The dynamic relationship between BTC with BIST and NASDAQ indices

Ulu, Cagri Article The dynamic relationship between BTC with BIST and NASDAQ indices Financial Internet Quarterly Provided in Cooperation with: University of Information Technology and Management, Rzeszów Suggested Citation: Ulu, Cagri (2023) : The dynamic relationship between BTC with BIST and NASDAQ indices, Financial Internet Quarterly, ISSN 2719-3454, Sciendo, Warsaw, Vol. 19, Iss. 4, pp. 115-128, https://doi.org/10.2478/fiqf-2023-0030 This Version is available at: https://hdl.handle.net/10419/329861 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/ 10.2478/fiqf-2023-0030 Abstract The significance of digital investment has grown substantially, enabled by advancing technology, which provides digital monitoring of investment instruments. Consequently, analyzing these instruments has become imperative. In particular, investors are inclined to compare new investment opportunities with well-established global stock markets, seeking to capitalize on their advanced financial literacy. This study aims to employ econometric analysis to explore the dynamic relationship between Bitcoin and the BIST100 and NASDAQ 100 indices. The time frame for this investigation spans from January 1, 2017, to March 10, 2022. Stationarity was confirmed through unit root tests (ADF, PP, KPSS, ZA, FADF, and FFFFF ADF) for the subsequent utilization of Autoregressive Conditional Variance Models. Additionally, Generalized Autoregressive Conditional Variance and Dynamic Conditional Correlation Tests were conducted. Results from the Dynamic Conditional Correlation Test model revealed no statistically significant dynamic conditional correlation between Bitcoin and BIST 100. Conversely, a negative and significant dynamic conditional correlation emerged between Bitcoin and NASDAQ 100. Investors should not only monitor the market but also review academic studies before making investment decisions. In this regard, this study holds significant importance. The study is limited to the BTC, BIST, and NASDAQ indices. Researchers interested in the topic can increase the dataset to further enrich the study. JEL classification: E00, F3, C58 Keywords: Dynamic Relations, DCC GARCH, Bitcoin, Finance, Stock Market Received: 19.07.2023 Accepted: 07.09.2023 Cite this: Cagri U. (2023) The dynamic relationship between BTC with BIST and NASDAQ indices. Financial Internet Quarterly 19(4), pp. 113-126. © 2023 Cagri ULU, published by Sciendo. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. 1 Izmir Kavram Vocational School, Türkiye, e-mail: cagri.ul[email protected].tr, https://orcid.org/0000-0001-5338-2987. ous Wavelet Transforms (CWT), and Maximum Overlap Discrete Wavelet Transform (MODWT) - to assess the correlation between Bitcoin and Shari'ah stock indices. The study's findings reveal a notably low and negative correlation between Bitcoin and Shari'ah stock indices, suggesting that Islamic stock investors could gain from diversifying their portfolios with Bitcoin. Furthermore, these results emphasize the potential benefits of further exploration into the fundamentals of cryptocurrencies within Islamic capital markets. Conrad et al. (2018) conducted a study focusing on the relationship between volatility and stock market movements in cryptocurrencies, specifically Bitcoin (BTC). The research analyzed long-term and short-term volatility using the GARCH-MIDAS model, which extracts the components of longand short-term fluctuations in cryptocurrencies. The study covered data from May 2013 to November 2017. Results indicated that the volatility of the S&P 500 had a negative and highly significant impact on long-term BTC volatility. Additionally, the S&P 500 volatility risk premium had a significantly positive influence on long-term BTC volatility. Moreover, a strong positive relationship was found between the Baltic exchange rate index and long-term BTC volatility, indicating a close link between BTC volatility and global economic activity. Naimy and Hayek (2018) conducted a study aiming to predict volatility in BTC. The analysis focused on the BTC/USD exchange rate between April 1, 2013, and March 31, 2016. Different models, including GARCH (1,1), EWMA, and EGARCH (1,1), were compared to determine the most effective in