EWS-GARCH: New Regime Switching Approach to Forecast Value-at-Risk

Marcin Chlebus

doi:10.1515/ceej-2017-0014

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EWS-GARCH: New Regime Switching Approach to Forecast Value-at-Risk

Central European Economic Journal

Volume 3 (2017): Issue 50 (December 2017)

By: Marcin Chlebus

Open Access

|Dec 2018

Figures & Tables

The concept of Value-at-Risk forecasting using an EWS-GARCH model

Tab. 1

The results of the analysis of the quality of Value-at-Risk forecasts obtained from the EWS-GARCH(1,1) models

SFM	TSVM	TUSVM	VALUE-AT-RISK (WHOLE OUT-OF-SAMPLE )									STRESSED VALUE-AT-RISK (THE WORST 250 DAYS)
			EN	ER	ABAD	LOPEZ	CAPORIN	EXCOST	GREEN	AT LEAST YELLOW	RED	EN	ER	GREEN	AT LEAST YELLOW	RED
NONE	GARCH-t	NONE	1.25	0.24%	6.3%	2.46	12.5%	11.6%	98.7% 1	98.7% 1	1.3%	1.03	0.4%	97.5%	98.7%	1.3%
PROBITSEL	GARCH	EX9JI0	4.39	0.84%	8.4%	4.51	11.1%	10.3%	93.7%	98.7%	1.3%	3.56	1.4%	72.2%	93.7%	6.3%
LOGITSEL	GARCH	EX9JI0	4.44	0.85%	8.6%	4.56	11.0%	10.1%	93.7%	98.7%	1.3%	3.61	1.4%	68.4%	93.7%	6.3%
CLOGLOG SEL	GARCH	EX9JI0	4.53	0.86%	8.7%	4.59	10.9%	10.0%	93.7%	98.7%	1.3%	3.66	1.5%	68.4%	93.7%	6.3%
PROBIT	GARCH	EX9JI0	4.56	0.87%	8.5%	4.62	11.0%	10.2%	93.7%	97.5%	2.5%	3.63	1.5%	70.9%	93.7%	6.3%
PROBITSEL	GARCH	EM9JI0	4.58	0.87%	8.8%	4.71	8.7%	7.8%	92.4%	97.5%	2.5%	3.71	1.5%	68.4%	92.4%	7.6%
CLOGLOG	GARCH	EX9JI0	4.59	0.88%	8.6%	4.66	10.8%	10.0%	93.7%	97.5%	2.5%	3.67	1.5%	73.4%	93.7%	6.3%
NONE	GARCH EMP	NONE	4.61	0.88%	9.2%	4.67	7.2%	6.4%	94.9%	97.5%	2.5%	3.73	1.5%	68.4%	96.2%	3.8%
LOGIT	GARCH	EX9JI0	4.62	0.88%	8.6%	4.68	10.9%	10.0%	92.4%	97.5%	2.5%	3.67	1.5%	70.9%	93.7%	6.3%
LOGITSEL	GARCH	EM9JI0	4.63	0.88%	9.0%	4.76	8.6%	7.8%	92.4%	98.7%	1.3%	3.78	1.5%	64.6%	93.7%	6.3%
PROBITSEL	GARCH	EXOJIO	4.67	0.89%	9.0%	4.80	7.9%	7.1%	92.4%	96.2%	3.8%	3.80	1.5%	65.8%	91.1%	8.9%
CLOGLOG SEL	GARCH	EM9JI0	4.71	0.90%	9.1%	4.77	8.5%	7.7%	92.4%	98.7%	1.3%	3.82	1.5%	64.6%	93.7%	6.3%
LOGITSEL	GARCH	EXOJIO	4.75	0.90%	9.1%	4.81	7.8%	7.0%	92.4%	97.5%	2.5%	3.90	1.6%	59.5%	92.4%	7.6%
CLOGLOG SEL	GARCH	EX9_5	4.76	0.91%	9.0%	4.82	17.1%	16.3%	93.7%	98.7%	1.3%	3.81	1.5%	69.6%	93.7%	6.3%
PROBITSEL	GARCH	EX9_5	4.77	0.91%	8.9%	4.84	21.6%	20.8%	93.7%	98.7%	1.3%	3.84	1.5%	69.6%	93.7%	6.3%
PROBIT	GARCH	EM9JI0	4.77	0.91%	8.9%	4.84	8.6%	7.8%	91.1%	97.5%	2.5%	3.80	1.5%	68.4%	93.7%	6.3%
LOGITSEL	GARCH	EX9_5	4.80	0.91%	9.0%	4.86	17.1%	16.3%	93.7%	98.7%	1.3%	3.87	1.5%	69.6%	92.4%	7.6%
CLOGLOG SEL	GARCH	EXOJIO	4.80	0.91%	9.2%	4.80	7.8%	7.0%	92.4%	97.5%	2.5%	3.91	1.6%	59.5%	92.4%	7.6%
CLOGLOG	GARCH	EM9JI0	4.81	0.92%	9.0%	4.88	8.6%	7.7%	91.1%	97.5%	2.5%	3.84	1.5%	69.6%	92.4%	7.6%
LOGIT	GARCH	EX9_5	4.84	0.92%	8.8%	4.90	16.8%	16.0%	92.4%	98.7%	1.3%	3.95	1.6%	64.6%	92.4%	7.6%
PROBIT	GARCH	EX9_5	4.84	0.92%	8.8%	4.90	16.9%	16.1%	92.4%	98.7%	1.3%	3.95	1.6%	64.6%	92.4%	7.6%
LOGIT	GARCH	EM9JI0	4.84	0.92%	9.0%	4.90	8.6%	7.7%	91.1%	97.5%	2.5%	3.85	1.5%	68.4%	93.7%	6.3%
CLOGLOG	GARCH	EX9_5	4.86	0.93%	8.8%	4.93	16.8%	16.0%	92.4%	98.7%	1.3%	3.99	1.6%	64.6%	92.4%	7.6%
