WALT DISNEY COMPANY-ECONOMETRICS

Walt Disney Company-Econometrics

Walt Disney Company-Econometrics

In this study we calculate the Pearson coefficient for stock price data on the Disney (Walt) company. These companies are included in the daily Dow Jones Stock Index and represent four different industries. The data was collected from Yahoo Finance and spans the period 22 October 2010 - 22 January 2011, summing up 2324 observations. Figure 1 and Figure 2 show graphs of the financial returns and their volatility evolutions. In Table 1, where we report some summary statistics, we observe that the four returns series are negatively skewed and have a kurtosis between 6.159 and 10.068.

This robustness of stochastic volatility models is shown analytically in two theorems. In the ¯rst theorem, the least-squares estimator of a VAR(1) model (nesting AR(p), HAR-RV, and VAR(p)) is considered. This covers the case where the volatility equation has a separate source of randomness. The main insight of the theorem is that the larger the variance (volatility of volatility) in relation to the magnitude of level shifts, the less bias there is in the estimation of persistence within regimes. The second theorem shows that for a suitably defined method of moments estimator, there is no such trade-o® between variance and level shifts, and even small shifts can induce large bias in the estimation of persistence. It is shown that the quasi-maximum likelihood estimator of GARCH is such an estimator.

A stochastic volatility model with a low-persistence Ornstein-Uhlenbeck volatility equation undergoing level shifts generates high-frequency data (100 observations per day), and the data are used to estimate (1) a HAR-RV model of realized volatility, and (2) a GARCH(1,1) model. For both models the sum of the autoregressive coe±cients approaches one as the level shifts increase in size, but it does so much faster in the case of GARCH than in the case of HAR-RV.

Estimating a GARCH(1,1) model and a HAR-RV(1,5,21) model on price data of the 30 constituting stocks of the Dow Jones Industrial Average between 1995 and 2007, we ¯nd strong empirical evidence for the theoretical ¯ndings of this paper. Persistence, as measured by the sum of the estimated autoregressive coe±cients of the two models, di®ers by about 0.10, being close to 0.90 in the case of HAR-RV(1,5,21) and close to one in the case of GARCH. The implied average time to revert to the unconditional mean of volatility is of order of magnitude 10 days in the case of HAR-RV and of the order of magnitude 100 days in the case of GARCH.



Fig 1

Fig 2

Table 1

Moreover, the individual significance tests show evidence (at a 5% significance level) that both returns and squared observations are autocorrelated, although the autocorrelation is much stronger for the series of squared returns.

Table 2

Table 3

In this section it is shown that in GARCH models, the estimator is not subject to a trade-o® between volatility of volatility and level shift size. Consider estimators ©^c 2 RN; ^© 2 RN£N : Et¡¿ (yt ¡ ^yt) = 0ª; (14)

where ^yt = ^c + ^©yt¡1 and ¿ ...