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Say you have a generator that emits random numbers in the range [0,6]. Now construct a fake timeseries by sampling that generator about 50 times. Fit a curve or moving average using the same method that you used here. What is the probability that your random series will exhibit an upward trend as great as the one you saw here?

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The probability of an upward trend when sampling is pretty much nil if you are sampling from a uniform series. A [0,6] uniform distribution will follow a Normal distribution with mean = 3 and variance = 3 after enough resampling. 95% confidence interval for true mean would be (-0.3948196, 6.39482).

The LOESS regression lines do have a confidence interval to reflect the uncertainty. It's a visual aid to illustrate the trend.

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