Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

## Exercise - Determine time shift by autocorrelation

Assume that you are staying at the beach of Florida and your kids are playing in the water. Your two sons are quarreling about when the water reaches it's maximum temperature during the day. The youngest son (he's just six years old)  insists on his point of view that the water is warmest around noon, whereas the older son (he's nine)  thinks that the water reaches its highest temperature about two hours later. Is he right?

In order to find the answer you should start  DataLab  and use the data of a nearby weather station. This data contains, among other variables, the sun light intensity, the air, and the water temperature, measured every 15 minutes over 9 days. Use the autocorrelation function to find the time delay between the maximum sun radiation and the maximum temperatures.