_MACHINE LEARNING AND HIGH-FREQUENCY SURVEYS IN PAPUA NEW GUINEA 11_ of the time series, that stacks the share of complete survey responses across all food items. I.e., when _Si,t_ equals 0 _._ 5 then at location _i_ and time _t_ , a 50% share of the data needed to calculate the basked price was observed. Let _ma_ ( _·, p_ ) be a _p−_ period moving average function and _S_<sup>12</sup> := _ma_ ( _S,_ 12) denote its 12-month moving average so that each entry corresponds to the share of observed data needed to calculate the basket inflation rate. Figures B3 show how the response rates varies over time. Let _P_ ̄ _N_<sup>beasingletimeseriesoflength</sup><sup>_T_,thataverages</sup> the imputed food price index of _N_ markets, and let _SN_<sup>12</sup> ̄<sup>equivalentlybethetime</sup> series that contains the market average of the 12-month moving average data availability rates.<sup>5</sup> Finally, let _SN,d_<sup>12</sup> ̄<sup>betheitem-specificanalog,and</sup><sup>_S_</sup> _N,_<sup>12</sup> ̄ _−d_<sup>bethe</sup> quantity constructed for a basket that excludes item _d_ .

Recall that _R_<sup> ̃2</sup> is the average reliability of the food price index, thus it coincides with the estimated average reliability of _PN_ ̄<sup>evaluatedattheapproximatemean</sup> value of _S_<sup>12</sup> ̄<sup>thelatterbewrittenas</sup><sup>_μS_12</sup> ̄<sup>Toproduceatime-varyingproxy</sup> _N_<sup>,</sup> _N_<sup>.</sup> for _R_<sup> ̃2</sup> that is reflective of reliability when _SN_<sup>12</sup> ̄<sup>isrespectivelyhighorlow,we</sup> need to construct reasonable lower and upper bounds for _R_<sup> ̃2</sup> and a transition path between them across the _S_ plane. The low point _Rlow_<sup>2issetbyfirstcross-</sup> validating a third-order Taylor expansion of a trend component estimated with a small Ridge penalty against the full price index, allowing for fixed seasonal variation captures with dummies.

If the price index evolves following a basic trend with seasonal component, then its _R_ ̃<sup>2</sup> extrapolationis high. If thecanpricebe indexdone reliablyevolves evenwithoutwithouta seasonaldata andtrendthestructure,low pointthenfor the low point of _R_<sup> ̃2</sup> is essentially 0 so that no reliable estimate can be produced without data.

The functional form mapping the data availability to the associated _R_<sup> ̃2</sup> value is constructed by upsampling the vectors _R_<sup>2</sup> := ( _Rlow_<sup>2</sup><sup>_, ..., R_2</sup><sup>_, ...,_1)and</sup><sup>_S_:=</sup> (0 _, ..., μSN_<sup>12</sup> ̄<sup>_, ...,_1)toagridof100elementsandusingasplineinterpolationon</sup> log scale to interpolate the missing entries ( _..._ ), and then constructing a map _h_ : _R_<sup>2</sup> _→S_ using a local exponential smoother. The trust scores _T_<sup> ̃</sup> are generated at the one-digit level using the function:

> 5Since fully observing prices at one market has a higher impact on the ability to model realistic price trends than observing a equal total amount of data distributed across all markets, the shares are averaged using the Root-Mean-Squared to give more weight to the presence of unmodeled data series. This is omitted from notation to avoid further cluttering.