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I originally posted this question on stackoverflow and was recommended to post here instead.

I am trying to derive high frequency data from low frequency data. I also have a number of other related datasets at this higher frequency that I am trying to use to assist with the temporal disaggregation. I am not sure what the best way to approach this is!

For example:

Suppose you are trying to convert from: annual volume of gas used (for heating) to monthly volume of gas used.

You also have temperature, population, etc. on a monthly level. You know that there will be a relationship between these independent variables and the dependent variable that you are trying to estimate at a higher frequency (monthly volume of gas used).

Does anyone know the best approach here? For example, can you average/aggregate your independent variables to the lower frequency (say annual level), perform a regression, and then reduce the dependent variable to the higher frequency subject to this relationship ?

Any help would be greatly appreciated !

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There are many traditional statistical approaches here, and none are a silver bullet for every circumstance. Sax and Steiner (2013; PDF link) collect several methods in the R package tempdisagg, namely Denton, Denton-Cholette, Chow-Lin, Fernandez and Litterman.

[...] On the one hand, Denton (Denton, 1971) and Denton-Cholette (e.g. Dagum and Cholette, 2006) are primarily concerned with movement preservation, generating a series that is similar to the indicator series whether or not the indicator is correlated with the low frequency series. Alternatively, these methods can disaggregate a series without an indicator. On the other hand, Chow-Lin, Fernandez and Litterman use one or several indicators and perform a regression on the low frequency series. Chow-Lin (Chow and Lin, 1971) is suited for stationary or cointegrated series, while Fernandez (Fernández, 1981) and Litterman (Litterman, 1983) deal with non-cointegrated series.

Also see Montazerin and Zarandi (2015, abstract) which discusses temporal disaggregation of natural gas time series specifically.

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