Discrete Samples and Moving Sums in Stationary Stochastic Processes
Lester G. Telser · Journal of the American Statistical Association · 1967
Assume that an autoregression generates the basic data but that the observations are an equi-spaced sample of moving sums of the basic data for non-overlapping discrete intervals. Simple least squares estimates of the underlying autoregression are not consistent. It is shown that it is possible to estimate consistently the coefficients of the underlying autoregression based on the equi-spaced sample. These results are equivalent to showing how to interpolate a finite number of missing values between adjacent sample observations if it is assumed that the underlying model is an autoregression of a specified order. It is not possible to interpolate a continuum of missing observations on the basis of an equi-spaced sample; this assertion is equivalent to the aliasing problem well known in spectral analysis. Finally, the analysis is extended to an autoregression including exogenous variables.