I am trying to detect anomalous values in a time series of climatic data with some missing observations. Searching the web I found many available approaches. Of those, stl decomposition seems appealing, in the sense of removing trend and seasonal components and studying the remainder. Reading STL: A Seasonal-Trend Decomposition Procedure Based on Loess, `stl`

appears to be flexible in determining the settings for assigning variability, unaffected by outliers and possible to apply despite missing values. However, trying to apply it in `R`

, with four years of observations and defining all the parameters according to http://stat.ethz.ch/R-manual/R-patched/library/stats/html/stl.html , I encounter error:

`"time series contains internal NAs"`

(when `na.action=na.omit`

), and

`"series is not periodic or has less than two periods"`

(when `na.action=na.exclude`

).

I have double checked that the frequency is correctly defined. I have seen relevant questions in blogs, but didn't find any suggestion that could solve this. Is it not possible to apply `stl`

in a series with missing values? I am very reluctant to interpolate them, as I do not want to be introducing (and consequently detecting…) artifacts. For the same reason, I do not know how advisable it would be to use ARIMA approaches instead (and if missing values would still be a problem).

Please share if you know a way to apply `stl`

in a series with missing values, or if you believe my choices are methodologically not sound, or if you have any better suggestion. I am quite new in the field and overwhelmed by the heaps of (seemingly…) relevant information.

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#### Best Answer

ARIMA models easily incorporate dummy variables to deal with missing values. These are called Pulse Indicators . The methodology is straightforward and documented in http://www.unc.edu/~jbhill/tsay.pdf. In general the method extracts from the current residual series information regarding Pulses, Level Shifts, Seasonal Pulses and Local Time Trends.

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