As has been mentioned, the flaw of this concept is that feedback control systems (like a thermostat) are perfectly well understood. If you gave me a time series with the outside temperature and inside temperature I could calculate the transfer function of your thermostat/furnace in two minutes... and I would have a statistic called coherence (like an R-squared) to determine how well this model fit. Even if we exclude the possibility of choosing a better model (frequency vs. time domain) to fit to the data, we're left with outside temperature correlating with the furnace (or the pedal with hills) which, while imperfect, is not erroneous.