A GARCH model with modified grey prediction model for US stock return volatility

Abstract

This study proposes a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) with modified Grey prediction model to investigate the transmission of volatility through analysis of the error terms. Generally, the higher the sample size, the better GARCH models describe variation. However, the GARCH( $p$ , $q$ ) model often causes the problem of time delay by assuming that the conditional variance and the squared error term have lags $p$ and $q$ periods, respectively. Consequently, this paper utilizes a Grey Model (GM), modified for general residual sequences and generalizing the squared error terms to incorporate influence by unexpected factors such as previous process states or delayed impact of information. Furthermore, this study illustrates the proposed model with daily NASDAQ closing prices for a total of 1265 observations. The modified Grey-GARCH model demonstrates improved accuracy over the Grey-GARCH model and the traditional GARCH model. The results of this study have practical implications for optimal investment strategies.

Keywords

Grey model GARCH Grey-GARCH residual sequences modified Grey-GARCH

Get full access to this article

View all access options for this article.

References

Pagan

A.R.

and Schwert

G.W.

, Alternative models for conditional stock volatility, Journal of Econometrics 45 (1990), 267–290.

Iqelan

B.M.

, Forecasts of female breast cancer referrals using grey prediction model GM(11), Applied Mathematical Sciences l(11) (2017), 2647–2662.

Amado

and Teräsvirta

, Specification and testing of multiplicative time-varying GARCH models with applications, Econometric Reviews 36(4) (2014), 421–446.

Tseng

C.H.

Cheng

S.T.

Wang

Y.H.

and Peng

J.T.

, Artificial neural network model of the hybrid GARCH volatility of the Taiwan stock index option prices, Physica A: Statistical Mechanics and its Applications 387(13) (2008), 3192–3200.

Tseng

C.H.

Cheng

S.T.

and Wang

Y.H.

, New hybrid methodology for stock volatility prediction, Expert Systems with Applications 36 (2009), 1833–1839.

Nelson

D.B.

, Stationarity and persistence in the GARCH(1,1) model – modelling stock market volatility, Econometric Theory 6(3) (1990), 318–334.

Nelson

D.B.

, Conditional Heteroskedasticity in asset returns: a new approach, Modelling Stock Market Volatility 59(2) (1991), 37–64.

Fama

E.F.

and Engle

R.F.

, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom Inflation, Econometrica 50(4) (1982), 987–1007.

Box

G.E.P.

Jenkins

G.M.

and Reinsel

G.C.

, Time series analysis: forecasting and control, Journal of Marketing Research 14(2) (1994), 199–201.

10.

Schwarz

, Estimation The Dimension of A Model, Annals of Statistics 6(2) (1978), 15–18.

11.

H.C.

and Yeh

M.F

, Some basic features of GM(1,1) model(II), Journal of Grey System 9(4) (1997), 307–321.

12.

Deng

J.L.

, Control problems of grey systems, Systems and Control Letters 1 (1989), 288–294.

13.

Chou

and Kroner

, ARCH modeling in finance: A review of the theory and empirical evidence, Journal of Econometrics 52(1–2), (1992), 5–59.

14.

Shephard

, Statistical aspects of ARCH and stochastic volatility, Time Series Models in Econometrices, Finance and Other Fields, Chapman and Hall, London, 1995.

15.

Sayahi

Kazemi

and Kamali-Mohammadzadeh

, A Comparison Among Regression, Grey, and Adaptive Grey Prediction Models for Electricity Consumption Forecasting: A Case Study Of Iran, International Conference on Computers & Industrial Engineering, 2017.

16.

Molnár

, High-low range in GARCH models of stock return volatility, Applied Economics 51 (2017), 1–15.

17.

Engle

R.F.

and Ng

V.K.

, Measuring and testing the impact of news on volatility, Journal of Financial Economics 48 (1993), 1749–1778.

18.

Ruey

S.T.

, Analysis of Financial Time Series, John Wiley & Sons, USA, 2002.

19.

Chen

Jeong

and Härdle

W.K.

, Support vector regression based GARCH model with application to forecasting volatility of financial returns, Social Science Electronic Publishing 92(4) (2017), 398–399.

20.

Bollerslevb

, Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics 31(3) (1986), 307–327.

21.

Chang

T.C.

Wen

K.L.

Fang

and Hsu

F.Y.

, An artificial Grey-GARCH model transmission of return volatility in NASDAQ index, Journal of Grey System 7(1) (2004), 28–37.

22.

Niu

Cheng

and Wang

, Applications of extension grey prediction model for power system forecasting, Journal of Combinatorial Optimization 26(3) (2013), 555–567.

23.

, Research on a Novel Kernel Based Grey Prediction Model and Its Applications, Mathematical Problems in Engineering 2016 (ID5471748), 1–9.

24.

and Liu

Z.H.

, The kernel-based nonlinear multivariate grey model, Applied Mathematical Modelling 56 (2018), 217–238.

25.

Wang

Y.H.

, Nonlinear neural network forecasting model for stock index option Price: hybrid GJR-GARCH approach, Expert Systems with Applications 36 (2009), 564–570.

26.

Chai

Y.C.

Huang

Y.C.

and Dang

H.S.

, An application of grey prediction to estimate the market size of tutoring industry in Taiwan, International Conference on Applied System Innovation (2017), 1740–1743.