PROBIT	GARCH	EXOJIO	4.86	0.93%	9.1%	4.86	7.9%	7.1%	89.9%	97.5%	2.5%	3.87	1.5%	65.8%	92.4%	7.6%
CLOGLOG SEL	GARCH	EM9_5	4.87	0.93%	9.3%	4.94	8.6%	7.8%	92.4%	98.7%	1.3%	3.92	1.6%	64.6%	93.7%	6.3%
PROBITSEL	GARCH	EM9_5	4.87	0.93%	9.1%	4.94	8.6%	7.8%	92.4%	98.7%	1.3%	3.94	1.6%	67.1%	92.4%	7.6%
LOGITSEL	GARCH	EM9_5	4.91	0.94%	9.2%	4.98	8.6%	7.8%	92.4%	98.7%	1.3%	3.99	1.6%	64.6%	91.1%	8.9%
CLOGLOG	GARCH	EXOJIO	4.91	0.94%	9.2%	4.92	7.8%	7.0%	89.9%	96.2%	3.8%	3.92	1.6%	65.8%	88.6%	11.4%
LOGIT	GARCH	EXOJIO	4.92	0.94%	9.2%	4.93	7.8%	7.0%	89.9%	94.9%	5.1%	3.92	1.6%	65.8%	89.9%	10.1%
LOGIT	GARCH	EM9_5	4.95	0.94%	9.1%	5.02	8.5%	7.6%	91.1%	98.7%	1.3%	4.04	1.6%	64.6%	92.4%	7.6%
PROBIT	GARCH	EM9_5	4.95	0.94%	9.1%	5.02	8.5%	7.7%	91.1%	98.7%	1.3%	4.06	1.6%	63.3%	92.4%	7.6%
CLOGLOG	GARCH	EM9_5	4.97	0.95%	9.1%	5.04	8.5%	7.7%	91.1%	98.7%	1.3%	4.08	1.6%	64.6%	92.4%	7.6%
CLOGLOG SEL	GARCH	EX8_5	5.23	1.00%	10.1%	5.23	7.3%	6.5%	91.1%	96.2%	3.8%	4.23	1.7%	58.2%	89.9%	10.1%
PROBITSEL	GARCH	EX8_5	5.25	1.00%	10.0%	5.26	7.3%	6.5%	92.4%	96.2%	3.8%	4.25	1.7%	60.8%	89.9%	10.1%
LOGIT	GARCH	EX8_5	5.27	1.00%	9.9%	5.27	7.3%	6.5%	89.9%	97.5%	2.5%	4.32	1.7%	55.7%	89.9%	10.1%
LOGITSEL	GARCH	EX8_5	5.28	1.01%	10.1%	5.28	7.3%	6.5%	92.4%	96.2%	3.8%	4.28	1.7%	59.5%	87.3%	12.7%
PROBIT	GARCH	EX8_5	5.29	1.01%	9.9%	5.30	7.3%	6.5%	89.9%	97.5%	2.5%	4.33	1.7%	54.4%	89.9%	10.1%
CLOGLOG	GARCH	EX8_5	5.29	1.01%	9.9%	5.30	7.3%	6.5%	88.6%	97.5%	2.5%	4.35	1.7%	55.7%	89.9%	10.1%
CLOGLOG SEL	GARCH	EMOJIO	6.01	1.15%	12.6%	6.02	6.8%	6.0%	82.3%	92.4%	7.6%	4.99	2.0%	50.6%	79.7%	20.3%
PROBITSEL	GARCH	EMOJIO	6.03	1.15%	12.4%	6.03	6.8%	6.1%	82.3%	93.7%	6.3%	4.99	2.0%	51.9%	79.7%	20.3%
LOGITSEL	GARCH	EMOJIO	6.04	1.15%	12.7%	6.04	6.8%	6.0%	83.5%	92.4%	7.6%	5.01	2.0%	48.1%	79.7%	20.3%
PROBIT	GARCH	EMOJIO	6.19	1.18%	12.7%	6.20	6.8%	6.0%	81.0%	92.4%	7.6%	5.08	2.0%	46.8%	81.0%	19.0%
CLOGLOG	GARCH	EMOJIO	6.20	1.18%	12.8%	6.21	6.8%	6.0%	79.7%	92.4%	7.6%	5.05	2.0%	49.4%	79.7%	20.3%
LOGIT	GARCH	EMOJIO	6.23	1.19%	12.8%	6.23	6.8%	6.0%	81.0%	92.4%	7.6%	5.09	2.0%	48.1%	79.7%	20.3%
CLOGLOG SEL	GARCH	EM8_5	6.29	1.20%	13.2%	6.30	6.7%	5.9%	81.0%	91.1%	8.9%	5.15	2.1%	43.0%	75.9%	24.1%
PROBITSEL	GARCH	EM8_5	6.37	1.21%	13.1%	6.37	6.7%	5.9%	81.0%	92.4%	7.6%	5.22	2.1%	43.0%	77.2%	22.8%
LOGITSEL	GARCH	EM8_5	6.37	1.21%	13.2%	6.37	6.7%	5.9%	79.7%	89.9%	10.1%	5.24	2.1%	43.0%	77.2%	22.8%
LOGIT	GARCH	EM8_5	6.39	1.22%	12.9%	6.40	6.7%	5.9%	79.7%	92.4%	7.6%	5.29	2.1%	36.7%	79.7%	20.3%
CLOGLOG	GARCH	EM8_5	6.39	1.22%	12.9%	6.40	6.7%	5.9%	78.5%	92.4%	7.6%	5.32	2.1%	38.0%	78.5%	21.5%
NONE	GARCH	NONE	6.42	1.22%	12.5%	6.42	6.6%	5.8%	78.5%	93.7%	6.3%	5.18	2.1%	39.2%	78.5%	21.5%
PROBIT	GARCH	EM8_5	6.43	1.22%	13.1%	6.44	6.7%	5.9%	79.7%	91.1%	8.9%	5.34	2.1%	35.4%	78.5%	21.5%
NONE	EGARCH	NONE	6.53	1.24%	12.5%	6.54	6.7%	5.9%	78.5%	92.4%	7.6%	5.19	2.1%	40.5%	81.0%	19.0%

[i] Notes: In the table, white fields refer to the EWS-GARCH models, while grey fields to the benchmark models.

