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)
“The white man regards the universe as a gigantic machine hurtling through time and space to its final destruction: individuals in it are but tiny organisms with private lives that lead to private deaths: personal power, success and fame are the absolute measures of values, the things to live for. This outlook on life divides the universe into a host of individual little entities which cannot help being in constant conflict thereby hastening the approach of the hour of their final destruction.”
—Policy statement, 1944, of the Youth League of the African National Congress. pt. 2, ch. 4, Fatima Meer, Higher than Hope (1988)