What methods are available for forecasting with a sample of the data

Question

In predictive analytics, specifically forecasting, what methods are available for getting the same predictive accuracy with $n$ (a sample of the data) which would be achievable with $N$ (all of the data)?

Question Motivation

Personally I think that sampling $N$ and getting the same predictive accuracy is a very interesting problem on its own. Sampling from populations has been central to statistics for over 100 years.

Alternatively, some may be concerned with possible business implications.

Companies spend money on cluster computing. The justification for this roughly follows the logic below:

1. Better predictions drive more value

2. Predictions with $N$ will always be better than $n$

3. Predictions with $N$ requires cluster computing

4. Therefore, cluster computing is purchased to drive more value

If it is provable that predictions with $n$ have accuracy greater than or equal to $N$ (premise 2 is false) and $n$ is small enough to run without clusters then there may be a potential for cost savings.

Uniqueness of This Question

Many of the related questions I have read on this topic mostly deal with classification. Few posts address continuous outcomes. Fewer, if any, address forecasting. In forecast settings $N$ is large due to a larger number of times series and high granularity. For example in retail you may get $N$ from item level forecasting for many outlets at 30 minute intervals. If one wanted to get better item level forecasts with smaller data what options exist? Some potential questions in this setting are:

1. Can each individual time series be sampled without loss of information? (Decrease the length of a time series)

2. Can related time series be clustered by their features? (Decrease the number of time series)

3. How would one ensure that relevant predictors that impact the time series don't get under sampled? (Forecasting with external predictor issues)

Related work/posts

Much of the work I am aware of has been in classification settings, not forecasting settings

Fast Generalized Linear Models by Database Sampling and One-Step Polishing - Fantastic paper. Sparked my interest in the topic.

Progressive Sampling

Does increase in training set size help in increasing the accuracy perpetually or is there a saturation point?

Answer 1

"Can each individual time series be sampled without loss of information? (Decrease the length of a time series)"

If the model changes over time OR if the paramaters of the best model change over time , it may be more prudent to use less data based upon a homogeneous past thus decreasing the length.

A feature of software that I have written actually tests for these conditions and I suggest this approach. It uses an extension of the CHOW test to summarily evaluate break points in the model parameters.