[ii] In the table, the following abbreviations are used: SFM – the state forecasting model, TSVM – the Value-at-Risk forecasting model in the state of tranquillity, TUSVM – the Value-at-Risk forecasting model in a state of turbulence, EN – the average number of exceedances, ER – the average excess ratio, ABAD – the average value of the Abad & Benito cost function, LOPEZ – the average value of the Lopez cost function, CAPORIN – the average value of the Caporin cost function, EXCOST – the average value of the excessive cost function, GREEN – the average frequency of a model being in the green zone, AT LEAST YELLOW – the average frequency of a model being at least in the yellow zone, RED – the average frequency of a model being in the red zone. In the states forecasting model abbreviation SEL means that stepwise selection process was used.

[iii] Short names of Value-at-Risk models in the state of turbulence are in the form DRQ_CP, where the DR defines a distribution of returns, Q defines the quantile for which Value-at-Risk was forecasted and CP defines the cut-off point that was used to forecast the state of turbulence in the states forecasting model. For the distributions in the state of turbulence following abbreviations are used: EX − exponential distribution, EM − empirical distribution; Q equal to 9 represents the 99th percentile, 0 represents the 90th percentile, and 8 represents the 80th percentile; 5% cut-off is denoted by 5 and the cut-off point equal to 10% by 10.

[iv] Source: Author’s own calculations.

Tab. 2

The results of the analysis of the quality of Value-at-Risk forecasts obtained from the EWS-GARCH(1,1) models – coverage tests results

SFM	TSVM	TUSVM	LR_UC	LR_IND	LR_CC	Z_UC	Z^D_UC	Z^G_UC
LOGIT	GARCH	EX8_5	5.06%	6.33%	5.06%	12.66%	2.53%	10.13%
PROBIT	GARCH	EX8_5	5.06%	6.33%	5.06%	12.66%	2.53%	10.13%
CLOGLOG	GARCH	EX8_5	5.06%	6.33%	5.06%	13.92%	2.53%	11.39%
PROBIT SEL	GARCH	EX8_5	6.33%	12.66%	6.33%	10.13%	2.53%	7.59%
CLOGLOG	GARCH	EX9_5	6.33%	10.13%	6.33%	12.66%	5.06%	7.59%
LOGIT	GARCH	EX9_5	6.33%	10.13%	6.33%	12.66%	5.06%	7.59%
PROBIT	GARCH	EX9_5	6.33%	8.86%	6.33%	12.66%	5.06%	7.59%
CLOGLOG	GARCH	EM9_5	6.33%	8.86%	6.33%	13.92%	5.06%	8.86%
LOGIT	GARCH	EM9_5	6.33%	8.86%	6.33%	13.92%	5.06%	8.86%
PROBIT	GARCH	EM9_5	6.33%	7.59%	6.33%	13.92%	5.06%	8.86%
LOGIT SEL	GARCH	EX9_5	6.33%	12.66%	8.86%	11.39%	5.06%	6.33%
LOGIT SEL	GARCH	EM9_5	6.33%	12.66%	8.86%	12.66%	5.06%	7.59%
NONE	GARCH EMP	NONE	7.59%	8.86%	5.06%	10.13%	5.06%	5.06%
LOGIT SEL	GARCH	EX8_5	7.59%	11.39%	6.33%	11.39%	3.80%	7.59%
CLOGLOG SEL	GARCH	EX8_5	7.59%	11.39%	6.33%	12.66%	3.80%	8.86%
CLOGLOG SEL	GARCH	EX9_5	7.59%	12.66%	8.86%	12.66%	6.33%	6.33%
CLOGLOG SEL	GARCH	EM9_5	7.59%	12.66%	8.86%	13.92%	6.33%	7.59%
PROBIT SEL	GARCH	EM9_5	7.59%	12.66%	8.86%	13.92%	6.33%	7.59%
PROBIT SEL	GARCH	EM0_10	7.59%	12.66%	8.86%	18.99%	1.27%	17.72%
NONE	GARCH	NONE	8.86%	8.86%	7.59%	24.05%	2.53%	21.52%
PROBIT SEL	GARCH	EX9_5	8.86%	12.66%	8.86%	13.92%	7.59%	6.33%
LOGIT SEL	GARCH	EM0_10	8.86%	13.92%	11.39%	17.72%	1.27%	16.46%
CLOGLOG SEL	GARCH	EM0_10	8.86%	15.19%	11.39%	18.99%	1.27%	17.72%
LOGIT	GARCH	EM0_10	8.86%	12.66%	11.39%	20.25%	1.27%	18.99%
PROBIT	GARCH	EM0_10	8.86%	12.66%	11.39%	20.25%	1.27%	18.99%
PROBIT SEL	GARCH	EM8_5	8.86%	11.39%	11.39%	20.25%	1.27%	18.99%
CLOGLOG	GARCH	EM0_10	8.86%	15.19%	12.66%	21.52%	1.27%	20.25%
LOGIT	GARCH	EM8_5	8.86%	11.39%	12.66%	21.52%	1.27%	20.25%
CLOGLOG	GARCH	EM8_5	8.86%	11.39%	12.66%	22.78%	1.27%	21.52%
CLOGLOG SEL	GARCH	EX0_10	10.13%	11.39%	7.59%	15.19%	7.59%	7.59%
LOGIT	GARCH	EX9_10	10.13%	12.66%	7.59%	15.19%	7.59%	7.59%
LOGIT	GARCH	EM9_10	10.13%	12.66%	7.59%	16.46%	7.59%	8.86%
LOGIT SEL	GARCH	EX0_10	10.13%	8.86%	8.86%	15.19%	7.59%	7.59%
CLOGLOG SEL	GARCH	EM9_10	10.13%	11.39%	8.86%	16.46%	8.86%	7.59%
NONE	EGARCH	NONE	10.13%	5.06%	8.86%	24.05%	2.53%	21.52%
PROBIT	GARCH	EM8_5	10.13%	11.39%	13.92%	21.52%	1.27%	20.25%
LOGIT	GARCH	EX0_10	11.39%	12.66%	6.33%	16.46%	6.33%	10.13%
CLOGLOG	GARCH	EX0_10	11.39%	11.39%	6.33%	17.72%	7.59%	10.13%
PROBIT	GARCH	EX0_10	11.39%	12.66%	6.33%	18.99%	8.86%	10.13%
CLOGLOG	GARCH	EX9_10	11.39%	11.39%	7.59%	15.19%	8.86%	6.33%
CLOGLOG	GARCH	EM9_10	11.39%	11.39%	7.59%	17.72%	8.86%	8.86%
CLOGLOG SEL	GARCH	EX9_10	11.39%	11.39%	8.86%	16.46%	10.13%	6.33%
PROBIT SEL	GARCH	EX9_10	11.39%	8.86%	11.39%	16.46%	10.13%	6.33%
LOGIT SEL	GARCH	EM9_10	11.39%	8.86%	11.39%	17.72%	10.13%	7.59%
CLOGLOG SEL	GARCH	EM8_5	11.39%	11.39%	11.39%	21.52%	2.53%	18.99%
LOGIT SEL	GARCH	EM8_5	11.39%	11.39%	12.66%	21.52%	1.27%	20.25%
PROBIT	GARCH	EX9_10	12.66%	12.66%	7.59%	16.46%	10.13%	6.33%
PROBIT	GARCH	EM9_10	12.66%	12.66%	7.59%	18.99%	10.13%	8.86%
PROBIT SEL	GARCH	EX0_10	12.66%	8.86%	10.13%	16.46%	8.86%	7.59%
LOGIT SEL	GARCH	EX9_10	12.66%	8.86%	11.39%	17.72%	11.39%	6.33%
PROBIT SEL	GARCH	EM9_10	12.66%	8.86%	11.39%	17.72%	10.13%	7.59%
NONE	GARCH-t	NONE	77,22%	2,53%	51,90%	77,22%	75,95%	1,27%

