This data  ![enter image description here][1]has similar statistical characteristics identical except for the placement of the anomalies ( i.e. non time series data riddled by a number of pulses AND missing values as http://stats.stackexchange.com/questions/28737/which-model-should-i-prefer-for-time-series-forecasting/28753#28753. As Micheal Chernick has suggested identify and estimate a parsimonious model ![enter image description here][2] providing actual/fit/forevast ![enter image description here][3] . Now a review of the identified interventions which reflects adjustments for both unusual data and NA data which is treated as a "0.0" to begin with we see ![enter image description here][4] . The estimates of the three missing values are simply 1.123 per the equation. The missing value (NA) at the end of the series is simply the 1 period out forecast which in this case is 1.123. This query and my answer points out that Intervention Detection is in reality the imputation for bad/missing values. Now another trick suggested to me about 30 years by T.W. Anderson was to reverse the time series and like Michael reflected predict backwards. In my opinion for AMELIA to delivery anything useful the robust estimate of the mean (1.123) would have had to be suggested. For AMELIA to do this it would have had to detect the anomalies and to identify an approriate underlying ARIMA model of (0,0,0)(0,0,0) or maybe that model is assumed. If the series had seasonal pulses , level shifts and/or local time trends , procedures like AMELIA my come up short. It looks like AMELIA doesn't handle univariate time series [ Amelia Error Code: 42 There is only 1 column of data. Cannot impute ] or maybe even multivariate time series unless it makes a ton of assumptions about dependencies.


  [1]: https://i.sstatic.net/TjpR0.jpg
  [2]: https://i.sstatic.net/LIrVU.jpg
  [3]: https://i.sstatic.net/eKqVb.jpg
  [4]: https://i.sstatic.net/RCq0K.jpg