I want to apply auto correlation function to time series of observations. Unfortunately, the observations have some data gaps. The data gaps are not uniform. So, i would like to know is there any condition to estimate the auto correlation function validity with respect to the data gaps.
Thank you in advance,
time series models generally require sequential, evenly-spaced, observations.Thus, if your data are not evenly-spaced, you will run into estimation problems. Moreover, if you have missing data, then autocorrelation cannot be computed.
You may have to consider a different approach, so as longitudinal models (general estimating equation, fixed effects, or mixed models). These models do not require evenly-spaced observations, and the ML estimation can help with missing values. Perhaps you should consider multiple imputation for missing values, assuming your data is suitable for that?
What about these papers?
Jones 1971, http://www.ism.ac.jp/editsec/aism/pdf/023_3_0387.pdf
parzen 1963, on spectral analysis with missing observations and amplitude modulation.
If you assume the data are from a stationary sequence, then some missing data will not sink you. Say you want to estimate R(k) where k is lag. Then assuming a zero mean, you would form
\hat{R(k)} = (1/N_k) \sum_{j \in I_k} X_j X_{j+k} where I_k are the indexes for which the product is non-zero and N_k is the number of elements in I_k. You can modify it for non zero mean.
I tried for a data in which I create artificial data gaps. I noticed the shape of the Auto co variance function is varying as I increased the data gap. the power spectrum estimated from ACF also reveal the changes.
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