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I am working on a time series problem with a single variable which has consecutive zeroes at different periods. The TS plot looks like this: Full Time Series Plot Upon closer examination, the variable has consecutive zeroes in between spikes of activity. Time series plot of a subset

Following are the acf and pacf plots. I am not quite able to wrap my head around these.

enter image description hereenter image description here

Any pointers on which techniques could be used to develop a forecast model for such data?

EDIT: Because the initial time series plot looked very much like a stationary differenced series, i tried to apply a inverse (discrete integration) on it.

Here is what the plots look like: enter image description here Acf and Pacf indicate an AR(1) component. I am very new to forecasting, so I am doubtful if this makes sense.

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    $\begingroup$ A lot will depend on contextual information about the data and your goals. You could start just by predicting active/not active, for example. $\endgroup$ – Gregor May 9 '17 at 18:39
  • $\begingroup$ The y axis on your graph suggests you have a tiny negative autocorrelation at lag 1 (-.017, roughly), so really no autocorrelation at all. So there's no pattern in the ACF to interpret. It only looks "statistically significant" because you have so many observations. I like @Gregor's suggestion to model active/not active and then model size of response given it's nonzero. $\endgroup$ – zbicyclist May 10 '17 at 17:06
  • $\begingroup$ Your descriptive plots are not enough. Segment the time series into active and non-active periods and visualize the one and two-variable marginal distributions of times between activity bursts, activity burst lengths, and activity burst magnitudes. Are longer pauses followed by longer or stronger activity? Are stronger bursts also longer, or are they shorter, or neither? Have you looked into the bursts to see if there is more structure to study? $\endgroup$ – eric_kernfeld May 12 '17 at 22:36

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