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I'm new to data analysis. I was wondering how I could recognize hyped (fake) growth and word of mouth (true) growth in Google Trends specifically (but I guess it applies even to stock markets and the rest).

For example, the image below is based on the Google Trends plot when you search for 'iPhone':

iPhone trend

(Orange, magenta, and green annotation were added to the original.)

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What operational distinction are you making about "fake" versus "true" growth? By definition, Google Trends "compute[s] how many searches have been done for the terms you enter, relative to the total number of searches done on Google over time." And that's that: it's neither fake nor true, it is what it is. – whuber Nov 18 '11 at 16:11
So, issues of interpretation aside, would it be correct to understand your question as asking how to separate a time series into one part that reflects "slow but sure" change and another part that consists of "huge spikes"? – whuber Nov 18 '11 at 16:37
We're back to the beginning, then: your question is without meaning, and therefore has no valid objective answer, unless you can characterize "trend" and "fad" in terms of the plots produced by Google Trends. – whuber Nov 18 '11 at 17:06
I think @whuber's point is this: Unless you define trend and fad in more quantitative terms it is not possible to answer your question. Consider an analogy: I want to distinguish between tall and short people in a group. Unless I define what tall/short might mean I have no way of moving ahead with the task. For example, I could define tall: Average height + at least 1 standard deviation and so on. In summary: you need to tell us what is your operational definition for trend and fad before an answer can be given. – varty Nov 18 '11 at 17:20
I think what you really want to know is if what looks like a movement in the ticker is likely to continue. I think this is what you mean by 'real' vs. 'fake' and 'trend' vs. 'fad'. This is a big deal in time series and forcasting, but it requires a book-length treatment. Moreover, I think the short answer is: you can't tell (until after the fact). – gung Nov 19 '11 at 4:29

You can apply all sorts of smoothing functions to your time series. A simple one would be a linear regression, and a more complicated one would be a loess function.

Your orange line looks suspiciously like a linear regression.

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Not sure how to use it. – user2534 Dec 8 '11 at 23:51
@user2534: if you're going to do any serious stats, you should get a stats packages, such as R, SAS, Matlab, Stata, etc. etc. – Zach Dec 9 '11 at 0:50

This answer uses Varsity-level statistics, but people interested in separating long-term trends from shorter-term spikes should really take a look at the discussion in this post about using Gaussian processes to model this sort of thing.

The blue line in the top graph is a smoothed trendline showing more-or-less seasonal variation, the blue spikes in the second graph show the periodic (weekly?) component, and the third graph shows residual patterns (e.g. holidays).

The Matlab code used to do the analysis is available here, as described in one of the comments.

Again, this is probably too advanced for most people (including me!), but it's the best example I know of where someone tried to tackle a problem like this.

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