Forecasting the Volatility of the Tehran Stock Market Index Using ARCH Models Family

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1 International Research Journal of Applied and Basic Sciences 2013 Available online at ISSN X / Vol, 6 (8): Science Explorer Publications Forecasting the Volatility of the Tehran Stock Market Index Using ARCH Models Family Tooran Habibi 1*,Mehran Habibi 2, Farhad Gheisari 3 1. Master of Accounting, Islamic Azad University Baghmalk, izeh, Iran 2. Master of Public Administration, Islamic Azad University Baghmalk, izeh, Iran 3. PhD student in Public Administration, Islamic Azad University Ramhormoz, Ramhormoz, Iran *Corresponding Author habibi. yahoo.com ABSTRACT: In this study, the function of predicting conditional fluctuation models (5 models) for predicting the total index of Tehran Stock Exchange has been evaluated by using the root-mean-square errors criteria, the mean absolute value of errors and the mean absolute value of errors percentage. The used data of this study is a daily time series of total stock price index from the beginning of the year 2006 to the end of the year The estimation was done using the Excel and EViews7 software. The results show that the root-mean-square errors of different modeling (ARCH family) is very close to each other and the other criteria are also equal for different modeling. The ARCH family models results furthermore show that ability of predicting GARCH, EGARCH, GJR, PGARCH and CGARCH models in the prediction of total index of Tehran Stock Exchange are both equal and there is no significant difference between their predictions. Key words: stock price total index, volatility and types of ARCH models. INTRODUCTION One of the most important sectors of the countries' economy has been the capital markets whose importance is acknowledged by everyone. Capital market has been closely related to the structure of the country economy and its strengths and weaknesses can be indicative of the economic situation of any country. Development of the capital market can play an important role in the growth of national income and the general welfare of the community (Abbasian et al., 2008). The Stock Exchange is a key component of the capital market investment and actually the Stock Exchange means the formal organized market in which sale and purchase of the government bonds and corporate shares of public or private reliable institutions, done under certain rules and regulations. The main characteristic of stock exchange is in the law support of the owners of savings and stagnate investment capitals and legal requirements for investment applicants. Stock exchange, on one hand, acts as a savings and cash collection center from private sector in order to finance the long-term investment projects and on the other hand, as the official and secured authority through which the holders of stagnate savings can search for a safe and proper place and invest their surplus funds in the companies and or benefit from the certain guaranteed profit by buying the bonds of governments and liable companies (Amani & Davani, 2011). The stock index as a thermometer shows the status of the capital market and the economic conditions of a country. Index reduction generally means the economic recession and its increase means the economic briskness. Stock market's Indicators are a useful summarized criterion of the current expectations regarding the stock future which, like a sensitive thermometer, reflects the effects of the political, economic and phenomenon and reflects the long-term structural changes in the economy. In addition, since the stock price fluctuates by the changes in shareholders expectations of the corporate economic situation and these price fluctuations affect the market index, therefore the market index can be considered as the future status and function of the economics at the national level (Ahmadpoor, 2007). Statement of the problem The development of the economic structure involves several mechanisms that in the field of financial and monetary markets, the stock exchange is one of the most important of these mechanisms. Attention to the stock exchange and its establishment is considered as the definite requirements and essence of the normal sound