explaining BTC volatility. The study identified EGARCH (1,1) as the most effective model. However, it was noted that early BTC behavior should be closely monitored, as future results may vary. Gyamerah (2019) analyzed the volatility of BTC returns using sGARCH, iGARCH, and tGARCH models, covering the period from January 01, 2014, to August 16, 2019. The study revealed that the TGARCH-NIG model was the most effective in predicting BTC return series volatility. Ardia et al. (2019) tested the presence of regime changes in the GARCH volatility dynamics of Bitcoin daily returns using MSGARCH models. They used a dataset of 2355 observations of BTC prices in USD, spanning from August 18, 2011, to March 3, 2018. The study found strong evidence for regime changes in the GARCH process, and MSGARCH models outperformed single regime specifications when estimating VAR. Segnon and Bekiros (2020) proposed approaches to model the dynamics governing the mean and variance processes of BTC markets. The study used price observations between January 1, 2013, and November 28, 2018. Markov variation multifractal and FIGARCH Over the years, investment instruments have undergone diversification, and stock exchanges have established a mutually advantageous relationship between consumers and companies. Companies secure short-term financial resources from consumers, in return for which consumers are entitled to a share of the profits from these firms, a practice commonly encountered in traditional trading methodologies. Traditionally, the provision of resources has relied on liquid assets such as bank loans and foreign currency accounts. However, the advent of technology has ushered in a new era of investment tools, among which Bitcoin (BTC) emerges as a prominent contemporary option. BTC made its first appearance in 2009 through a 9-page manifesto published on bitcoin.org by an individual named Satoshi Nakamoto. This introduction integrated BTC into a "Peer to Peer" system and explained the utilization of blockchain technology for secure transactions (Nakamoto, 2022). Subsequently, BTC has become a subject of discussions and comparisons with other financial investment instruments. This study analyzes the dynamic relationship between BTC and BIST 100, an index of Borsa Istanbul, and NASDAQ 100, an index of an American stock exchange. As global financial assets are interconnected, investors need to monitor the global market and adjust their investments accordingly. The time interval for this analysis spans from January 1, 2017, to March 10, 2022. To ensure stationarity, unit root tests (ADF, PP, KPSS, ZA, FADF, and FFFFF ADF) were conducted in the initial stage of analysis. Based on the results of these tests, Autoregressive Conditional Variance Models (ARCH) were employed. Following that, the Generalized Autoregressive Conditional Variance (GARCH-EGARCH) and Dynamic Conditional Correlation Test (DCC GARCH) were performed. The Literature Review section provides an overview of prior research pertaining to the subject, offering insights into their respective findings. The subsequent section explains the econometric models used in this study. The results derived from these models are comprehensively examined, culminating in the Conclusion section, where the ultimate findings of the study are summarized. Jin and Masih (2017), gathered daily closing price data for five indices, including the FTSE Bursa Malaysia Emas Shari'ah Index, spanning from January 1, 2013, to January 2, 2017. The Bitcoin price index was sourced from Coindesk, recognized as one of the most active Bitcoin exchanges. During this period, the study applied three distinct methodologies: M-GARCH-DCC, Continu- to the BTC velocity but positively to the size of the BTC economy. Akin et al. (2023), conducted data collection from CoinMarketCap on the three largest cryptocurrencies (Bitcoin, Ethereum, and Binance Coin) on a weekly basis, spanning from August 1, 2017, to April 1, 2022. This period constituted the data collection window for the study. Employing the dynamic conditional correlationgeneralized autoregressive conditional heteroskedasticity (DCC-GARCH) model, the study analyzed the CoinMarketCap dataset. The results of the investigation indicated a noteworthy impact of news and events concerning central bank