Question

Question 6 [Avec R] Consider the following dataset that has a volatility measure for 30 stocks 0.5974090 5.7420023 9.5334667 2.0089723 38.6716167 3.9366327 27.7419840 5.6029157 3.5437040 0.8317833 1.6134417 18.1795990 32.8353140 1. 1497677 8.1007240 4.3894207 3.8839490 2.4667357 9.0249373 7.2506833 2.7767457 2.0062077 0.8373807 3.3444917 1.8748643 7.0183583 8.9134893 0.8701540 2.4200127 9.8454307 (a). Plot a histogram of the dataset and describe it (b). Fit a normal distribution. Use a QQ-plot to check if your fitted model is appropriate. (c). Another distribution to consider is the log-normal. This says that the logs of the observation follow a normal distribution. Fit a log-normal distribution and uses a QQ-plot to check if your fitted model is appropriate.

Answer 1

### R command

Volatility=c(0.597409,3.9366327,0.8317833,8.100724,9.0249373,3.3444917,0.870154,
5.7420023,27.741984,1.6134417,4.3894207,7.2506833,1.8748643,2.4200127,9.5334667,
5.6029157,18.179599,3.883949,2.7767457,7.0183583,9.8454307,2.0089723,3.543704,
32.835314,2.4667357,2.0062077,8.9134893,38.6716167,1.1497677,0.8373807)

## a) Histogram
hist(Volatility)

## b) QQ plot for the original data.
qqnorm(Volatility)
qqline(Volatility)

## b) QQ plot for the log transformed data.
log_Volatility=log(Volatility)
qqnorm(log_Volatility)
qqline(log_Volatility)

a) Histogram of the Volatility data

Comment: The histogram shows a half positive skewed distribution. Hence, the given data does not follow a normal distribution.

b)

Data points at both the tails of the above QQ-plot dispersed from the straight line, Hence, the given dataset does not fit for normal distribution.

c)

Normal Q-Q Plot 2 0 2 Theoretical Quantiles

The log-transformed data fall near to the straight line from one trail to another tail. Hence, the log-transformed data is fit for the normal distribution.