[i] Notes: In the table, white fields refer to the EWS-GARCH models, while grey fields to benchmark the models.

[ii] In the table, the following abbreviations are used: SFM – the state forecasting model, TSVM – the Value-at-Risk forecasting model in a state of tranquillity, TUSVM − the Value-at-Risk forecasting model in a state of turbulence, LR_UC − the ratio of cases in which the null hypothesis was rejected in the Kupiec test, LR_IND − the ratio of cases in which the null hypothesis was rejected in the LR_IND part of the Christofferssen test, LR_CC − the ratio of cases in which the null hypothesis was rejected in the Christofferssen test, Z_UC − the ratio of cases in which the null hypothesis was rejected in the asymptotic test of unconditional coverage, Z_DUC − the ratio of cases in which the null hypothesis was rejected in the asymptotic test of unconditional coverage in favour of alternative hypothesis that the actual excess ratio is significantly lower than expected, Z_GUC − the ratio of cases in which the null hypothesis was rejected in the asymptotic test of unconditional coverage in favour of an alternative hypothesis that the actual excess ratio is significantly higher than expected. All tests were performed for the 5% significance level, except the asymptotic test of unconditional coverage, where level of significance was set up to 10% (5% for each tail).

[iii] Short names of the Value-at-Risk models in the state of turbulence are in the form DRQ_CP, where the DR defines a distribution of returns, Q defines the quantile for which Value-at-Risk was forecasted and CP defines the cut-off point that was used to forecast the state of turbulence in the states forecasting model. For the distributions in the state of turbulence following abbreviations are used: EX − exponential distribution, EM − empirical distribution; Q equal to 9 represents the 99^th percentile, 0 represents the 90^th percentile, and 8 represents the 80^th percentile; 5% cut-off is denoted by 5 and the cut-off point equal to 10% by 10.

[iv] Source: Author’s own calculations.

Tab.3

The results of the analysis of the quality of Value-at-Risk forecasts obtained from the EWS-GARCH(1,1) models with the amendment to the empirical distribution of random errors

