I am applying an unsupervised outlier detection model called isolation-Forest to detect outliers using unlabelled time-series data. I do not have labels that distinguish a true outlier from a false outlier, Therefore I cannot use regular evaluation metrics such as accuracy or F1-score.
I will give a brief overview of the data that can help understand what is a true outlier and a false outlier. This data contains the temperature values of a city from Dec 1990 to Aug 1990. True outliers are the extreme temperature values (>95 F) during June, July, and August. False outliers are the extreme values from December to March.
Coming back to the model, it basically identifies all outliers from Dec to Aug. Using the above definition now I have the labels of true and false outliers after running the model. What metric would be ideal to assess the model performance here?