What is the best way to handle missing observations for ACF / PACF?

Question

I have a time series with daily retail sales with two types of missing values

1. Stores are closed on Sundays such that there are no observations.
2. Stores are closed on public holidays (approx. 10 days per year)

I want to calculate and plot ACF and PACF for this time series. How can I handle the missing observations?

My idea is that dropping the Sundays from the time series is fine as long as one keeps in mind that when interpreting the plot - A peak on lag 6 indicates a weekly seasonality which usually is associated with a peak for lag 7.

What about the other missing values? Simply dropping would result in a wrongly calculated ACF since the lag-order is disturbed.

Answer 1

I'm afraid there is no ideal solution for such case but there could be interesting ways to deal with that.

As you mentioned, removing days could alter the seasonality detection.

One solution (among others) is to calculate the previous mean variations (ex: 3 previous weeks) on the public holiday.

For instance, if Christmas is a Wednesday December 25th, you can take the variations on previous Wednesdays (4th,11th,18th) regarding their previous days:

Tue 3rd: 5.3

Wed 4th: 6.1 => +15%

Tue 10th: 6.4

Wed 11th: 6.2 => -3%

Tue 17th: 5.6

Wed 18th: 6.5 => +16%

Tue 24th: 6.3

Wed 25th: ? => Apply ~+10% => 6.9

Another interesting solution is to take last year's variation because the weekday is usually not the same.