# Imputation in monthly univariate time series

I have a time series of the amount of apples sold in a specific Region. The time series include monthly values of 10 years (2006-2016). However two months are missing (February 2009 and July 2014). After imputing the data my foremost aim is a forecast for the upcoming months.

The imputeTS package in R includes various methods for my case, e.g. linear, spline, Stineman Interpolation or Kalman Smoothing.

• Which is the most appropriate imputation method in my case?
• How can I make an appropriate forecast although I have missing data?
• Would you recommend another R package or function?
• The time series has a Unit root in July 2014 and the data in July 2014 is missing. How can I deal with this issue?

Unfortunately most linear about the topic focuses on multivariate time series (Have a look at the Links below).

• What is the intuitive difference between imputation methods for univariate and for multivariate time series?
• How do I have to take this into account when looking at my "apple time series"?

References

Honaker, J. and King, G. (2010). What to do about missing values in time-series cross-section data What to do about missing values in time-series cross-section data. American Journal of Political Science, 54(2):561–581.

Spratt, M., Carpenter, J., Sterne, J. A. C., Carlin, J. B., Heron, J., Henderson, J., and Tilling, K. (2010). Strategies for multiple imputation in longitudinal studies. American Journal of Epidemiology, 172(4):478–4876.

• Depends on what data you have available to predict apple sales. What does your data look like? – Morgan Ball Dec 15 '16 at 17:40
• Thank you for your question. I have monthly absolut numbers ranging from ~500 to ~2000. The data includes at least one structural break. Seaonality and trend should not make a difference in our case as I could also de-seasonalize and de-trend the data. – Ferdi Dec 15 '16 at 17:47
• If all you have is the volume of sold apples then you probably want to look at an autocorrelation approach like ARIMA. Such as this stats.stackexchange.com/questions/251794/… – Morgan Ball Dec 15 '16 at 17:51
• Have a look at the forecast package and auto.arima. – Morgan Ball Dec 15 '16 at 17:52
• If you're using R, there is the imputeTestBench package arxiv.org/pdf/1608.00476.pdf – Jon Dec 15 '16 at 20:05