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Detrending is removing a trend from a time series; a trend usually refers to a change in the mean over time. When you detrend data, you remove an aspect from the data that you think is causing some kind of distortion.

To detrend a time series you first need to estimate the trend and there is multiple ways to do that

  • moving average method
  • parametric regression
  • non parametric regression

my question is how do we know which method gives us the best estimation for the trend ? in other word , if we conduct all these methods what are the caractiristics that tells us which is the best estimator

Richard Hardy
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ayoub
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    This can also be viewed more broadly as a question of which model is the best (for whatever application). Information criteria and cross-validation are a couple of ways of evaluating that. – Richard Hardy Jan 20 '20 at 10:20
  • Parametric trends can be of two forms y(t)=y(t−1)+θ (A) Stochastic Trend or Y(t)=a+bx1+cx2 (B) Deterministic Trend etc where x1=1,2,3,4....t and x2=0,0,0,0,0,1,2,3,4 thus one trend applies to observations 1−t and a second trend applies to observations 6 to t. There can be multiple trends in either case .. For more see https://stats.stackexchange.com/questions/103193/stochastic-vs-deterministic-trend-seasonality-in-time-series-forecasting/103404#103404 – IrishStat Jan 20 '20 at 10:34

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