digital currencies (CBDCs) on Bitcoin returns. Both the CBDC uncertainty index and CBDC attention index exhibited a considerable influence on Bitcoin returns, signifying that positive news in this context could yield substantial returns. These findings underscore the notion that investors' future expectations regarding cryptocurrencies are significantly molded by CBDC-related news and events. While working on a time series, it is of great importance that the series be stationary. Depending on the stationarity, the method is selected by which the series will be advanced. Different stationarity tests are used to understand the reliability of the series (Petrica et al., 2017). In this study, first of all, ADF, PP and KPSS tests, which are traditional and do not allow structural break, were performed. Then, ZA, FADF and FFFF ADF unit root tests were carried out, which allow for modern and structural breaks. After the test results, VAR analysis was performed, and ARCH effects were investigated in the series. The study was terminated with the DCC GARCH test to analyze the dynamic relationship between the series. Stationarity tests were conducted to check the significance of the series. Augmented Dickey-Fuller (ADF), Phillips Perron (PP) and Kwiatkowski, Phillips, Schmidt and Shin (KPSS) unit root tests, which do not take into account the structural break, were applied. Stationarity is of great importance in determining the analyses to be made on the time series. models were found to outperform other GARCH-type models in estimating BTC return volatility. Combined estimates were observed to improve individual model estimates. Venter and Maré (2020) used the GARCH model to analyze the pricing performance of BTC. They also evaluated implied volatility indices of BTCUSD and Cryptocurrency Index (CRIX) datasets. Daily data from January 1, 2016, to January 3, 2019, were considered. The study showed that BTCUSD and CRIX volatility indices exhibited a similar course when tested with the GARCH model. Short-term volatility (30 days) was generally lower compared to longer maturities. Wang (2021) studied the volatility of BTC returns using the GARCH (1,1) model and other asymmetric models, such as TARCH and EGARCH. The analysis covered the period from October 2013 to July 31, 2020. The study revealed that the GARCH (1,1) model exhibited clustering characteristics in BTC volatility and return, with the volatility being a permanent process but decreasing over time. BTC was found to have a revised asymmetric effect between positive and negative shocks, making it suitable for investors to add to their portfolios as a safe-haven asset during economic depressions. Sui and Elliott (2021) examined the pricing of BTC options, incorporating both conditional varying variance and regime switching in BTC returns. The study employed a nonlinear time series model combining the SETAR model and the GARCH model to model Bitcoin return dynamics. Daily data between July 18, 2010, and May 31, 2018, were used. The GARCH model showed implied volatility skewness for short-term options. Abar (2020) aimed to make successful predictions in cryptocurrencies, particularly BTC, using the GARCH model and SVM-EKK regression. The study used BTC price series data from January 1, 2017, to February 29, 2020. Both models provided healthy predictions for the cryptocurrency price series. Ciaian et al. (2021) estimated BTC's transaction demand and speculative demand equations with a GARCH model using high-frequency data covering hourly data from 2013 to 2018. The results showed that both transaction demand and speculative demand had a statistically significant effect on BTC price formation. Additionally, the BTC price reacted negatively bility values are greater than 0.05. When the KPSS test results are examined, it is seen that the series are not stationary. ADF, PP and tests, which are unit root tests that do not consider structural break, were applied. All tests were examined at the level and it is understood that stationarity could not be achieved because the probaTable 1: ADF, PP and KPSS Unit Root Test Results in Level Characteristics ADF PP KPSS Intercept Interceptand Trend Intercept Interceptand Trend Intercept Interceptand Trend BTC Test Statistics -1.667067 -1.914840 -1.670458 -1.993322 3.269261 