Gaps in time series and time series validity After doing some reading on CrossValidated, I understood that we can use "imputation" techniques to fill in the gaps (if they are random). But I am not clear on following questions:


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*How many consecutive gaps may make data set invalid for forecasting?

*How many total gaps in data set makes it as invalid.
For example I have hourly data for week, which means 188 total points in my data set


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*Case 1: assume if we are missing 3 consecutive days of data is missing, can we still consider that data set as valid data set?

*Case 2: assume overall 80 data points are missing out of 188 points, can we still consider data set as valid?


I am using HoltWinters implementation in java for forecasting. 
Any help would be appreciated.
 A: I am not sure what you mean by "a valid data set". Are you sure what you mean by it? There are reasons why, in a single or in multiple time series consecutive missingness would be irrelevant to the validity of an analysis, and reasons why it would be lethal to valid inference.
However, Honaker and King are at the head of practical multiple imputation within a time-series context:
Honaker, J. and King, G. (2010). What to do about missing values in time-series cross-section data. American Journal of Political Science, 54(2):561–581. (See also, the related R package Amelia II on CRAN)
It is not clear how familiar you are with multiple imputation, but it has two aims (1) to support inference that is unbiased by MAR and MCAR (i.e. to impute a set of reasonable values), and (2) in doing so to incorporate the additional uncertainty in one's analysis that is due to the presence of missing data (i.e. to incorporate the extra variation resulting from imputed values not all agreeing with one another).
A: The Kalman filter is one alternative to fill in missing observations in time series. See this post as an example. The Kalman filter is a common algorithm that will be available in most languages and statistical software. Contrary to the Holt-Winters filter you have to specify a model for the data.

"How many consecutive gaps may make data set invalid for forecasting?
  How many total gaps in data set makes it as invalid."

I don't know a rule to measure this. I would say it depends on how much 
we know about the data and their context. Forecasting and, in general, the analysis of data involve a combination of our knowledge or theories and statistical methods to test our theories or find some further facts that we may have overlooked.
The amount of data or the presence of gaps may or may not be critical. For example, I have not looked at historical data about temperatures recorded in my town but I would be quite confident to give you a relatively narrow interval 
about the temperatures that will be observed in the next days. On the other hand, I have a data base with thousands of flight prices and at this moment 
I wouldn't dare to tell you whether you should buy a ticket today or wait 
until tomorrow.
So there is a combination of knowledge and data. On one side, we may know a lot about the data but we lack a minimal amount of data. On the other side, we may have a huge amount of data but they don't have much meaning to us. In the former case, we may decide to throw the data away and trust our expert knowledge to foresee the future. In the latter case, we may throw the data into a brute force algorithm (some kind of machine learning algorithm) and let it find patterns and forecasts for us.
Usually we are at some point in-between these extreme cases. You are the one who knows how much the available data can contribute to your knowledge and how much uncertainty will be in the forecasts.
A: If you have enough data to do a meaningful test, you could look at a chunk of the data with no missing values. Then remove some values and fill in the missing values with interpolations. Fit the Holt Winters model on the interpolated data, and look at the error of the model on a holdout section of your data to see how it compares to forecasting from the original data set. Then you can experiment with removing different numbers of values to see what kind of effect it has on the error.
