Download daily prices for the S&P500 and DJI. Use the time period from January 24, 2019 to January 12, 2023. This should give you 1001 daily prices. Use the closing price.

For each index use maximum likelihood estimation to fit an EWMA model for the variance process of the daily percentage price changes. Set (1)^2 equal to the sample variance.

NOTE the estimated variance for day 1, January 25, 2019, is the sample variance. u1 is the percentage price change from January 24 to January 25. Then use the formula to estimate the variance for day 2, January 26, 2019.

Given the estimated value of lambda and the value for the log-likelihood.

Make a plot of the volatility process vs time.