0.340945 1% -3.435161 -3.965109 -3.435161 -3.965109 0.739000 0.216000 5% -2.863552 -3.413266 -2.863552 -3.413266 0.463000 0.146000 10% -2.567891 -3.128657 -2.567891 -3.128657 0.347000 0.119000 Prob. 0.447900 0.646100 0.446100 0.603900 BIST100 Test Statistics -0.619607 -1.617013 -0.488347 -1.539903 2.824638 0.704447 1% -3.435169 -3.965120 -3.435161 -3.965109 0.739000 0.216000 5% -2.863556 -3.413271 -2.863552 -3.413266 0.463000 0.146000 10% -2.567893 -3.128660 -2.567891 -3.128657 0.347000 0.119000 Prob. 0.863700 0.786100 0.890900 0.815500 NASDAQ 100 Test Statistics -1.032457 -2.234098 -1.112875 -2.367322 4.045332 0.721599 1% -3.435196 -3.965159 -3.435161 -3.965109 0.739000 0.216000 5% -2.863568 -3.413290 -2.863552 -3.413266 0.463000 0.146000 10% -2.567899 -3.128671 -2.567891 -3.128657 0.347000 0.119000 Prob. 0.743500 0.469600 0.712700 0.396600 Note: ***, **, * indicate significance at 1%, 5% and 10% significance levels. Source: Author’s own work. Table 2: ADF, PP and KPSS Unit Root Test Results in 1st Difference Characteristics ADF PP KPSS Intercept Interceptand Trend Intercept Interceptand Trend Intercept Interceptand Trend BTC Test Statistics -36.94505 -36.949500 -36.97179 -36.972170 0.13498 0.103774 1% -3.43517 -3.965115 -3.43517 -3.965115 0.73900 0.216000 5% -2.86355 -3.413269 -2.86355 -3.413269 0.46300 0.146000 10% -2.56789 -3.128659 -2.56789 -3.128659 0.34700 0.146000 Prob. 0.00000 0.000000 0.00000 0.000000 BIST100 Test Statistics -22.97963 -22.980120 -36.46394 -36.460150 0.13504 0.080503 1% -3.43517 -3.965120 -3.43517 -3.965115 0.73900 0.216000 5% -2.86356 -3.413271 -2.86355 -3.413269 0.46300 0.146000 10% -2.56789 -3.128660 -2.56789 -3.128659 0.34700 0.119000 Prob. 0.00000 0.000000 0.00000 0.000000 NASDAQ 100 Test Statistics -11.80934 -11.813670 -44.35551 -44.350220 0.07610 0.073464 1% -3.43520 -3.965159 -3.43517 -3.965115 0.73900 0.216000 5% -2.86357 -3.413290 -2.86355 -3.413269 0.46300 0.146000 10% -2.56790 -3.128671 -2.56789 -3.128659 0.34700 0.119000 Prob. 0.00000 0.000000 0.00010 0.000000 Note: ***, **, * indicate significance at 1%, 5% and 10% significance levels. Source: Author’s own work. The same tests were applied again by taking the first differences of the series. Since the probability values for ADF and PP are less than 0.05 in all series, it can be said that stationarity is achieved. When the KPSS test results are examined, it is seen that stationarity is provided. At the 1% significance level, all tests are significant. Unit root tests are essential in increasing reliability. After the traditional models, modern unit root tests started to be applied to the series. Table 3: ZA Unit Root Test Results Characteristics Model A (Intercept) Model B (Trend) Model C (Intercept and Trend) BTC Test Statistics -2.870013 -2.206822 -3.431682 1% -5.340000 -4.800000 -5.570000 5% -4.930000 -4.420000 -5.080000 10% -4.580000 -4.110000 -4.820000 Break Point 10.19.2020 11.19.2019 01.08.2018 BIST100 Test Statistics -3.720117 -3.864384 -3.953157 1% -5.340000 -4.800000 -5.570000 5% -4.930000 -4.420000 -5.080000 10% -4.580000 -4.110000 -4.820000 Break Point 4.20.2018 3.11.2020 2.18.2020 NASDAQ100 Test Statistics -4.388460 -2.872674 -3.644380 1% -5.340000 -4.800000 -5.570000 5% -4.930000 -4.420000 -5.080000 10% -4.580000 -4.110000 -4.820000 Break Point 4.03.2020 12.17.2018 10.04.2018 Source: Author’s own work. BTC, BIST and NASDAQ indices. The absolute values of the test statistics are greater than the critical value. For this study, Zivot Andrews (ZA), Fractional Augmented Dickey Fuller (FADF) and Fractional Frequency Flexible Fourier Form Augmented Dickey-Fuller (FFFFADF) tests, which allow structural break, were applied. Table 4: FADF and FFFF ADF Unit Root Test Results Series Min. KKT k FADF BTC 3.270491 1.0 3.198692 (10) BIST 100 0.276864 1.0 3.290393 (12) NASDAQ 100 0.273501 1.0 3.357170 (12) Fractional FADF BTC 3.268545 1.4 2.892659 (10) BIST 100 0.275422 0.1 7.044294 (12) NASDAQ 100 0.272455 0.5 4.595373 (12) sis for the series is the ADF Unit Root Test, which takes into account the structural break. Upon analyzing the results of the ADF unit root test, it is observed that the series become I(1) stationary when the first difference is taken. In I(1) stationary series, ARCH and GARCH effects are chosen as suitable modeling approaches for