Changing the frequency of time series data

When working with time series, and especially financial ones, we often need to change the frequency (periodicity) of the data. For example, we receive daily OHLC prices, but our algorithm works with weekly data. Or we have daily alternative data, and we want to match it with our live feed of intraday data.

The general rule of thumb for changing frequency can be broken down into the following:

• Multiply/divide the log returns by the number of time periods.
• Multiply/divide the volatility by the square root of the number of time periods.

For any process with independent increments (for example, the geometric Brownian motion), the variance of the logarithmic returns is proportional to time. For example, the variance of r_t3 - r_t1 is going to be the sum of the following two variances: r_t2−r_t1 and r_t3−r_t2, assuming t₁≤t₂≤t₃. In such a case, when we also assume that the parameters of...