SFM	TSVM	TUSVM	VALUE-AT-RISK (WHOLE OUT-OF-SAMPLE )									STRESSED VALUE-AT-RISK (THE WORST 250 DAYS)
			EN	ER	ABAD	LOPEZ	CAPORIN	EXCOST	GREEN	ATLEASTYELLOW	RED	EN	ER	GREEN	ATLEASTYELLOW	RED
NONE	GARCH-t	NONE	1.25	0.24%	6.3%	2.46	12.5%	11.6%	98.7%	98.7%	1.3%	1.03	0.4%	97.5%	98.7%	1.3%
PROBITSEL	GARCH EMP	EX9_10	3.06	0.58%	6.4%	3.27	11.6%	10.7%	100.0%	100.0%	0.0%	2.56	1.0%	88.6%	100.0%	0.0%
LOGITSEL	GARCH EMP	EX9_10	3.09	0.59%	6.4%	3.26	11.4%	10.6%	100.0%	100.0%	0.0%	2.58	1.0%	89.9%	98.7%	1.3%
CLOGLOG SEL	GARCH EMP	EX9_10	3.16	0.60%	6.6%	3.34	11.3%	10.5%	100.0%	100.0%	0.0%	2.62	1.0%	91.1%	98.7%	1.3%
CLOGLOG	GARCH EMP	EX9_10	3.18	0.61%	6.3%	3.31	11.3%	10.5%	100.0%	100.0%	0.0%	2.67	1.1%	88.6%	100.0%	0.0%
PROBIT	GARCH EMP	EX9_10	3.18	0.61%	6.3%	3.31	11.5%	10.7%	100.0%	100.0%	0.0%	2.66	1.1%	87.3%	100.0%	0.0%
LOGIT	GARCH EMP	EX9_10	3.20	0.61%	6.3%	3.33	11.3%	10.5%	100.0%	100.0%	0.0%	2.68	1.1%	88.6%	100.0%	0.0%
PROBITSEL	GARCH EMP	EM9_10	3.25	0.62%	6.8%	3.48	9.1%	8.3%	100.0%	100.0%	0.0%	2.72	1.1%	86.1%	100.0%	0.0%
LOGITSEL	GARCH EMP	EM9_10	3.28	0.62%	6.8%	3.46	9.1%	8.3%	100.0%	100.0%	0.0%	2.76	1.1%	87.3%	98.7%	1.3%
CLOGLOG SEL	GARCH EMP	EM9_10	3.34	0.64%	7.0%	3.52	9.0%	8.2%	100.0%	100.0%	0.0%	2.77	1.1%	88.6%	98.7%	1.3%
PROBITSEL	GARCH EMP	EX0_10	3.34	0.64%	6.9%	3.52	8.4%	7.5%	100.0%	100.0%	0.0%	2.80	1.1%	86.1%	100.0%	0.0%
CLOGLOG	GARCH EMP	EM9_10	3.39	0.65%	6.8%	3.53	9.0%	8.2%	100.0%	100.0%	0.0%	2.81	1.1%	84.8%	100.0%	0.0%
LOGITSEL	GARCH EMP	EX0_10	3.39	0.65%	7.0%	3.53	8.3%	7.5%	100.0%	100.0%	0.0%	2.86	1.1%	84.8%	98.7%	1.3%
PROBIT	GARCH EMP	EM9_10	3.39	0.65%	6.7%	3.53	9.1%	8.3%	100.0%	100.0%	0.0%	2.80	1.1%	83.5%	100.0%	0.0%
PROBITSEL	GARCH EMP	EX9_5	3.39	0.65%	6.5%	3.48	22.1%	21.3%	100.0%	100.0%	0.0%	2.81	1.1%	87.3%	100.0%	0.0%
LOGIT	GARCH EMP	EM9_10	3.42	0.65%	6.8%	3.56	9.0%	8.2%	100.0%	100.0%	0.0%	2.82	1.1%	84.8%	100.0%	0.0%
CLOGLOG SEL	GARCH EMP	EX0_10	3.43	0.65%	7.1%	3.57	8.3%	7.5%	100.0%	100.0%	0.0%	2.85	1.1%	86.1%	98.7%	1.3%
CLOGLOG SEL	GARCH EMP	EX9_5	3.43	0.65%	6.7%	3.52	17.6%	16.8%	100.0%	100.0%	0.0%	2.81	1.1%	87.3%	100.0%	0.0%
LOGITSEL	GARCH EMP	EX9_5	3.47	0.66%	6.6%	3.56	17.6%	16.8%	100.0%	100.0%	0.0%	2.87	1.1%	83.5%	100.0%	0.0%
LOGIT	GARCH EMP	EX9_5	3.48	0.66%	6.3%	3.57	17.3%	16.5%	100.0%	100.0%	0.0%	2.92	1.2%	87.3%	100.0%	0.0%
PROBIT	GARCH EMP	EX0_10	3.48	0.66%	6.9%	3.57	8.3%	7.5%	100.0%	100.0%	0.0%	2.87	1.1%	82.3%	98.7%	1.3%
CLOGLOG	GARCH EMP	EXCMO	3.49	0.67%	7.0%	3.59	8.3%	7.5%	100.0%	100.0%	0.0%	2.90	1.2%	82.3%	98.7%	1.3%
CLOGLOG	GARCH EMP	EX9_5	3.49	0.67%	6.3%	3.59	17.3%	16.5%	100.0%	100.0%	0.0%	2.95	1.2%	86.1%	100.0%	0.0%
PROBIT	GARCH EMP	EX9_5	3.49	0.67%	6.4%	3.59	17.4%	16.6%	100.0%	100.0%	0.0%	2.92	1.2%	87.3%	100.0%	0.0%
PROBITSEL	GARCH EMP	EM9_5	3.49	0.67%	6.7%	3.59	9.1%	8.3%	100.0%	100.0%	0.0%	2.89	1.2%	87.3%	100.0%	0.0%
LOGIT	GARCH EMP	EX0_10	3.51	0.67%	7.0%	3.60	8.3%	7.5%	100.0%	100.0%	0.0%	2.90	1.2%	82.3%	98.7%	1.3%
CLOGLOG SEL	GARCH EMP	EM9_5	3.54	0.68%	6.8%	3.59	9.1%	8.3%	100.0%	100.0%	0.0%	2.90	1.2%	86.1%	100.0%	0.0%
LOGITSEL	GARCH EMP	EM9_5	3.58	0.68%	6.7%	3.63	9.1%	8.3%	100.0%	100.0%	0.0%	2.96	1.2%	83.5%	100.0%	0.0%
LOGIT	GARCH EMP	EM9_5	3.59	0.68%	6.6%	3.64	9.0%	8.2%	100.0%	100.0%	0.0%	3.01	1.2%	87.3%	100.0%	0.0%
CLOGLOG	GARCH EMP	EM9_5	3.61	0.69%	6.6%	3.66	9.0%	8.2%	100.0%	100.0%	0.0%	3.04	1.2%	86.1%	100.0%	0.0%
PROBIT	GARCH EMP	EM9_5	3.61	0.69%	6.6%	3.66	9.0%	8.2%	100.0%	100.0%	0.0%	3.03	1.2%	87.3%	100.0%	0.0%
PROBITSEL	GARCH EMP	EX8_5	3.87	0.74%	7.6%	3.93	7.8%	7.0%	100.0%	100.0%	0.0%	3.19	1.3%	78.5%	100.0%	0.0%
CLOGLOG SEL	GARCH EMP	EX8_5	3.90	0.74%	7.7%	3.90	7.8%	7.0%	100.0%	100.0%	0.0%	3.19	1.3%	79.7%	98.7%	1.3%
LOGIT	GARCH EMP	EX8_5	3.91	0.75%	7.4%	3.91	7.8%	7.0%	100.0%	100.0%	0.0%	3.29	1.3%	82.3%	98.7%	1.3%
CLOGLOG	GARCH EMP	EX8_5	3.92	0.75%	7.4%	3.93	7.8%	7.0%	100.0%	100.0%	0.0%	3.32	1.3%	81.0%	98.7%	1.3%
LOGITSEL	GARCH EMP	EX8_5	3.95	0.75%	7.6%	3.95	7.8%	7.0%	100.0%	100.0%	0.0%	3.24	1.3%	77.2%	98.7%	1.3%
PROBIT	GARCH EMP	EX8_5	3.95	0.75%	7.5%	3.95	7.8%	7.0%	100.0%	100.0%	0.0%	3.30	1.3%	79.7%	98.7%	1.3%
NONE	GARCH EMP	NONE	4.61	0.88%	9.16%	4.67	7.23%	6.43%	94.9%	97.5%	2.5%	3.73	1.49%	68.4%	96.2%	3.8%
NONE	EGARCH_EMP	NONE	4.84	0.92%	9.46%	4.84	7.29%	6.49%	93.7%	96.2%	3.8%	4.01	1.61%	74.7%	94.9%	5.1%
NONE	GARCH	NONE	6.42	1.22%	12.48%	6.42	6.58%	5.79%	78.5%	93.7%	6.3%	5.18	2.07%	39.2%	78.5%	21.5%
NONE	EGARCH	NONE	6.53	1.24%	12.48%	6.54	6.68%	5.90%	78.5%	92.4%	7.6%	5.19	2.08%	40.5%	81.0%	19.0%