capturing volatility and dynamics in the data. Based on the results of the FADF Unit Root Test, the application of the FADF for analysis is rejected because the F constraint value was lower than the F table value in all series. To increase the reliability of the stationarity analysis, the FFFFF ADF test was conducted. The FFFFF ADF test results indicate that the F table value is greater than the actual fractional FADF values in all series. Therefore, the appropriate unit root analySource: Author’s own work. According to Table 3 when the statistical values of the series and the critical values are compared, it is understood that stability cannot be achieved for the According to the significance of the coefficients and the minimum Akaike and Schwarz information criteria, which are the model selection criteria, the ARMA(3,3) model was determined as the appropriate model for the BTC return variable. The results are given in Table 5. After unit root tests for the variables, appropriate ARMA models should be determined. The ARMA models for the series and the number of alternative GARCH models after the ARCH effect were estimated as follows. BTC – ARMA (3,3) and GARCH (1,1) BIST100 – ARMA (3,3) and GARCH (1,1) NASDAQ100 – ARMA (4,4) and EGARCH (1,1) Table 5: ARMA(3,3) Model Result on BTC Index Return Variable Coefficient (Std. Error) t-Statistics Prob. Constant Term 0.00276000 (0.00192700) 1,431.969 0.1524*** AR(1) 0.81941800 (0.14335000) 5,716.197 0.0000*** AR(2) -0.69738700 (0.15441200) -4,516.406 0.0000*** AR(3) 0.79733400 (0.11020600) 7,234.958 0.0000*** MA(1) -0.85103100 (0.14375600) -5,919.970 0.0000*** MA(2) 0.74547700 (0.15730600) 4,739.035 0.0000*** MA(3) -0.79002000 (0.11588500) -6,817.280 0.0000*** SIGMASQ 0.00250700 (0.00000517) 4,850.710 0.0000*** Akaike -3.13855900 Schwarz -3.10678200 Note: ***, **, * indicate significance at 1%, 5% and 10% significance levels Source: Author’s own work. words, it shows the error term. Looking at the MA(1) (-0.851031) coefficient, it is seen that a shock that occurred a period ago has a decreasing effect on the BTC return in the current period. Looking at the MA(2) (0.745477) coefficient, it was observed that a shock that occurred two periods ago increased the BTC return in the current period, and looking at the MA(3) (-0.790020) coefficient, it is possible to say that a shock that occurred three periods ago reduced the return in the current period. When the AR and MA coefficients are examined from the table, it is seen that they are significant according to the 1% significance level. When the table is examined, the AR(1) coefficient (0.819418) expresses the value of BTC index return one period ago. The coefficient AR(2) (-0.697387) represents its value two periods ago, and the coefficient AR (3) (0.797334) represents its value three periods ago. In other words, an increase in the BTC return that occurred a period ago has an increasing effect on the current return of BTC. An increase in the return of two periods ago affects the current return negatively. An increase in the return of three periods ago affects the return positively in the current period. The MA coefficient represents the shocks to the system. In other in the system. With a β coefficient of 0.598011, it can be interpreted that the shock to the system is not permanent, as the coefficient is close to 1. The half-life shock value was calculated to determine the duration of the shock in the system. However, the specific formulation for calculating the half-life shock value is not provided in the given text. Half-life Shock (1) According to the value obtained, the shock to the system regarding the BTC index return stays in the system for an average of 3 days. From this point of view, it is seen that the shock to the system is not permanent. To determine whether there is an ARCH effect in the residues obtained from ARMA(3,3) - GARCH(1,1) model, ARCH(5) statistics were examined and the obtained value was found as 5.493894 and the probability value as 0.3586. Therefore, the ARCH effect is eliminated in the model. In addition, looking at the Q(10) statistics, it is seen that there is no autocorrelation problem in the model. The following figure shows the conditional variance graph obtained from the ARMA(3,3) - GARCH(1,1) model. When analyzing the results