**5. Conclusions**

value close to that value. This proposal is fulfilled, as shown in **Table 6**, because the kurtosis is more than twice that for the non-standardized residual. Fourth, in a proprietary unpublished paper reported by Keam and Pagan, we are using the Pagan and Sabau [36] specification test. In particular, Kearn and Pagan are proposing to square residue out of the mean equation and regress to perform their tests with a constant and conditional variation (h2) in the following ways: (24) Alles and

**Standard GARCH TGARCH**

(s,/h,<sup>0</sup> 2) L-B (10) �0.011 �0.011 3.5 L-B (10) �0.009 �0.010 3.9 s (s,/h,″)<sup>0</sup> L-B (10) �0.028 �0.028 4.3 L-B (10) �0.029 �0.030 5.0

Skewness �0.369 �0.280

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

Kurtosis 5.804 13.96•• 6.048 14.00\*\*

*"••" and "\*\*" shows the significance at p = 0.000*

*Standard GARCH and TGARCH models.*

**Table 6.**

**AC PAC Q AC PAC Q**

In fact, model (9) investigates how many variances can be clarified by situation variances in the unknown actual volatility (proxied by e). As the regressed as well as the regressor are at least theoretically the same in the ARCH model's framework, the equation slope (9) should ideally be equal to unity, with zero intercept. Then you

The findings of the Keam-Pagan (K-P) check in **Table 7** prove that the evidence supports the theoretical assumptions. First, the intercepts (called C) vary little to zero. Secondly, there are extremely positive and high slope coefficients. Third, with standard errors insignificantly different from zero, both coefficients are statistically significant in less than five percent. Fourthly, it is important to remember that the TGARCH is greater in R<sup>2</sup> than the regular GARCH, and the model's explanatory forces are R2-based. It should not come as a surprise that TGARCH should be able to collect asymmetries from the data better than the standard GARCH does. This is an indirect proof of the overall asymptotic superior success of Glosten et al. in the recording results gap for both models (1993) as Engle and Ng [34] models of capture of asymmetries in volatility. In the same way, the results discrepancies give

s—c þ bh þ e (9)

Murray ([37], p. 140) included this test in "a diagnostic test":

can determine the fit of the model using R2. **Table 7** reports the results.

subtle proof that the traditional GARCH model struggles to chart the data's

Finally, Diebold [38] suggests, among other things, that, if the GARCH model is defined correctly, no ARCH effects in mean and variance equations respectively in the uniform residual rates and squares will remain. This test is a Lagrange multiplier test asymptotically equivalent to T \* R2, where T is the sample number, and R2 the known determination coefficient. This test is also a K-degree free chi-square test.

C 7.1E�5 (1.6E�5) 4.4 3.1E�05 (1.3E�5) 1.79 b-coefficient 0.519 (0.049) 9.9 0.699 (0.08) 12.8

R<sup>2</sup> 0.513 0.842

**Standard GARCH t-ratio TGARCH t-ratio**

asymmetries.

**Table 7.**

**200**

*Keam-Pagan (K-P) test.*

This chapter addresses the value of high stock market fluctuations and three predictions: economists, investors, and policy makers. The fact that uncertainty is an important phenomenon to these institutions is illustrated by quotes from current literature in financial economy. While much analytical attention has been paid to the volatility of large cap inventory indices, there is been little concern for the volatility of the small cap indices. At least three methodological problems to be explored using small caps (SC) 600 for analysis purposes are described in this article.

The primary focus of the chapter is on these testable theories. Hypothesis 1 is a validation of the statement that SC 600 variance cannot be expected. This theory has been refuted on the basis of evidence that low cap volatility of 600 can be forecasted in the same way as other stock prices are expected by regular GARCH and TGARCH models. Hypothesis 2 is a hypothesis to the extent that SC 600 is not similarly empirically compatible with other stock values. The findings demonstrate, in terms of observable methodological regularities that govern the empiric distribution of stock prices in general, that the SC 600 exhibits the same statistical characteristics.

In conclusion, hypothesis 3 tests the argument that SC 600 cannot pass a rigorous market efficiency test for the form. This hypothesis is dismissed, which indicates that SC 600 has passed the Effective Hypothesis Test (EMH). Our findings may be seen as the start of further research on the behavior, particularly with respect to the EMH measure, of other small equity indices. Our findings especially encourage further research into a closer empirical study of the unresolved myth in investor perceptions.

**References**

[1] Engle, R. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of U.K. Inflation. Econometrica, 50, 987-1008.

*DOI: http://dx.doi.org/10.5772/intechopen.94119*

*An Econometric Investigation of Market Volatility and Efficiency: A Study of Small…*

Handbook of Econometrics, Vol. 4 (North Holland, Amsterdam, 1994).

of Financial Markets. Journal of Empirical Finance, 3, 15-102.

[11] Pagan, A. (1996). The Econometrics

[12] Black, F. (1976). Studies in stock volatility changes, in Proceedings of the 197d Meetings of the Business and Economics Statistics Section, I 77-181.

[13] Christie, A. (1982). The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects. Journal of Financial Economics,

[14] Schwert, G.W. (1989). Why Does Stock Market Volatility Change over Time?. Journal of Finance, 54, 1115-1151

[15] Campbell, J.Y., and L. Hentschel (1992). No News is Good News: an Asymmetric Model of Changing Volatility in Stock Returns. Journal of Financial Economics, 31, 281-318.

[16] French, K., G. Schwert, and R. Stambaugh (1987). Expected Stock Returns and Volatility. Journal of Financial Economics, 19, 3-29.

[17] Wu, G. (2001). The Determinants of Asymmetric Volatility. Review of Financial Studies, 14, 837-859.

Variation of Certain Speculative Prices. Journal of Business, 36, 394-419

[19] Fama, E. (1965). The Behavior of Stock Market Prices. Journal of

[20] McAleer, Michael, and Les Oxley (2002). The Econometrics of Financial Series. Journal of Economic Surveys, 16

[21] Fomari, F. and A. Mele (1996). Modeling the Changing Asymmetry of

[18] Mandelbrot, B. (1963). The

Business, 38, 34-105.

(3), 237-243.

10, 407-432.

Econometrics." University of California,

[3] Greenspan, Alan (1997). Maintaining Financial Stability in a Global Economy. *Symposium Proceedings*, The Federal Reserve Bank of Kansas City.

[4] Poshakwale, S., and V. Murinde (2001). Modeling the Volatility in East European Emerging Markets: Evidence on Hungary and Poland. Applied Financial Economics, 11, 445-456.

[5] Pindyck, R. (1984). Risk, Inflation, and the Stock Market. *American Economic Review*, 76, 335-351.

[6] Garner, C.A. (1990). Has the Stock Market Crash Reduced Consumer Spending?. *Financial Market Volatility and the Economy*, Federal Reserve Bank

[7] Maskus, K.E. (1990). Exchange Rate Risk and U.S. Trade: A Sectoral Analysis. *Financial Market Volatility and the Economy*, Federal Reserve Bank of

[8] Yu, Jun (2002). Forecasting Volatility in the New Zealand Stock Market. Applied Financial Economics,

[9] Bera, A., and M. Higgins (1993). ARCH Models: Properties, Estimation and Testing. Journal of Economic

[10] Bollerslev, T., R. Engle, and D. Nelson (1994). ARCH Models," in R. Engle and D. McFadden (eds.),

Surveys, 7(4), 305-362.

[2] Engle, R., and V. Ng, "An Introduction to the Use of ARCH/ GARCH models in Applied

San Diego (1991).

of Kansas City.

Kansas City.

12, 193-202.

**203**