[i] Notes: In the table, white fields refer to the EWS-GARCH models, while grey fields to benchmark the models

[ii] In the table the following abbreviations are used: SFM – the state forecasting model, TSVM – the Value-at-Risk forecasting model in the state of tranquillity, TUSVM − the Value-at-Risk forecasting model in a state of turbulence, EN − the average number of exceedances, ER – the average excess ratio, ABAD − the average value of the Abad & Benito cost function, LOPEZ − the average value of the Lopez cost function, CAPORIN − the average value of the Caporin cost function, EXCOST − the average value of the excessive cost function, GREEN – the average frequency of a model being in the green zone, AT LEAST YELLOW – the average frequency of a model being at least in the yellow zone, RED – the average frequency of a model being in the red zone. In the states forecasting model abbreviation SEL means that stepwise selection process was used.

[iii] Short names of the Value-at-Risk models in the state of turbulence are in the form DRQ_CP, where the DR defines a distribution of returns, Q defines the quantile for which Value-at-Risk was forecasted and CP defines the cut-off point that was used to forecast the state of turbulence in the states forecasting model. For the distributions in the state of turbulence following abbreviations are used: EX − exponential distribution, EM − empirical distribution; Q equal to 9 represents the 99th percentile, 0 represents the 90th percentile, and 8 represents the 80th percentile; 5% cut-off is denoted by 5 and the cut-off point equal to 10% by 10.

[iv] Source: Author’s own calculations.

Tab. 4

The results of the analysis of the quality of Value-at-Risk forecasts obtained from the EWS-GARCH(1,1) models with the amendment to the empirical distribution of random errors - coverage tests results