in the table, it was determined that there is no autocorrelation problem in the ARMA(3,3) model according to the Q(10) statistic for the 10th delay. However, the Q2(10) statistic is significant, indicating that the model has a different variance, implying an ARCH effect. The ARCH(5) value of 13.83629 with a corresponding probability value of 0.0167 shows the presence of an ARCH effect in the ARMA(3,3) model at the 5% significance level. Due to the presence of the ARCH effect in the ARMA(3,3) model, the modeling continued with autoregressive conditional heteroskedasticity (ARCH) models. Different GARCH-type models were tried for BTC, and the most suitable (minimum) model for BTC was determined to be ARMA(3,3) - GARCH(1,1) based on assumptions, significance of coefficients, and minimum Akaike and Schwarz information criteria. Upon examining the results in the last table for the ARMA(3,3) - GARCH(1,1) model, the coefficients α (0.148011) and β (0.598011) were found to be positive and statistically significant at the 1% significance level. The non-negativity condition for variance coefficients was satisfied. In the GARCH model, α indicates the initial effect of the shock, and β indicates the persistence of the shock Table 6: ARCH Effect in ARMA(3,3) Model of BTC Index Q Statistics Prob. ARCH(5) 13.83629 0.0167 Q(10) 13.67910 0.4510 Q2(10) 17.41300 0.0660 Source: Author’s own work. ln(0.5) ln(0.5) 2.86 ln( ) ln(0.1480 0.5998)ab − = − = ++ Figure 1: Conditional Variance Chart for BTC Return .000 .005 .010 .015 .020 .025 .030 .035 .040 III III IV III III IV III III IV III III IV III III IV I 2017 2018 2019 2020 2021 Conditional variance Source: Own elaboration with using the EViews package program. the appropriate model for the BIST 100 return variable according to the minimum Akaike and Schwarz information criteria, which are the model selection criteria. The results are as in the table below: Alternative ARMA(p,q) models have been tried for the BIST 100 index return. The significance of the coefficients was determined as the ARMA(3,3) model as Table 7: ARMA(3,3) Model Result on BIST100 Index Return Variable Coefficient T-Statistics Prob. Constant Term 0.00074000 (0.00046200) 1.600027 0.1098*** AR(1) -0.31207000 (0.10665500) -2.925940 0.0035*** AR(2) -0.25749000 (0.07437900) -3.461840 0.0006*** AR(3) -0.76769000 (0.07899300) -9.718440 0.0000*** MA(1) 0.30009800 (0.10457300) 2.869748 0.0042*** MA(2) 0.33213000 (0.06745900) 4.923416 0.0000*** MA(3) 0.80202800 (0.07991300) 10.036280 0.0000*** SIGMASQ 0.00021100 (0.00000446) 47.260720 0.0000*** Akaike -5.61514600 Schwartz -5.58336900 Note: ***, **, * indicate significance at 1%, 5% and 10% significance levels Source: Author’s own work. od ago has an increasing effect on the BIST 100 return in the current period. Looking at the MA(2) (0.33213) coefficient, it is observed that a shock that occurred two periods ago increased the BIST 100 return in the current period, and looking at the MA(3) (0.802028) coefficient, it is possible to say that a shock that occurred three periods ago increased the return in the current period. When the AR and MA coefficients are examined from the table, it is seen that they are significant according to the 1% significance level. The Q and Q2 statistics of the ARMA(3,3) model and ARCH statistics were examined to determine whether the model has an ARCH effect. When the table is examined, the AR(1) coefficient (-0.31207) represents the value of the BIST 100 index return a period ago. The coefficient AR(2) (-0.25749) represents its value two periods ago, and the coefficient AR(3) (-0.76769) represents its value three periods ago. In other words, an increase in the BIST 100 return that occurred a period ago has a reducing effect on the current return of BIST 100. An increase in the return from two periods ago affects the current return negatively. It can be said that an increase in the return of three periods ago affects the return negatively in the current period. The MA coefficient represents the shocks to the system. Looking at the MA(1) (0.300098) coefficient, it is seen that a shock that occurred a periTable 8: ARCH Effect on the ARMA(3,3) Model of the BIST 100 Index Q Statistics Prob. ARCH(5) 78.30416 0.000 Q(10) 5.49580 0.240 Q2(10) 129.71000 0.000 Source: Author’s own work.