I have some data in an Excel spreadsheet, which represents a bunch of date-times where samples have been taken. The dates are increasing linearly but there are some periodic gaps (leading to discontinuities in the date-data).
See the attached image as this shows the periodic nature of the data. Notice the rate of change shows clear spikes where discontinuities occur.

The data is a single column in an Excel spreadsheet of DateTimes. I would like to forecast this repeating series into the future so as to make estimates of future discontinuities.
Ultimately I want to code this in C# but if anyone has an idea of an algorithm that can perform such a forecast, either in Excel, or C#/C it would be great!
I thought about Auto-Correlation however can’t figure out how to do that in Excel to test it.
to explain my comments about correct data representation:

if the data can be represented by a linear function, i.e.:
then you can do a simple linear regression – in my excel example use this LINEST function (entered in 2 cells at the same time as an array formula with Ctrl+Shift+Enter):
the results (6, -220436) are linear and constant factors of a linear regression formula:
=>
f(date) = 6 * date - 220436