A Novel Fuzzy Linear Regression Sliding Window GARCH Model for Time-Series Forecasting

Round 1

Reviewer 1 Report

Review for Manuscript Applied Sciences-726599

1. General remarks

The authors some experience in research using GARCH model:

Hanapi, A. L. M., Othman, M., Sokkalingam, R., & Sakidin, H. (2018, November). Developed A Hybrid Sliding Window and GARCH Model for Forecasting of Crude Palm Oil Prices in Malaysia. In Journal of Physics: Conference Series (Vol. 1123, No. 1, p. 012029). IOP Publishing.

1. Specific observations concerning Manuscript Applied Sciences-726599

2.1. Positive aspects

The manuscript is confined to the thematic sphere of the Applied Sciences journal and deals with an interesting topic.

2.2. Negative aspects

2.2.1. Manuscript Manuscript Applied Sciences-726599 does not consider few significant studies on the topic.

2.2.2. This manuscript does not include bibliographic references of interest from 2019 and 2020.

III. Conclusion

The introduction, the literature review section must be supplemented with ideas from significant studies in the chronology of the GARCH model as the following

Lamoureux, C. G., & Lastrapes, W. D. (1990). Persistence in variance, structural change, and the GARCH model. Journal of Business & Economic Statistics, 8(2), 225-234.

Van der Weide, R. (2002). GO‐GARCH: a multivariate generalized orthogonal GARCH model. Journal of Applied Econometrics, 17(5), 549-564.

Jondeau, E., & Rockinger, M. (2006). The copula-garch model of conditional dependencies: An international stock market application. Journal of international money and finance, 25(5), 827-853.

Engle, R. F., & Rangel, J. G. (2008). The spline-GARCH model for low-frequency volatility and its global macroeconomic causes. The Review of Financial Studies, 21(3), 1187-1222.

Narayan, P. K., Liu, R., & Westerlund, J. (2016). A GARCH model for testing market efficiency. Journal of International Financial Markets, Institutions and Money, 41, 121-138.

Mao, H., Zhu, F., & Cui, Y. (2019). A generalized mixture integer-valued GARCH model. Statistical Methods & Applications, 1-26.

Zhang, Y. J., Yao, T., He, L. Y., & Ripple, R. (2019). Volatility forecasting of crude oil market: Can the regime switching GARCH model beat the single-regime GARCH models?. International Review of Economics & Finance, 59, 302-317.

Choudhry, T., Hasan, M., & Zhang, Y. (2019). Forecasting the daily dynamic hedge ratios in emerging European stock futures markets: evidence from GARCH models. International Journal of Banking, Accounting and Finance, 10(1), 67-100.

Ma, X., Yang, R., Zou, D., & Liu, R. (2020). Measuring extreme risk of sustainable financial system using GJR-GARCH model trading data-based. International Journal of Information Management, 50, 526-537.

Bollerslev, T., Patton, A. J., & Quaedvlieg, R. (2020). Multivariate leverage effects and realized semicovariance GARCH models. Journal of Econometrics.

Lin, Y., Xiao, Y., & Li, F. (2020). Forecasting crude oil price volatility via a HM-EGARCH model. Energy Economics, 104693.

Author Response

Point 1: Manuscript Applied Sciences-726599 does not consider few significant studies on the topic.

Response 1:  We have added several significant studies as suggested by the reviewer. The added significant studies can be seen from line 47 until 73 in page 2.

“Bollerslev [6] developed the GARCH model to estimate and predict future values, given the existence of ARCH effects in return series in particular. The GARCH model has achieved significant success in describing in-sample forecasting characteristics [7]. Many studies used the GARCH model, for example, in a study of stochastic representation of impulsive noise in the frequency band [8], a study of stock exchange market of China [9] and a study of Bitcoin volatility [10].They found that the GARCH model is more accurate when compared to ordinary least square (OLS) and EWMA. From these studies, despite having publicly accessible tools to easily forecast data, the GARCH model performed better than the EWMA. Thus, our study considers on improving the GARCH model.

