Is there a simplistic model to disaggregate census data based on years and smaller zones? In a nutshell, here's what I have:


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*Annual population estimates for the State

*Periodical (5 years) age, population, and basic census data per zones


Here's what I want to do:


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*Create a simplistic model to generate the data for the missing years between the period for each zone, and have the total sums add up to where the yearly state population estimate is.


All in all, I'm looking for a non complicated statistical model that is able to generate values with an acceptable (doesn't have to be super high) precision.
 A: About the simplest thing you can do is interpolate normalized counts over time and (almost) the simplest form of interpolation is linear.
Specifically, suppose $y_i$ is the state population at time $i$ and $x_i$ is some other count (by age, tract, or whatever).  Define $\xi_i = x_i/y_i$.  Suppose $i$ is a year for which you do not have the periodic data.  Let $i_{-}$ and $i_{+}$ be the years immediately preceding and following $i$, respectively, for which $x_i$ is available.  The linearly interpolated estimate of $\xi_i$ is
$$\hat{\xi}_i = \frac{\xi_{i_{-}} (i_{+} - i) + \xi_{i_{+}} (i - i_{-})} {i_{+} - i_{-}} \text{.}$$
The estimate of $x_i$ is
$$\hat{x}_i = \hat{\xi}_i y_i.$$
The sums will come out correctly because this estimator is linear with weights summing to unity.  For example, suppose you are tracking two variables $x$ and $z$ which count complementary parts of the population (such as males and females), so that $x_i+z_i = y_i$ whenever you have all three counts.  Defining $\xi_i = x_i/y_i$ as before and, similarly, $\zeta_i = z_i/y_i$, the two fractions sum to unity: $\xi_i + \zeta_i = y_i/y_i = 1$ for all $i$.  Therefore the interpolated fractions also sum to unity:
$$\hat{\xi}_i + \hat{\zeta}_i = \frac{\xi_{i_{-}} (i_{+} - i) + \xi_{i_{+}} (i - i_{-})} {i_{+} - i_{-}} +  \frac{\zeta_{i_{-}} (i_{+} - i) + \zeta_{i_{+}} (i - i_{-})} {i_{+} - i_{-}}$$
$$= \frac{(\xi_{i_{-}} + \zeta_{i_{-}}) (i_{+} - i) + (\xi_{i_{+}} + \zeta_{i_{+}}) (i - i_{-})} {i_{+} - i_{-}}$$
$$= \frac{(i_{+} - i) + (i - i_{-})} {i_{+} - i_{-}}$$
$$= 1.$$
Whence $\hat{x}_i + \hat{z}_i = y_i(\hat{\xi}_i + \hat{\zeta}_i) = y_i$ as desired.  This generalizes to population partitions of any size, such as age distributions.