SFM	TSVM	TUSVM	LR_UC	LR_IND	LR_CC	Z_UC	Z^D_UC	Z^G_UC
NONE	GARCH EMP	NONE	7.59%	8.86%	5.06%	10.13%	5.06%	5.06%
CLOGLOG	GARCH EMP	EX8_5	8.86%	5.06%	1.27%	8.86%	8.86%	0.00%
LOGIT	GARCH EMP	EX8_5	8.86%	5.06%	1.27%	8.86%	8.86%	0.00%
PROBIT	GARCH EMP	EX8_5	8.86%	5.06%	1.27%	8.86%	8.86%	0.00%
NONE	GARCH	NONE	8.86%	8.86%	7.59%	24.05%	2.53%	21.52%
LOGIT SEL	GARCH EMP	EX8_5	10.13%	7.59%	2.53%	10.13%	10.13%	0.00%
PROBIT SEL	GARCH EMP	EX8_5	10.13%	8.86%	3.80%	10.13%	10.13%	0.00%
NONE	EGARCH	NONE	10.13%	5.06%	8.86%	24.05%	2.53%	21.52%
CLOGLOG SEL	GARCH EMP	EX8_5	11.39%	7.59%	2.53%	11.39%	11.39%	0.00%
CLOGLOG	GARCH EMP	EM9_5	11.39%	6.33%	3.80%	11.39%	11.39%	0.00%
LOGIT	GARCH EMP	EM9_5	11.39%	6.33%	3.80%	11.39%	11.39%	0.00%
PROBIT	GARCH EMP	EM9_5	11.39%	5.06%	3.80%	11.39%	11.39%	0.00%
CLOGLOG	GARCH EMP	EX9_5	11.39%	6.33%	5.06%	11.39%	11.39%	0.00%
LOGIT	GARCH EMP	EX9_5	11.39%	6.33%	5.06%	11.39%	11.39%	0.00%
PROBIT	GARCH EMP	EX9_5	11.39%	6.33%	5.06%	11.39%	11.39%	0.00%
LOGIT SEL	GARCH EMP	EM9_5	13.92%	8.86%	6.33%	13.92%	13.92%	0.00%
LOGIT SEL	GARCH EMP	EX9_5	13.92%	8.86%	7.59%	13.92%	13.92%	0.00%
LOGIT	GARCH EMP	EX0_10	15.19%	8.86%	5.06%	15.19%	15.19%	0.00%
CLOGLOG SEL	GARCH EMP	EM9_5	15.19%	8.86%	6.33%	15.19%	15.19%	0.00%
CLOGLOG SEL	GARCH EMP	EX0_10	15.19%	8.86%	7.59%	15.19%	15.19%	0.00%
CLOGLOG SEL	GARCH EMP	EX9_5	15.19%	8.86%	7.59%	15.19%	15.19%	0.00%
CLOGLOG	GARCH EMP	EX0_10	16.46%	7.59%	5.06%	16.46%	16.46%	0.00%
PROBIT	GARCH EMP	EX0_10	16.46%	8.86%	5.06%	16.46%	16.46%	0.00%
LOGIT	GARCH EMP	EM9_10	16.46%	8.86%	6.33%	16.46%	16.46%	0.00%
PROBIT SEL	GARCH EMP	EM9_5	16.46%	8.86%	7.59%	16.46%	16.46%	0.00%
LOGIT	GARCH EMP	EX9_10	17.72%	8.86%	6.33%	17.72%	17.72%	0.00%
PROBIT	GARCH EMP	EM9_10	17.72%	8.86%	6.33%	17.72%	17.72%	0.00%
CLOGLOG	GARCH EMP	EM9_10	17.72%	7.59%	7.59%	17.72%	17.72%	0.00%
LOGIT SEL	GARCH EMP	EX0_10	17.72%	7.59%	7.59%	17.72%	17.72%	0.00%
PROBIT SEL	GARCH EMP	EX9_5	17.72%	8.86%	7.59%	17.72%	17.72%	0.00%
CLOGLOG SEL	GARCH EMP	EM9_10	17.72%	8.86%	10.13%	17.72%	17.72%	0.00%
PROBIT	GARCH EMP	EX9_10	18.99%	8.86%	6.33%	18.99%	18.99%	0.00%
CLOGLOG	GARCH EMP	EX9_10	18.99%	7.59%	7.59%	18.99%	18.99%	0.00%
PROBIT SEL	GARCH EMP	EX0_10	20.25%	6.33%	8.86%	20.25%	20.25%	0.00%
CLOGLOG SEL	GARCH EMP	EX9_10	20.25%	7.59%	10.13%	20.25%	20.25%	0.00%
LOGIT SEL	GARCH EMP	EM9_10	21.52%	7.59%	11.39%	21.52%	21.52%	0.00%
PROBIT SEL	GARCH EMP	EM9_10	21.52%	6.33%	12.66%	21.52%	21.52%	0.00%
PROBIT SEL	GARCH EMP	EX9_10	22.78%	6.33%	12.66%	22.78%	22.78%	0.00%
LOGIT SEL	GARCH EMP	EX9_10	24.05%	6.33%	11.39%	24.05%	24.05%	0.00%
NONE	GARCH-t	NONE	77.22%	2.53%	51.90%	77.22%	75.95%	1.27%

[i] Notes: In the table, white fields refer to the EWS-GARCH models, while grey fields to benchmark the models.

[ii] In the table, the following abbreviations are used: SFM – the state forecasting model, TSVM – the Value-at-Risk forecasting model in the state of tranquillity, TUSVM − the Value-at-Risk forecasting model in a state of turbulence, LRUC − the ratio of cases in which the null hypothesis was rejected in the Kupiec test, LRIND − the ratio of cases in which the null hypothesis was rejected in the LRIND part of the Christofferssen test, LRCC − the ratio of cases in which the null hypothesis was rejected in the Christofferssen test, ZUC − the ratio of cases in which the null hypothesis was rejected in the asymptotic test of unconditional coverage, ZDUC − the ratio of cases in which the null hypothesis was rejected in the asymptotic test of unconditional coverage in favour of alternative hypothesis that the actual excess ratio is significantly lower than expected, ZGUC − the ratio of cases in which the null hypothesis was rejected in the asymptotic test of unconditional coverage in favour of an alternative hypothesis that the actual excess ratio is significantly higher than expected. All tests were performed for the 5% significance level, except the asymptotic test of unconditional coverage, where level of significance was set up to 10% (5% for each tail).

[iii] Short names of the Value-at-Risk models in the state of turbulence are in the form DRQ_CP, where the DR defines a distribution of returns, Q defines the quantile for which Value-at-Risk was forecasted and CP defines the cut-off point that was used to forecast the state of turbulence in the states forecasting model. For the distributions in the state of turbulence following abbreviations are used: EX - exponential distribution, EM - empirical distribution; Q equal to 9 represents the 99th percentile, 0 represents the 90th percentile, and 8 represents the 80th percentile; 5% cut-off is denoted by 5 and the cut-off point equal to 10% by 10.

[iv] Source: Author’s own calculations.

Tab. A1

Industries and capitalizations in the end of the year 2011 of companies considered in the modelling

