Noisy Time Series, and An Example
It is harder to see a trend in a noisy time series. For example, if the true series is 0, 1, 2, 3 all plus some independent normally distributed "noise" e of standard deviation E, and we have a sample series of length 50, then if E = 0.1 the trend will be obvious; if E = 100 the trend will probably be visible; but if E = 10000 the trend will be buried in the noise.
If we consider a concrete example, the global surface temperature record of the past 140 years as presented by the IPCC: then the interannual variation is about 0.2°C and the trend about 0.6°C over 140 years, with 95% confidence limits of 0.2°C (by coincidence, about the same value as the interannual variation). Hence the trend is statistically different from 0. However as noted elsewhere this time series doesn't conform to the assumptions necessary for least squares to be valid.
Read more about this topic: Trend Estimation
Famous quotes containing the words noisy and/or time:
“My noisy denunciation trails off in doubt.”
—Mason Cooley (b. 1927)
“Even if fathers are more benignly helpful, and even if they spend time with us teaching us what they know, rarely do they tell us what they feel. They stand apart emotionally: strong perhaps, maybe caring in a nonverbal, implicit way; but their internal world remains mysterious, unseen, “What are they really like?” we ask ourselves. “What do they feel about us, about the world, about themselves?””
—Augustus Y. Napier (20th century)