2 economic life of the community which can origin the positive effects, the considerable benefits and merits in all of economic, social and cultural aspects of each society (Rahnamaye Roodpooshti & Salehi, 2011). Stock Exchange's main role as the linchpin of the capital organized market is to absorb and redirect the savings and the wander and scattered liquidity towards the optimal paths; as a matter of fact it can be said that the main function of the stock is the optimal allocation of the rare financial resources, so that major part of the capital is absorbed to the most profitable activities and projects (Ebrahimi Kordlar et al. 2008). Meanwhile, investment companies are among the active parts in the financial markets whose major activities are to invest the funds that are deposited by the share purchasers to be used in the optimum way. These companies make investments using financial analysis based on available evidence in the national monetary and financial markets. One of the major programs of the corporate is the investment in the Stock Exchange. Stock price is considered as one of the most important evidences in making decisions for the companies and also all of the potential investors. Changes in stock prices are the important source of information for investors in evaluating the performance of the managers that these changes are measured by the name of stock exchange index (Stock Price Index) (Allah Noori, 2011). Stock market index is a useful summarized criterion of current expectations about the future of the stock which, as a sensitive thermometer, reflects the effects of the political, economic, phenomena and reflects the long-term structural changes in the economy. Moreover, since the stock price fluctuates with the change of the shareholders expectations from the company economic situation and this price fluctuation affect the market index, therefore the market index is considered as the future status and performance of the economics at the national level (Ahmadpoor, 2007). The stock indexes are considered as the most important criteria to evaluate the performance of the investment in the Stock Exchange, even the non-financial investment. Currently, most of the institutional and individual investors periodically measure the stock market with this criterion (Allah Nouri, 2011). The stock price volatility has attracted much attention from academic researchers as well as the practitioners from the financial markets. High price volatilities can be used as a criterion of risk measurement in financial markets; the importance of this issue is originated from this point that the fluctuations in the financial markets is one of the important variables in terms of investment decision-makings and bond pricing which emphasizes on importance of the modeling and forecasting the conditional return volatility; in additions, volatility of financial markets has an important impact on the national economy through the creation or loss of public confidence and trust (Tehrani et al, 2010). Wide fluctuations, nonetheless, cause the entry and exit of a great amount of capital, so that, in developing countries, the impacts inflicted on the economy body due to the shocks of the capital markets is of greater depth compared with the developing countries because the fear of loss of capital compared with the concerns originated by the evident instability in the economy may be intensified (Ahmadpoor, 2010); hence, identifying the volatility pattern in Tehran Stock Exchange can be a step in the right direction for the investment and policy decision-makings. The necessity and importance of the research A common feature of moving towards sustainable economic development is to obtain necessary resources for the economic activities setting by mobilizing savings resources available in the national economy. In recent decades, the role of the capital markets and the expansion of the financial markets have had a relatively high correlation with economic growth. The most important factors affecting the increase in investment, economic growth and development are the possession of the strong and efficient financial markets associated with the appropriate and active financial institutions operating in this market. Stock exchange market which is the component of financial markets plays an important role in collecting and transferring funds to individuals (Najarzadeh et al., 2009). World countries have always witnessed different fluctuations in the stock exchange; so that these volatilities have caused many governments and companies suffering losses and financial problems. Moreover, the economical fluctuations and their instability during the time cause troubles during the economic decision-makings and forecasting of these firms (Yahyazadehfar & Babai, quoting Alikhani, 2010). Regarding the changes that have occurred in recent years in Tehran Stock Exchange, the investment institutions with adopting appropriate policies can step forward in order to gain the trust of investors. Stock price index can be used to help that aim as one of the policy tools. In case the right index can be used for the performance changes in the investing companies and provide a suitable situation to compare their performance, then we can step forward in line with trustiness in this index (Allah Nouri, 2011). Since the investment to produce the commodities is considered necessary and essential in any country, and one approach for financing the cash requirements for investments by companies share circulation, therefore this matter lead to perform the theoretical and empirical researches concerning the volatility of Tehran Stock Exchange index.

