On Stochastic Interpolation of Omitted Observation

Abstract

Most series of meteorological observations may be considered as a stationary autoregressive stochastic process of order, say, h. In such a series, it is proved that, for the interpolation of an omitted observation by a linear scheme, the observations more than h terms apart before or after the omitted term need not be taken into consideration. Precision formulae, by which we can indicate the probability that the true value be within any range around the estimated value, are derived for various cases.
The theories and formulae are extended to the case of vector or multivariate time series which may often come out in practice.