Let's say I have 5 numbers as below and that I need to calculate the skewness over the last 5 observations (it will be a rolling skewness that will always take as input only the last 5 observations). If I do that in Excel using the SKEW function I have a skewness of -0.84.
Observations: -1.5%, -0.9%, 0.5%, 0.65% and 0.50%
Skewness using Excel's SKEW function on these observations: -0.84
How can I find the closest point to the last/current one (in the case above 0.5%) that would flip the sign of the rolling skewness from negative to positive assuming that the skewness is still computed on the last 5 observations (so the first one above, 1.5%, will leave the sample and be replaced by the new number, still unknown but it will be the one that will make the skewness change sign)?
New observations: -0.9%, 0.5%, 0.65%, 0.50% and X (i.e. the new value that will flip the sign of the skewness to positive)
Is there a way to do that and can you show a pseudo code to implement the idea?