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:
“A man who whinnies with noisy laughter, surpasses all the animals in vulgarity.”
—Friedrich Nietzsche (1844–1900)
“A sleeping man holds in a circle around him the thread of the hours, the order of years and of worlds. He consults them instinctively upon awaking and in one second reads in them the point of the earth that he occupies, the time past until his arousal; but their ranks can be mingled or broken.”
—Marcel Proust (1871–1922)