Dependent or Independent...a little intuition I have a time series that describe the power consumption of a building. For every hour of the day I have a measurement (e.g Hour 0 = 2.3 kWh, Hour 1 = 4.2 kWh etc).
Do you believe that the measurements for different hours are dependent or independent variables?
 A: When I see "dependent or independent variables", I do not think of "statistically independent", but rather experimentation and modeling, where there are dependent and independent variables. [Edited per amoeba's comment.]
So if you are doing a regression to predict electricity usage, electricity usage would be your dependent (target) value. Other measurements (temperature, etc) and lagged values for these measurements (temperature two hours ago, or temperature same time yesterday) and of the electricity usage itself (usage two hours ago, usage same time yesterday) would be your independent variables.
If you are asking if each hour's electricity usage is independent of other values, Dilip Sarwate's comment is correct: time series like this have autocorrelation and an hour is not independent of the previous hour.
A: Here's an explanation by contradiction.  If it was independent, that would mean time of day doesn't impact the power consumption at all. Do you think the power consumption of a building is the same during the daylight when all the lights are on as it as at night when everyone is sleeping? Obviously not.
A: Obviously, knowledge of previous power consumptions improves the prediction for power consumption of the next hour, even after taking into account the periodicity.
