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I am using Arima and Kalman smoothing to impute missing values in univariate time series (similar way to this post: https://stats.stackexchange.com/questions/104565/how-to-use-auto-arima-to-impute-missing-values)

However, my time series have more than 20 000 values (60 years of data with daily frequency) and therefore the process crashes when I try to run ARIMA and Kalman on it.

I found two solutions so far:

  1. I decompose my Time series in 31 Time series, one with each day of the month (all the first of each month, then all the second etc...). I run Arima and Kalman on each sub Time Series and recompose the final imputed Time series at the end by remerging the 31 Time Series
  2. I split the Time Series in chunks of 5 years, run ARIMA and Kalman on each sub Time Series and remerge all the Time Series at the end.

What are your thoughts regarding my two solutions? Do you have any better ideas?

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