- #1

fog37

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- TL;DR Summary
- Time series and why removing of seasonality and trend

Hello,

I understand a few things about time series but I am unclear on other main concepts. Hope you can help me get on the right track.

The goal in time series analysis is generally coming up with a model that predicts future values using past values. Why would we want to remove seasonality and/or trend from ##X(t)##? That would seem to change the identity of the signal....I get that removing them would make the signal stationary if it is not...But I am thinking how two different signals ##X(t)## are indeed different because they are holistically different in their seasonality, trend, etc.

If a signal is truly ##X(t) = seasonality+trend+random component##, removing the first two leaves us with only the random part...

I see how removing seasonality may make sense sometimes. For example, the earnings of a company may go up and down over the course of a year simply due to what generally happens during a specific month. That is useful to know even if it makes the time series not stationary....

Thank you!

I understand a few things about time series but I am unclear on other main concepts. Hope you can help me get on the right track.

- A time series is simply a 1D signal with the variable time ##t## on the horizontal axis and another variable of choice ##X## on the vertical axis. The time implies a precise order of the samples of the variable ##X## (sequence).
- I understand that the time signal ##X(t)## can be viewed as the sum of 3 components which are a) seasonality, b) trend, c) random component. Seasonality means a there is a periodic component (not matter its functional shape, sine, etc.). Trend is another functional shape (linear, curvilinear, etc.). The random component is obvious.
__Signals can be stationary or not.__Stationarity simply means if we take a segment of the ##X(t)##, say from 5s to 8s, and another sample from 10-13s, the two segments are not identical but statistically similar (mean, correlation, etc.): the statistical properties of ##X(t)## don't change over time.

The goal in time series analysis is generally coming up with a model that predicts future values using past values. Why would we want to remove seasonality and/or trend from ##X(t)##? That would seem to change the identity of the signal....I get that removing them would make the signal stationary if it is not...But I am thinking how two different signals ##X(t)## are indeed different because they are holistically different in their seasonality, trend, etc.

If a signal is truly ##X(t) = seasonality+trend+random component##, removing the first two leaves us with only the random part...

I see how removing seasonality may make sense sometimes. For example, the earnings of a company may go up and down over the course of a year simply due to what generally happens during a specific month. That is useful to know even if it makes the time series not stationary....

Thank you!