Critical Event In Complex Financial System - MyAssignmenthelp.com

Question: Discuss about the Critical Event In Complex Financial System. Answer: Description of the data The data presents the stock prices from 8th Dec 2014 to 1st Dec 2016 (383 days). In addition, the data contains inputs from 8 independent variables and one dependent variable (future prices of McDonalds). For each of the 383 days the change in prices of the assets measured are: Copper Aluminium West Texas Intermediate Oil The Baltic Dry Index The Standard and Poors 500 Index of stock prices (the SP500) Also McDonalds future prices Most of the variables used to predict the future change are interaction variables. Moreover, some of the variables have a suffix vel or acc. vel followed by a number refers to the change in price in the number of days. acc refers to the change in velocity. Thus while copper would have referred to the price of copper, copper_acc1 would indicate how the price of copper accelerates (decelerates) over a period of 2 days. Similarly MCD_vel2 means the change in price of McDonalds going back one day. Variance Inflation Factor Variance inflation factor (VIF) is used to assess multi-collinearity in a data-set. Multi-collinearity refers to the phenomenon of correlation between two or more variables in multi-regression. In the situation that Multi-collinearity exists in a model, with the addition of more predictors the precision of the regression coefficient of the model decreases. The test for VIF showed that there is no or very low correlation between the input variables. The VIF for each of the 8 factors was found to be . PhSTAT software was used to find multi-collinearity. Thus it can be inferred that all the 8 response variables which are used to measure the future prices of McDonalds are independent and thus can be used in the model. Residual Analysis To assess the distribution in a data set the normal probability plot is used. The normal probability plot of the residuals shows that the data is normally distributed. Hence, it can be inferred that further calculations done with the data set would be valid. Figure 1: Normal Probability Plot of Residuals The histogram presented below represents the distribution of the residuals of multiple regression analysis. The histogram even though is not completely bell shaped but can be said to be normally distributed even though it looks like it has slight positive skewness. Generally, it seems that the residuals to the regression analysis are normally distributed, and thus further analysis and thus predictions can be done. Figure 2: Histogram of Residuals Analysis of Variance The output of ANOVA for multiple regression is presented in figure 3. Analysis of variance in multiple regression provides information about the relationship between predictor and response variables. From the figure it is seen that p-value is 3.43x10-12 which is much less than 0.05 (level of significance). Thus, the Null hypothesis is rejected. Hence, it can be said that there exists a relationship between the predictor and response variables. Thus, there is a linear relationship between the future prices of McDonalds and one or more of the 8 predictor variables. Figure 3: ANOVA Table However, the above figure does not tell us how strong the relationship is between the variables. The following section provides information regarding the strength of the relationship between response and predictor variables. Coefficient of Determination R2 The value of R2 is shown in figure 4. The proportion of variation in the response variable that can be explained by the predictor variables is 0.1712. Thus, 17.12% of the variation is the future prices of McDonalds can be predicted by the given model. Hence, it can be inferred that the model does not explain too much of the future prices of McDonalds. From the above figure it can be inferred that if the future prices of McDonald become unpredictable, then the value of R2 would be close to or equal to zero. In other terms we may say that the future prices are not all random (Sornette, 2017). Thus we are left to ask if the relationship between the input and output variables is strong enough to make a prediction. Hypothesis tests for the inputs The coefficients and p-value of the response variables is presented in figure 5. From the figure we find that except for Baltic_x_Copper_vel1 the p-values are less than 0.05. Thus except for Baltic_x_Copper_vel1 all the other variables have a significant relationship on the output. Figure 5: Coefficients and p-value of response variables Coefficients The second column in figure 5 presents the Coefficients which provides the information regarding how the input affects the future prices of McDonalds. We would ignore the y-intercept and thus investigate other variables as to how they affect the future prices. From the figure it is seen that the highest coefficient (0.9554) is for Year_x_Wheat which is an interaction variable which is created by multiplying The production of wheat The stock prices of wheat Though the values provided are open to interpretation but the values suggest that there is a seasonal variance in the values. When the production of wheat goes up then the stock prices is high and vice versa. Thus, it seems that the higher the prices of wheat the higher would be the prices of McDonalds. The largest negative coefficient (-1.2640) is for MCD_x_West_Texas. The variable presents the interaction between: The prices of West Texas and The prices of McDonalds. It is difficult to predict how the price of West Texas would affect the price of future shares of McDonalds but one can say that the higher the prices of West Texas oil the more McDonalds would have to spend to keep itself running. Thus the higher prices of West Texas would influence the stock prices of McDonalds. However, this explanation is subject to interpretation. Since, neither of the coefficients of the input variables are close to zero, hence it can be said that the input variables have a relationship with the output variable. Thus, there is no need to delete any input variable. Prediction of Tomorrows Share Prices The past data, confidence interval estimation is used to predict the future changes in prices of McDonalds, and further used to compare it with actual data. The variation in the predicted and actual prices of McDonalds is shown in Figure 6. From the above figure we find that there are differences in the predicted and actual values (blue highlighted). The bottom rows present 95% confidence interval for predicted and actual values of the future prices. The values are in the range of 0 to 1, thus the they are not very helpful. From the above interval it is seen that the actual y-value is within the limits of the confidence interval. Thus it can be inferred that the selected model does not have errors. The brighter side of the of the prediction is On 21st October 2015 the maximum change (increase) took place, and the model predicted a change of 0.56141. Hence the model predicts a substantiate change in future prices. Similarly, on 25th July 2016 the maximum change (decrease) took place. Yet again, the predicted model showed changes in future values. Thus the model is not devoid of predictive value. However, due to the low value of R2 the ability to with accuracy is reduced. Conclusion The data set is used to predict the future changes in the stock prices of McDonalds. From the VIF test it is seen that there is no correlation between the independent variables. The normal probability plot and Histogram shows that the residual of the multiple regression is normally distributed. From the multiple regression it is found that the value of R2 is 0.1712. Thus, it can be said that 17.12% changes in the future stock prices of McDonalds can be predicted by the following model. Moreover, from the ANOVA table it is seen that a significant relationship exists between the input and out variables. Figure 6 presents the predicted changes in future prices of McDonalds. There exist differences in predicted and actual prices. The difference in values is due to the fact that the value of R2 can predict only 17.12% change. The difference between predicted and actual could plausibly be reduced with a higher value of R2. References Sornette, D. (2017).Why stock markets crash: critical events in complex financial systems. Princeton University Press.