Temperature Anomaly Detector

Time Series Sliding Window Arrays

Problem Description:

You are provided with an array of floating-point numbers representing daily temperature readings for a period of time (e.g., 30 days). Your task is to write a function that performs the following:

  1. Compute the moving average of the temperature readings using a given window size (w). The moving average for a window is the mean of all temperature values within that window.

  2. Identify anomalous segments where the absolute difference between the actual temperature and the corresponding moving average exceeds a given threshold (t). An anomalous segment is defined as one or more consecutive days where this condition holds true.

  3. Return a list of tuples (or pairs) where each tuple contains the starting index and ending index of an anomalous segment in the original array. If there are no anomalous segments, return an empty list.

Function Signature (in your language of choice):

def find_anomalies(temperatures: List[float], w: int, t: float) -> List[Tuple[int, int]]:

Example:

Given the inputs:

  • temperatures = [15.0, 16.2, 15.8, 20.5, 21.0, 20.8, 15.5, 16.0, 15.7, 15.9, ...]
  • w = 3
  • t = 2.0

Your function should compute the moving average for each window and then return the list of anomalous segments that satisfy the condition described above.

Notes:

  • Consider edge cases such as when the window size is larger than the number of temperature readings or when no anomalies are detected.
  • Efficiency is key for larger input arrays.
  • Write clean, modular code that handles potential errors gracefully.

Good luck!