Minimum number of data points required/resource runtime to get forecast cost of resources

To generate a forecast in AWS Cost Explorer, you need to provide sufficient historical data. For a new service or resource, you need at least 24 hours of data before a forecast can be generated. However, the effectiveness of the forecast improves with more historical data, with at least two weeks' worth of data being ideal for more accurate predictions.

For Cost Explorer specifically, resource-level data (like specific instance IDs) is only available for the last 14 days by default. If you're trying to get forecasts for specific resources, you'll need to ensure you have resource-level data enabled in your Billing & Cost Management Preferences.

When using the GetCostForecast API with MONTHLY granularity, you should be aware that the forecast quality depends on having adequate historical data. Since you mentioned your resources have only been running for 4 days, this may not be sufficient for generating a reliable monthly forecast.

For the best results, you should wait until you have at least two weeks of historical data before expecting accurate forecasts. In some AWS services like Amazon Connect, at least one data point from the previous 4 weeks is required to generate a forecast, which suggests that Cost Explorer may have similar minimum requirements.
Sources
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GetCostForecast - AWS Billing and Cost Management