# Can you spot trend in time series?

By | March 30, 2017

Past experiments have demonstrated that humans (with or without formal training) are quite good at visually identifying the structure of time series. Trend is a key component, and arguably the most relevant to practice, as many of the forecasts that affect our lives have to do with potential increases or decreases of economic variables. Forecasters and econometricians often rely on formal statistical tests, while practitioners typically use their intuition, to assess whether a time series exhibits trend. There is fairly limited research contrasting these two. Furthermore, sometimes trend is understood with a rather vague definition. I do not think it is an exaggeration to suggest that even experts often can be confused on the exact definition (and effect) of a unit root and a trend.

To understand more about this, I set up a simple experiment to collect evidence how humans perceive trends. The experiment below asks you to distinguish between trended and non-trended time series. Every 10 time series that you will assess it will provide you with some statistics on your accuracy and the accuracy of some statistical tests (by no means an exhaustive list!). It also provides overall statistics from all participants so far. As you can see, it is no so trivial to identify correctly the presence of trend! What do you think, can you better than the average performance so far?

## 9 thoughts on “Can you spot trend in time series?”

1. Forecaster

I’m curious to get your thoughts on why humans have such a low accuracy rate? Are there any learnings from this mathematical psychology or any other field that makes humans more biased in interpreting trend?

1. Nikos Post author

This is precisely why I set up this small experiment! I suspected that humans were not great at this task, even though intuitively one would expect that spotting a trend should be relatively easy. What complicates things is what exactly constitutes a trend, from an intuitive point of view and a modelling point of view. The design of the experiment will hopefully help me shed some more light on this, once I have enough sample. I will post my results here. Then it will be interesting to reflect back to that literature.

2. Mikkel Petersen

Hi Nikos,

Is there an R function or package that can be used to test for trend like the the AICc or MTA?
Also a question for the test. Do you consider level-shift count as trend? I am generally using STL by Loess to detect trend where a level shift would fall under Trend component.

Thanks,
Mikkel

1. Nikos Post author

Hi Mikkel,

I have added a new function in TStools package (available at GitHub). Check the function `trendtest`. It allows using AICc (of ETS models) or the Cox-Stuart, without or with MTA (Multiple Temporal Aggregation). It also allows decomposition by using the centred moving average, in case the series to be tested is seasonal. However, a word of caution! Although it seems that these tests work fine, I have not tested them thoroughly yet, to be able to tell you when they may break down! Nikos

3. David

I think the difference may be because of different interpretations of “trend.” I’d interpret it as a near term expectation of whether the value will be the same or higher / lower. Mostly the graphs raise the question “why did the trend change at this point?” rather than answering whether there’s a consistent trend across the whole time period.

1. Nikos Post author

Interesting argument, and I tend to agree – how people define a trend affects how they spot one or not. To add to this, I think textbooks are not particularly helpful in this and perhaps for a good reason! I hope that I will be able to provide some insight once I analyse the data.

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