Extensive research is being undertaken to improve the GARCH model by combining mathematical and statistical models thus creating new models. For instance, a Glosten-Jagannathan-Runkle-GARCH (GJR-GARCH) model was introduced to allow for the conditional variance to respond to previous negative and positive changes differently [11] and then was applied in measuring extreme risk of sustainable financial system [12]. A combination of artificial neural network (ANN) and GARCH was proposed for volatility forecasting of daily log-returns series in a study of international stock return volatility [13] and then was applied in a study of Chinese energy market [14]. More improved GARCH models were introduced for variance-covariance and correlation forecasting include the use of orthogonal components for displaying temporal aggregated properties that are not found when working with univariate models [15], the use of copulas for conveniently linking univariate GARCH [16] and the use of realized semi-variances, semi-covariances, and semi-correlations [17]. Most of the improved model was used for correlation components such as covariances and volatilities of stock and bond returns [18-21]. More extensive and complex GARCH models were developed to improve the forecasting model. For example, a fuzzy GJR-GARCH model using fuzzy inference systems [22], a hybrid neural network GJR-GARCH models [23-24] for volatility forecasting of indexes, a mixture of integer-valued models with different distributions in GARCH model [25] and a hidden Markov Exponential GARCH model for volatility forecasting of crude oil price [26].”

Point 2: This manuscript does not include bibliographic references of interest from 2019 and 2020.

Response 2: I have included several bibliographic references of interest from 2019 and 2020, which are numbered 12, 17, 21, 25, 26 in the references section (page 17-18).

Point 3: The introduction, the literature review section must be supplemented with ideas from significant studies in the chronology of the GARCH model.

Response 3: Thanks to the reviewer for pointing this out, I really appreciate it. The ideas from significant studies in the chronology of the GARCH model have been included in the introduction, the literature section. The chronology starts from the year 1986 until 2020, which can be seen in line 47- 73, mentioned in Response 1.

Reviewer 2 Report

A well-written paper on a popular and useful  topic.

Polish sentence in the abstract:

"The likelihood equations need to be specifically worked out when the distribution is known, however, there is uncertainties in the time series data thus no specific distribution can be specified. "

It might add a interesting point to put bipolar fuzzy sets (as recognized by Zadeh) and bipolar symmetry (called G-CPT symmetry) in perspective for future research.

Author Response

Point 1: Moderate English changes required.

Response 1: We have improved English language in the manuscript.

Point 2: Are the methods adequately described? Can be improved.

Response 2: We have added details of the steps starting from line 136-139 in page 3,

“The proposed model consists of four steps as shown in Figure 1. The first step is parameter estimation using fuzzy linear regression, the second step is return computation, the third step is fuzzy window variance computation and the last step is forecasting. The new combination of GARCH model with two methods is done in the first and third step. A fuzzy sliding window algorithm is developed in this model to be used in the first and the third step.”

We also added subsection 2.1.1, 2.1.2, 2.1.3 and 2.1.4 so that readers can easily refer to the model step-by-step.

Point 3: Are the conclusions supported by the results? Can be improved.

Response 3: Few sentences are added from line 320 until 328 in page 16 to show that the conclusions are supported by the results,

“Two datasets are used to test the performance of the proposed model; first is from economy field and second is from agriculture field. The forecast values obtained from the use of the proposed model are compared to the benchmark models. The empirical results show that the proposed FLR-FSWGARCH model produced high accuracy forecasting values and less mean absolute percentage error (MAPE) than the SWGARCH, GARCH, ARIMA-GARCH and EWMA models. This demonstrates that the FLR-FSWGARCH model is capable of giving a superior forecast compared to the benchmark models. Besides, the results also confirmed that the proposed model is highly reliable and significantly fit for forecasting time series data as the R-squared are more than 90% for both datasets.”

Point 4: Polish sentence in the abstract: "The likelihood equations need to be specifically worked out when the distribution is known, however, there is uncertainties in the time series data thus no specific distribution can be specified. "

Response 4: The sentence has been changed to

“For the likelihood method to work, there should be a known and specific distribution. However, due to uncertainties in time series data, a specific distribution is indeterminable.”

Point 5: It might add an interesting point to put bipolar fuzzy sets (as recognized by Zadeh) and bipolar symmetry (called G-CPT symmetry) in perspective for future research.

Response 5: Thanks to the reviewer for pointing this out, I really appreciate it. The bipolar fuzzy sets are interesting and considerable for future research in line 341-347 in page 16,

“For further studies, more attention should be paid to fuzzification process by imposing a bipolar fuzzy set to form the triangular fuzzy numbers. The bipolar fuzzy set is an extension of fuzzy set whose membership degree range is [-1, 1], which is different from current study whose membership degree range is [0, 1]. The performance of the proposed model will be more superior by using the bipolar fuzzy set as previous study has shown advantages in handling vagueness and uncertainty than fuzzy set.”

However, the bipolar symmetry is not in line with our study thus it is not considerable for future research. The bipolar symmetry is useful in optical, polarization and more to physics studies, which are very different from ours.