# Distinguish long and short term fluctuations in time series

I have a sequence of events $(e_1,e_2,\dotsc,e_n)$, and each event $(e_i)$ is described by two features $(t_i,F1,F2)$, where $t_i$ is the time of capturing the event.
The events $(e_i)$ are captured every second for 10 hours.

An example of the events is as follows:

{ (1,10,5), (2,10,4), (3,10,8), (4,10,0), (5,11,5), (6,11,5), (7,11,19), ... }

where the first element is $t$ (the time in seconds), the second element is $F1$ and the third element is $F3$.

My question: what is the statistical model that can tell whether $F1$ or $F2$ are long or short term fluctuations? Or if $F1$ or $F2$ have long- or-short variations based on the dataset?

• You need to provide more information about this sequence of events. For instance, it must be a time series. What is the temporal unit or frequency (e.g., hourly, daily, weekly, etc.) and how many periods are available? Also, note that CV is not intended to be a resource for software specific questions. – Mike Hunter Nov 24 '15 at 14:01
• Plz check the update above! – Omar14 Nov 24 '15 at 14:16
• Perhaps looking at the frequencies of the data could be relevant? That is, you would use the frequency domain instead of the time domain and see which frequencies dominate in each of the features $F1$ and $F2$. – Richard Hardy Nov 24 '15 at 18:45
• How can we model the frequencies to decide if F1 or F2 have long- or-short variations. On the other hand, do you think using the methods like "Linear trend estimation" can help? e.g. Fitting a trend using least-squares for F1 and F2 and compare them! – Omar14 Nov 24 '15 at 18:57
• Intuitively, I do not see how fitting a linear trend would be helpful. Regarding frequencies, you do not necessarily need to model them, you could first just look at them treating them as descriptive statistics. They should directly show whether the variations are short term (high frequencies dominate) or long term (low frequencies dominate). – Richard Hardy Nov 24 '15 at 20:08