3 Research Objectives With regard to the fact that, nowadays, one of the most important functions of any national stock exchange is to provide the possibility of the proper distribution of capitals and related information between market participants, in line with this and in terms of information and direction, the stock must, as a reliable guide, play an active and effective role to understand the present situation, the changes arising out and their consequences, and since in decision-makings of the investment in the Stock Exchange, the stock price index of one of the most important tools for the investors, and with regard to the importance of the volatility in the stock exchange, and this fact that any occasion or event in the market can cause an increase or decrease in the stock price index, hence in this study we have tried to, while reviewing the theoretical fundamentals of the ARCH family models and their applications in different markets, provide an appropriate model to predict the fluctuations in the Tehran Stock Exchange total index. Theoretical fundamentals and research background The term index refers to the determination means and an index number is a number by which the raised changes in a phenomenon can be examined during two different periods of time; therefore, it can be said that the index is a number for measurement and assessment the changes of various factors in the time or place intervals. In fact, the index is a representative of numerous autogenously similar quantities which shows the quantity and direction of the volatilities based on a basis number and in a given time (Ahmadpoor et al., 2007). Stocks Price Index History in the World For the first time, the stock price index was used in 1884 in the U.S. At that time, the calculation method was exceptionally simple, like the simple arithmetic mean, so that the total price of the one share of each company listed in the Stock Exchange was divided by the number of the companies. This method was invented by Charles Dow, whereby the average shares prices of 11 railway companies were obtained and was used as the stock price index in the railway industry. Tehran Stock Exchange Index The total stock price index is the most important economic indicators which represent the activity procedures and the direction of the national capital market and the market's ability to absorb liquidity in the community and is a measure for determination and completion of the investment behavior in the market and tips for buying and selling stocks for them. In Iran, determination and circulation of the index of the shares prices is new and for the first time, Kayhan International Newspaper (English version) calculated and published one weekly index for the average stock prices. This index showed the changes of the price of stocks of ten banks and ten industrial companies and was being published from December 1976 until early Stock price index in Tehran Stock Exchange was an index of the arithmetic mean with weights equal to the market value of corporate shares and is known by the name of TEPIX (Tehran Exchange Price Index). General formula to prepare the index Tehran Stock Exchange is the Laspeyres formula like other world stocks exchanges as follows: Total daily value of published by the listed companies TEPIX = 100 Total base value of shares issued by listed companies The base date of this index is on the 21/03/1980 and the base number is considered 100 which were prepared in the Research Center for the Capital Market of Tehran Stock Exchange (Ahmadpoor et al, 2007). In this formula, the numerator of the fraction was calculated by multiplication of individual shares released by the listed companies by the last share price and then the total sum of the stock value. Denominator of the fraction showed the total sum of the base value of the shares released that was obtained by the multiplication of individual shares released by the listed member companies at the base price (21/03/1980) (Amani & Davani, 2011). A review of previous studies Regarding the index volatilities and fluctuations of the stock prices several studies were conducted using a variety of ARCH models both in and out of the country. Some of these studies are reviewed in this section.

