table i, it can be concluded that the MSAGSARMACH.
,1,.
model can predict Hong Kong crisis conditions using export indicator correctly because the actual conditions and the predicted values are the same.
Hong KongAos economic conditions in 2021 can also be predicted using the MSAGSARMACH.
,1,.
model by looking at the prediction of the smoothed probability value in 2021.
The prediction results for 2021 can be seen in Table IV.
TABLE IV: Smoothed Probability Prediction for 2021 Periods January 2021 February 2021 March 2021 April 2021 May 2021 June 2021 July 2021 August 2021 September 2021 Prediction Condition Stable Stable Stable Stable Stable Stable Stable Stable Stable Table IV shows that throughout 2021 it is predicted that Hong Kong will not experience a financial crisis based on export indica IV.
CONCLUSION
Based on export indicator, the MS-AGSARMACH.
,1,.
model can accurately explain the financial crisis in Hong Kong in the 1997 Ae 1998 and 2008 Ae 2009 periods.
The model can also predict that there will be no crisis based on export indicator in 2021.
For future research, another macroeconomy indicators will be better to be considered in the model to improve forecast accuracy.
ACKNOWLEDGMENT