Suppose I'm measuring an athlete's 1 mile run time once every week-end. At different times during each week I measure regressors such as the amount of water that she drank each day, the amount of food eaten during each meal, daily minutes of exercise etc.
I'm trying to fit a regression model to my data and forecast the athlete's week-end run time on a daily frequency so I can custom tailor a daily diet/fitness plan, but I run into a dilemma here.
Subsampling my feature matrix on a weekly frequency and extrapolating my prediction from last week has stronger guarantees of independence. However, I have more recent data by the end of the week and so my forecast usually improves by the end of the week, so just subsampling seems inferior to taking the most recent data point each day.
On the other hand, if I used the highest granularity, i.e. every 7~ daily observations of feature vectors that map to the same week-end height, my observations become non-independent and so it hurts my $p$-values for most choices of models.
What is the best way I can combat this issue?