4 Studies conducted out of the country Caiado (2004) modeled the yield daily and weekly volatilities of the stock price indexes in Portugal (PSI-20) by using the models of GARCH, GARCH-M, Quadrant GARCH, (EGARCH) and Threshold ARCH (TARCH). Results indicated the existence of significant asymmetric shocks in daily output and lack of these stock shocks on weekly stock output. Ebeid and Bedeir (2004) have been assessed the predict performance of four alternative models of ARCH type for prediction of the stock price volatility using Egyptian daily data. Competing models include GARCH, EGARCH, GJR, and APARCH. Estimation results showed that the prediction performance of the asymmetric models of PARCH, GJR and ARCH, especially when the densities of the greater asymmetry are considered in conditional volatility are better than the symmetric GARCH. Furthermore, it was found that the APARCH (1,1) model provides the best symmetric of predictions in all of the selected models for market index volatility modeling in Egypt. Studies conducted in the country Tehrani et al. (2010) in their study reviewed the predict performance of the conditional and unconditional volatility models (12 models) concerning the prediction of the fluctuations in cash return index and prices of Tehran Stock Exchange (TEDPIX) based on the criterion of the root-mean-square error (RMSE) assessment. Results show that the performance of the moving average model, 25 days exponential smoothing and CGARCH according to RMSE is better than other models. Artificial model results show that in general, unconditional models have better performance than conditional models; Furthermore, the obtained results of the Diebold-Mariano Statistic indicate that there are significant differences between MA250 model prediction power and CGARCH model. Khalili (2004) has provided an appropriate model for predicting the stock prices of the group of investment companies using GARCH model. Results represent the suitable adaptation of the GARCH models with financial time series, especially the time series data of the stock prices. Hypothesis of the research There is no significant difference between the predictive power of the GARCH, EGARCH, GJR, PGARCH and CGARCH models in predicting Tehran Stock Exchange total index. RESEARCH METHODOLOGY Volatility of financial markets is biased the researchers toward the applicable models to measure and predict the volatility of stock returns and stock market price index. Ever since, many models concerning the analysis of the stock returns and volatility of the price index are proposed. For the first time, Autoregression Conditional heteroskedasticity (ARCH) model was introduced by Engle (1982) for modeling and forecasting the volatility as self-descriptive. Most of the analytical time series using ARCH model needs the long delays and a large number of estimated parameters (Samadi et al, 2007). Prediction models used in this article are GARCH, EGARCH, GJR, PGARCH and CGARCH. Information needed for this study was collected in the following ways: A) Library Method B) Field Methods In the library method which deals with the history, background and theoretical framework of the research, the Persian and Latin books and specialized journals were used. The field method which deals with documents and articles is limited to Tehran Stock Exchange. In order to collect data from Tehran Stock Exchange daily reports and its website, the volatility of the total index was examined and after preparation of the data in the Excel software, the models analysis and estimation and hypothesis testing was performed using EViews7 software. Statistical Population In this study, the volatility of the total index of Stock Exchange and the released reports by the capital market was considered as the statistical population and sample from the beginning of the year 2006 until the end of the year The used data in this research are the time series of the observation of the total index in Tehran Stock Exchange whose diagram is presented in figure 1. The mentioned diagram represents the total index of Tehran Stock Exchange from 25/03/2006 to 21/03/2010.

5 24,000 Figure1. Diagram of the time series of total index in Tehran Stock Exchange 20,000 16,000 12,000 8,000 4, Review of the time series characteristics of research observations In the first stage, the time series characteristics of Tehran Stock Exchange Index including descriptive statistics, reliability, detection of order and type of the self-descriptive processes and moving averages and test of ARCH effect availability and serial autocorrelation of the deranging components of the original model are examined. Descriptive statistics and reliability test results of total index of Tehran Stock Exchange is presented in Figure 2. Table1. Descriptive statistics and reliability test of study variables Statistics TEPIX Unit Root Test Type Test Level Statistics (significant) Average Level 2.18 (1.00) Generalized Dickey Fuller Middle First-order difference ** (0.00) Maximum Level 1.32 (1.00) Phillips and Perron Minimum First-order difference ** (0.00) Standard deviation ** Significance at 1% level Reliability result of generalized Dickey Fuller test shows that the series of Tehran Stock Exchange index in the level of (2.18) is not stable, but with a difference of (-11.59) is steady at 1% level. Reliability results of Philips and Perron test also confirm steadiness of the mentioned series with a difference of (-24.18). In the next stage, for basic modeling, type and order of processes of self-description and moving average is described using the Box- Jenkins process. In doing so, the Box-Jenkins process by using the program provided on the EViews website with the maximum 10 interruptions for the self-descriptive process, for the process of moving average 10 interruptions and 3 times of accumulation carried out after the initial modeling, we expect that there would not be any deranging and disturbing element in the serial autocorrelation. In additions, for decision-making on modeling with ARCH and GARCH approaches, it is necessary to carry out the conditional variance anisotropy test (ARCH effects testing). Results of tests for serial autocorrelation and the conditional variance heteroskedasticity test are presented in Table 3. Table2. Results of Box-Jenkins Process Variables Coefficient Student T-Test Significant Intercept MA (1) ** MA (2) Fisher's Test (Significant) ** (0.00) Adjusted Coefficient of Determination %30.86 Durbin-Watson Test 1.97 Schwartz Criterion Serial Autocorrelation Test (Significant) 0.32 (0.73) ARCH Impact Test (Significant) ** (0.00) ** Significant at 1% level The results presented in Figure 3 show that the process present in Tehran Stock Exchange Index is moving average series stage 2 and accumulation stage 2. As it can be seen, the coefficient of variation of MA(1) and MA(2) are significant at the 1% level. Significance of Fisher Statistic (255.67) indicates the overall model significance. Adjusted coefficient of determination also shows that the moving average process explains about 31

6 percent of Tehran Stock Exchange index. Durbin-Watson Statistic (1.97) and the serial autocorrelation test (0.32) reject the serial autocorrelation presence in prototype violation components. Nevertheless, the results of the conditional variance anisotropy test (39.64) do not reject ARCH effects in the residuals of the basic model. Therefore, for modeling the mentioned residuals, it is necessary to use ARCH and GARCH different approaches. Generalization of the basic modeling using different ARCH and GARCH approaches At this point, it residuals of the primary model resulted from the Box-Jenkins process are modeled using different ARCH and GARCH approaches. Approaches which are used are: GARCH, CGARCH, EGARCH, GJR and PGARCH which are described below. Modeling with GARCH Approach Modeling results from a prototype residuals resulted from the Box-Jenkins process are presented in Figure 4 using the GARCH approach. The presented results show that first- (-0.64) and second-order coefficient (-0.18) of the moving average process of the average equation are significant at the 1% level. Intercept (268.47) coefficient of ARCH (0.25) and GARCH (0.74) factors in the variance equation are significant at the 1% level. Adjusted coefficient of determination shows that in this model, the independent variables explain about 30% of the change of the total index of Tehran Stock Exchange. Durbin-Watson statistics (1.93) show that there is not any serial autocorrelation in deranging components of GARCH model. In additions, the lack of significance of ARCH statistics (0.17) showed the lack of the conditional variance in the components of GARCH model deranging. Figure 4. GARCH Modeling Results Table4. Variables Coefficient Statistics Z Significant Intercept Mean Equation MA (1) ** MA (2) ** Intercept ** Variance Equation ε 2 t ** σ 2 t ** Adjusted Coefficient of Determination %29.55 Durbin-Watson Test 1.93 ARCH Impact Test (Significant) 0.17 (0.68) ** Significant at 1% level This issue suggests that in the current model, all of the present ARCH model impact have been modeled and the rest do not have a problem with the conditional variance anisotropy. Modeling with CGARCH Approach Modeling results from prototype residuals resulted from the Box-Jenkins process are presented in Figure 5 using the CGARCH approach. The presented results show that first- (-0.67) and second-order coefficient (-0.19) of the moving average process in the mean equation are significant at the 1% level. The fitted results of the variance equation also show that the coefficients of β 4 ( ), β 5 (1.00), the coefficient of the variable ε 2 t-1 σ 2 t-1 (-0.02), β 7 (0.22), β 8 (0.12) and the coefficient of the variable σ 2 t-1 Q 2 t-1 (0.54) are significant at the 1% level. Adjusted coefficient of determination shows that in this modeling, the independent variables explain of about 30 percent of the changes of Tehran Stock Exchange index. Durbin - Watson Statistics (1.89) shows that there is no serial autocorrelation in the disturbing element of CGARCH model. In additions, the lack of significance of the ARCH statistical (0.00) showed the lack of the conditional variance components in the deranging components of the CGARCH model. Therefore, in the last model, all of the ARCH model impact has been modeled and the rest do not have a problem with the conditional variance anisotropy. 6404