COMPANY NAME	ORIGIN	INDUSTRY	CAPITALIZATION (MLN €)
AMPLI S.A	PL	WHOLESALE TRADE	€ 1
ASSECO POLAND S.A	PL	IT INDUSTRY	€ 852
ATLANTA S.A	PL	WHOLESALE TRADE	€ 15
ATLANTIS S.A	PL	FINANCE - OTHER	€ 13
ATM GRUPA S.A	PL	MEDIA	€ 21
AWBUD S.A	PL	CONSTRUCTION	€ 32
BBI ZENERIS NFI S.A	PL	FINANCE - OTHER	€ 12
BETACOM S.A	PL	IT INDUSTRY	€ 3
BIOTON S.A	PL	PHARMACEUTICAL	€ 90
BRE BANK S.A	PL	BANKS	€ 2345
CENTROZAP S.A	PL	METAL INDUSTRY	€ 12
CERAMIKA NOWA GALA S.A	PL	BUILDING MATERIALS	€ 27
CEZ A.S	FOREIGN	ENERGETICS	€ 18,043
COGNOR S.A	PL	WHOLESALE TRADE	€ 49
DM IDM S.A	PL	CAPITAL MARKET	€ 64
DOM DEVELOPMENT S.A	PL	DEVELOPERS	€ 164
DUDA S.A	PL	FOOD INDUSTRY	€ 40
ECHO INVESTMENT S.A	PL	DEVELOPERS	€ 313
EFEKT S.A	PL	WHOLESALE TRADE	€ 3
ELEKTRO BUDOWA S.A	PL	CONSTRUCTION	€ 104
ELZAB S.A	PL	IT INDUSTRY	€ 5
ENERGOMONTAŻ-POŁUDNIE S.A	PL	CONSTRUCTION	€ 30
ENERGOPOL-POŁUDNIE S.A	PL	CONSTRUCTION	€ 18
EUROCASH S.A	PL	RETAIL	€ 885
FAM GK S.A	PL	METAL INDUSTRY	€ 9
FAMUR S.A	PL	ELECTROMECHANICAL INDUSTRY	€ 313
FARMACOL S.A	PL	WHOLESALE TRADE	€ 121
FERRUM S.A	PL	METAL INDUSTRY	€ 46
FORTE S.A	PL	PULP AND PAPER INDUSTRY	€ 51
GLOBE TRADE CENTRE S.A	PL	DEVELOPERS	€ 462
HYDROTOR S.A	PL	ELECTROMECHANICAL INDUSTRY	€ 11
IMPEXMETAL S.A	PL	METAL INDUSTRY	€ 158
INSTAL KRAKÓW S.A	PL	CONSTRUCTION	€ 20
INTER GROCLIN AUTO S.A	PL	AUTOMOTIVE	€ 14
IZOLACJA JAROCIN S.A	PL	BUILDING MATERIALS	€ 2
KCI S.A	PL	DEVELOPERS	€ 4
KGHM S.A	PL	RAW MATERIALS	€ 5,008
KOGENERACJA S.A	PL	ENERGETICS	€ 234
LPP S.A	PL	RETAIL	€ 811
MCLOGIC S.A	PL	IT INDUSTRY	€ 16
MENNICA POLSKA S.A	PL	METAL INDUSTRY	€ 147
MOSTOSTAL WARSZAWA S.A	PL	CONSTRUCTION	€ 72
MOSTOSTAL- EXPORT S.A	PL	CONSTRUCTION	€ 7
MOSTOSTAL PŁOCK S.A	PL	CONSTRUCTION	€ 7
MOSTOSTAL ZABRZE - HOLDING S	A. PL	CONSTRUCTION	€ 43
MUZA S.A	PL	MEDIA	€ 3
NORDEA BP S.A	PL	BANKS	€ 489
NOVITA S.A	PL	LIGHT INDUSTRY	€ 11
OPAKOWANIA PLAST-BOX S.A	PL	PLASTICS INDUSTRY	€ 23
ORCO PROPERTY GROER S.A	FOREIGN	DEVELOPERS	€ 61
PBS FINANSE S.A	PL	FOOD INDUSTRY	€ 13
PEPEES S.A	PL	FOOD INDUSTRY	€ 16
PKO BP S.A	PL	BANKS	€ 9090
POLCOLORIT S.A	PL	BUILDING MATERIALS	€ 5
POLICE S.A	PL	CHEMICAL INDUSTRY	€ 169
POLNORD S.A	PL	DEVELOPERS	€ 73
PRÓCHNIK S.A	PL	LIGHT INDUSTRY	€ 8
PROJPRZEM S.A	PL	CONSTRUCTION	€ 9
PULAWY S.A	PL	CHEMICAL INDUSTRY	€ 348
REDAN S.A	PL	RETAIL	€ 16
SOPHARMA AD	FOREIGN	PHARMACEUTICAL	€ 211
STALEXPORT AUTOSTRADY S.A	PL	SERVICES - OTHER	€ 68
STOMIL SANOK S.A	PL	AUTOMOTIVE	€ 71
SUWARY S.A	PL	PLASTICS INDUSTRY	€ 15
SWISSMED CENTRUM ZDROWIA S.A	PL	SERVICES - OTHER	€ 8
SYGNITY S.A	PL	IT INDUSTRY	€ 48
TELECOMMUNICATION POLSKA S.A	PL	TELECOMMUNICATION	€ 5,210
TELL S.A	PL	RETAIL	€ 15
TRAVELPLANET.PL S.A	PL	SERVICES - OTHER	€ 5
TRION S.A	PL	BUILDING MATERIALS	€ 12
ULMA S.A	PL	CONSTRUCTION	€ 77
VISTULA GROER S.A	PL	RETAIL	€ 20
WASKO S.A	PL	IT INDUSTRY	€ 44
WILBO S.A	PL	FOOD INDUSTRY	€ 2
WISTIL S.A	PL	LIGHT INDUSTRY	€ 1
ZELMER S.A	PL	ELECTROMECHANICAL INDUSTRY	€ 92
ZETKAMA S.A	PL	METAL INDUSTRY	€ 27
ZO BYTOM S.A	PL	LIGHT INDUSTRY	€ 10
ŻYWIEC S.A	PL	FOOD INDUSTRY	€ 1,198

References

Authors

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Articles in this issue

DOI: https://doi.org/10.1515/ceej-2017-0014 | Journal eISSN: 2543-6821 | Journal ISSN: 2544-9001

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Language: English

Page range: 1 - 25

Published on: Dec 18, 2018

Published by: Faculty of Economic Sciences, University of Warsaw

In partnership with: Paradigm Publishing Services

Keywords:

GARCH,

JEL:

C53,

C58,

G17

Related subjects:

Business and economics,

Political economics,

Economic theory, systems and structures,

Microeconomics,

Macroeconomics,

Economic policy

© 2018 Marcin Chlebus, published by Faculty of Economic Sciences, University of Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 3 (2017): Issue 50 (December 2017)

EWS-GARCH: New Regime Switching Approach to Forecast Value-at-Risk

Figures & Tables

Fig. 1

Tab. 1

Tab. 2

Tab.3

Tab. 4

Tab. A1

Paradigm

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