We give you the exact hint you need: The variance of Microsoft price returns up to day 10 is 0.121. The autocorrelation is the autocovariance divided by the variance. Let’s follow the same exercise and compute the autocorrelation of the Microsoft price returns up to day 10 at lag 1. And for the PACF, there is a sistem of equations that connect the ACF correlations to it, known as the Levinson recursion (which also is explained in that answer). Calculation of the autocorrelation with an example. Then, you can get $\gamma_j$ and $\rho_j$ by the formula present in the most upvoted answer in ACF and PACF Formula. Obs: This is a more formal thing about statistics, ideally you should try to learn what exactly those things mean and how to see when you can make that assumption and when you can't, but it's best to ask that in another post. $$\bar u_t$.įor using the data of your time series to calculate the amostral counterpart of those statistics (without having to set a model as what i presented untill now), first you need to assume that your series is at least weakly stationary and ergodic, which in loose terms is like saying that the series "will not change its statistical properties with time", so that the values of the series that you observe can be meaningful to the process behind it. Well if you mean how to estimate the ACF and PACF, here is how it's done:
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