7 Figure 5. Results of CGARCH Modeling Table5. Variables Coefficient Statistics Z Significant Intercept Mean Equation MA (1) ** MA (2) ** β ** β ** Variance Equation β ** β ** β ** β ** Adjusted Coefficient of Determination %30.03 Durbin-Watson Test 1.89 ARCH Impact Test (Significant) 0.00 (0.98) Significant at 1% level ** Modeling of EGARCH Approach The modeling results of the residual prototype of the Box-Jenkins process is presented in figure 6 using the EGARCH approach. The presented results show that the intercept (-0.47), the first-order coefficient (-0.68) and the second-order coefficient (-0.19) of the moving average process out of the average equation are significant at the 1% level. Table 6. Results of EGARCH Modeling Variables Coefficient Statistics Z Significant Intercept ** Mean Equation MA (1) ** MA (2) ** β ** Variance Equation β ** β ** β ** Adjusted coefficient of determination %29.90 Durbin-Watson Test 1.86 ARCH Impact Test (significant) 1.76 (0/18) ** Significant at 1% level The results also show that the intercept of the variance equation (0.18) and the coefficient of variation (0.25), (0.07) and (0.96) are significant at the 1% level. Adjusted coefficient of determination shows that in this modeling, the independent variables explain about 30% of Tehran Stock Exchange Index. Durbin - Watson Statistics (1.86) shows that there is no serial autocorrelation in the disturbing element of EGARCH model. In additions, the lack of significance of ARCH statistics (1.76) indicates no difference in the conditional variance components in EGARCH models. Therefore, in the last model, all of the present ARCH model impact has been modeled, and the residuals have not any variance anisotropy problem. Modeling with GJR Approach Modeling results of the residuals of the prototype resulted from the Box-Jenkins process is presented in Figure 7 using the GJR approach. The presented results show that first- (-0.63) and second-order coefficient (- 0.19) of the moving mean out of the equation are significant at the 1% level. In the variance equation, the intercept 6406

8 (298.83) and the variation coefficient of (0/43), (-0.26) and (0.70) are significant at the 1% level. Mean equation Variance equation Table7. Results of GJR Modeling Variables Coefficient Statistics Z Significant Intercept MA (1) ** MA (2) ** Intercept ** ** ** Adjusted coefficient of determination % Durbin-Watson Test 1.95 ARCH impact test (significant) 0.01 (0.91) ** Significant at 1% level 0.70 ** The adjusted coefficient of determination indicates that in this modeling, the independent variables are explained about 30% of Tehran Stock Exchange total index. Durbin - Watson Statistics (1.95) shows that there is no serial autocorrelation in the disturbing element of the GJR model. In additions, the lack of significance of ARCH statistics (0.01) indicates no difference in the conditional variance components of GJR models. Therefore, in this model, all impacts of the present ARCH model have been modeled and the residuals have not any variance anisotropy problem. Modeling with PGARCH Approach Modeling results of the prototype residuals resulted from the Box-Jenkins process are presented in Figure 8 using the PGARCH approach. The presented results show that the intercept (-0.54), the first-order coefficient (- 0.71) and the second-order coefficient (-0.12) of the moving average process out of the mean equation are significant at the 1% level. Table8. Results of PGARCH Modeling Variables Coefficient Statistics Z Significant Intercept Mean equation MA (1) MA (2) β Variance equation β β β Adjusted coefficient of determination % Durbin-Watson Test 1.80 ARCH impact test (significant) 2.37 (0.12) ** Significant at 1% level In the variance equation, intercept (2.66) and the variation coefficient of (0.16), (-0.35) and (0.85) are significant at the 1% level. Adjusted coefficient of determination shows that in this model, the independent variables explain about 29% of Tehran Stock Exchange index. Durbin Watson Statistics (1.80) shows that there is no serial autocorrelation in the disturbing element of PGARCH model. In additions, the lack of significance of the ARCH statistics (2.37) indicates no difference in the conditional variance components of the PGARCH models. Therefore, in this model, all impacts of the ARCH model have been modeled and the residuals have not any problem with the conditional variance anisotropy.

