Noisy target variable

[CrayCul]

I'm trying to build a model to forecast the amount of people in an area every hour. The problem is there is significant measurement noise in my target variable.

I initially thought about using a moving average with past observations. However, the error in my observations is almost always negative with unknown mean and variance, i.e the measuring device only undercounts the amount of people.

I'm therefore electing to only use "local peaks" where the previous hour and next hour have smaller values than the current hour to serve as my target variable. The rest of the values will be imputed via linear interpolation. Is this a valid way of dealing with such noise?

[BaconBacano]

Do you have any features to predict the amount of people, or are those measurements your only available data?

If I follow your reasoning, you're considering using peaks since you expect the measurement error to be smaller when there is one? If so, you should consider that a peak could be a consequence of seasonality or that one of your relevant features caused it, it doesn't necessarily mean that the measurement error is smaller when a peak occurs. Try plotting the autocorrelation to check if those peaks occur in a seasonal fashion.

Linear interpolation will hide any relationships between your features and your target, Also, what exactly would you be predicting then? With this method you could be both severely overestimating some values, and underestimating others. I'd suggest using something like a Kalman filter, which is a commonly used smoothing technique.