"(Source : Analysed by reseracher through Gretl output file )Fig no-6 Auto correlation test between closing and opening price in 95% CIellipseFindings Ref to the fig no-6, 95% CI (Confidence interval) the opening price ofthe stock market is aligned with the closing price of the stock within a period of last6 years since June 2006. The centre of the ellipse represents the degree of autocorrelation that exists between the opening and the closing price.Interpretation The value of r (auto correlation coefficient 2.75 e+ 004) betweenthe opening and the closing price indicates that there is positive correlation them.48 So if one increases other will also increase and vice versa. The 955 marginalintervals indicate whether this effect is dependent with the lag variables or not. Thevalue of correlation coefficient at 95 % marginal intervals indicates 2.47 e 004.Though lag order is determined but the from the value of correlation coefficient it isclear that there is a positive lag effect exist between theopening and the closingprice of the market ( Masih andMasih, 2009).49 Fig no-7 Closing price of the LSE with respect to high and low value sinceJune 2006(Source : Analysed by reseracher through Gretl output file )Findings Ref to the figure no-7 closing price of the LSE are demonstrated withrespect to the high and low value . Ref to the fig green shde indicates the closingprice of the stock market where as red and blue colour represents the high and lowvalue of the market on the respective day. Most of the cases it is observed thatgreen sgades has able to overshadow the red zone in the lasdt 6 years . So over1722 days observation indicates that at more that 1200 the closing price is unableoverlap on the low price of the day on the last 1722 days observation.50 Fig no-8 VAR (Vector auto regression) residuals since 2005(Source: Analysed by researcher through Gretl output file)Findings Ref to the fig no-8 Variance auto regression indicates the degree ofvariability between the closing and the opening price in the market. It indicates thatthe degree of the return series within the time frame between ends of 2007 tobeginning of 2009 was quite uncertain the risk perspective was quite high at thattime. 51 Interpretation Levine et.al (2008) described that for a study that includes severaltime series (Ex – opening price, closing price, specific highs and lows of the market)thereresearcher need to take into account the interdependence between them. SoVector auto regressive approach (VAR) is utilized which is a multiple time seriesgeneralization of the AR model. Estimation of a VAR (P) model requiredetermination of optimum lag(P). To assign the optimum number of lag AkaikeInformation Criteria (AIC) is being utilized which determine that lag length shouldbe 3(Table-4).Table: 6VAR system, maximum lag order 6The asterisks below indicate the best (that is, minimized) values of the respectiveinformation criteria, AIC = Akaike criterion,BIC = Schwartz Bayesian criterion and HQC = Hannan-Quinn criterionLagsloglikp(LR) AICBICHQC 1-10672.3978572.88706073.413286* 73.0977982-10575.853940.00000 72.47519773.45247372.8665673-10512.322400.00000 72.287907* 73.71623472.859909* 4-10487.796830.07211 72.36596574.24534273.1185995-10462.190810.04797 72.43667274.76710073.369938 526-10433.200880.01156 72.48436075.26583873.598258 VAR (P) where P=3 is estimated to establish the relationship amongst the returnseries of the stock market on different parameters. Therefore considering the abovefact two hypotheses is generated H : There exists no association amongst the return series. o H : There exists association among the return series.1 The results in case of LSE as dependent variable reject the null hypothesis at 5 %level of significance which can be confirmed from the fact that p-values except thatof opening price with lag order 1 are greater than 0.05.So other than opening price there exits association amongst the return series of these stock markets.Longin and Solnik (2009) explainedthat VAR ( Vector auto regression) estimate ofLSE as dependent variable also show that autoregressive coefficient of the otherparameters like opening price , closing price, high and lows of the marketsasindependent variable is significant thus null hypothesis is rejected. Interestinglyextreme lows of the market in the return series is not dependent or influenced byLSE so null hypothesis is accepted at 5% level of significance both for lag order 1and 2.53 Fig no-9 VAR inverse root risk assessment cycle with respect to the unitrootVAR inverse root cycle mentioned in the fig no-9 indicates that there are variousrisk factors and their indirect effect on the stock market output. The number of bluepoint indicates the pattern and type of risk and uncertainties that LSE has ablepredict and measure within the last 5 to 6 years .Figure indicates that all the points(blue) are within the circumference of the circle. That illustrates that the marketwas shock prone and susceptible to it but has able to manage these shock over a54 period of time. Besides the distance of the point from the circumference indicatesthat risk vis a vis return scope in that particular market.Table no-7VAR system, lag order 6OLS estimates, observations 05/12/20-12/12/10 (T = 1760)Log-likelihood = -15551.223Determinant of covariance matrix = 162119.63AIC = 17.7082BIC = 17.8077HQC = 17.7450Portmanteau test: LB (48) = 337.664, df = 168 [0.0000]Equation 1: Opening_PriceCoefficient Std. Error t-ratio p-value const -4.7431 1.47135 -3.2236 0.00129 ***Opening_Price_1 -0.0668955 0.0245445 -2.7255 0.00649 ***-0.00353791 0.0246163 -0.1437 0.88574 Opening_Price_2Opening_Price_3 -0.0327558 0.0246211 -1.3304 0.18356 Opening_Price_4 0.00254083 0.0246368 0.1031 0.91787 0.0162987 0.0246454 0.6613 0.50849 Opening_Price_5Opening_Price_6 -0.0140786 0.0177941 -0.7912 0.42894 Closing_Price_1 0.950194 0.0217465 43.6941 <0.00001 ***0.00244405 0.0317811 0.0769 0.93871 Closing_Price_2Closing_Price_3 0.0307962 0.0318402 0.9672 0.33357 Closing_Price_4 -0.00530857 0.0318247 -0.1668 0.86754 Closing_Price_5 0.0273268 0.0318007 0.8593 0.39028 -0.0185924 0.0310958 -0.5979 0.54998 Closing_Price_6High 0.166327 0.0137904 12.0611 <0.00001 ***Low -0.0538757 0.0159202 -3.3841 0.00073 ***2.10929e-07 1.1107e-07 1.8991 0.05772 *VolumeMean dependent var968.2162S.D. dependent var313.9484Sum squared resid604223.0S.E. of regression18.61339R-squared0.996515Adjusted R-squared0.996485F(15, 1744)33244.83P-value(F)0.000000rho0.005629Durbin-Watson1.98856955 "