9 Comparison test of modeling prediction abilities In order to compare the prediction abilities of different modeling in the ARCH and GARCH family, the rootmean-square error, mean absolute error and mean absolute percentage error are used. Different criteria results of models prediction abilities are presented in Figure 9. Table9. Different modeling prediction abilities criteria Statistics GARCH CGARCH EGARCH GJR PGARCH Root-mean-square errors Average absolute errors Mean absolute percentage error The presented results show that the root-mean-square error of the GARCH (71.630), CGARCH (71.222), EGARCH (71.453), GJR (71.596) and PGARCH (72.020) modeling are very close to each other. Other parameters for different modeling are almost equal. These results provide preliminary evidence to confirm the study hypothesis, however, in order to obtain the definite results, the mean equity test and to median square root errors resulting from different models have been used. The mentioned results are presented in Figure 10. Results presented in Figure 10 show that the presented various statistics are not meaningful. Therefore, the research hypotheses based on the equality of the prediction abilities of different modeling of ARCH and GARCH families is not rejected in predicting the Tehran Stock Exchange index. Table10. Equality testing of models prediction abilities Mean Square Error Equality Test Mid-squared test of equality of error Statistic type Statistic (significance) Statistic type Statistic (significance) Anova F-test 0.03 (1.00) Med. Chi-square 1.31 (0.86) Welch F-test 0.03 (1.00) Adj. Med. Chi-square 1.18 (0.88) Kruskal-Wallis 1.03 (0.91) Kruskal-Wallis (tie-adj) 1.03 (0.91) van der Waerden 0.52 (0.97) Source: Research findings CONCLUSIONS AND RECOMMENDATIONS With attention to the importance of volatility in Stock Exchange, in this research we have tried to represent a suitable model from the ARCH family to predict the share price fluctuation in Tehran Stock Exchange. In order to compare the predictions abilities of different models in ARCH and GARCH family of standards, the rootmean-square error, mean absolute error and mean absolute percentage error are used. The presented results show that the root-mean-square errors of GARCH (71.630), CGARCH (71.222), EGARCH (71.453), GJR (71.596) and PGARCH (72.020) models are very close to each other. Almost all other criteria are equal. These results provide the preliminary evidence to confirm the study hypothesis, however, in order to obtain the definite results the test of equality of the median and root-mean-square errors resulted from different models have been used. The results of the different criteria of the prediction abilities of the models show that the results of the prediction abilities of the GARCH, CGARCH, EGARCH, GJR and PGARCH models are equal in prediction of Tehran Stock Exchange index. This means that the research hypothesis is not rejected. Therefore, the research hypothesis based on the equity of the prediction abilities of the various modeling of the ARCH and GARCH families in predicting Tehran Stock Exchange index does not rejected. REFERENCES Abbasian E, et al Effect of macroeconomic variables on Tehran Stock Exchange index. Journal of Economic Research, Vol. XII, No. 36, pp Abdoh Tabrizi H, Radpour M Articles on Financial And Investment 2. Tehran: Pishbord Publications. Ahmadpoor A, et al "Stock Exchange Index (with the emphasis on price indices)." Tehran: Termeh Publication, First print. Alikhani M The relationship between macroeconomic variables and stock returns of companies listed. MSc Thesis on Accounting, University of Khuzestan. Allah Nouri K Review of the Alterations and inadequate financial and economic events of the Economic Indicators on listed stock price index in Tehran Stock Exchange by the mass-circulation newspapers. MSc Thesis on Accounting, University of Khuzestan. Caiado J Modeling and Forecasting the Volatility of the Portuguese Stock Index PSI -20, MPRA Paper. No. 2077, Posted 07. Davani G, Amani A "Stock Exchange, Shares and Stock Price." Tehran: Kiumars Publishing, first printing. Ebeid ST, Bedeir GB Volatility Modeling and Forecasting of the Egyptian Stock Market Index Using ARCH Models. Ebrahimi Kordlar A, et al Review of the Weak-form Efficiency of the Capital Market in Stock. Stock Exchange Quarterly, Vol. 1, Issue 4. Pages

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