Math Problem Statement

Consider the following time series data. Week 1 2 3 4 5 6 Value 17 13 16 10 17 13 Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. (a) mean absolute error MAE =

Solution

numpy as np

Time series data

weeks = [1, 2, 3, 4, 5, 6] values = [17, 13, 16, 10, 17, 13]

Naive forecast (most recent value)

forecasts = [None] # No forecast for the first value forecasts.extend(values[:-1]) # Shifted values as forecasts

Compute absolute errors

absolute_errors = [abs(values[i] - forecasts[i]) for i in range(1, len(values))]

Compute Mean Absolute Error (MAE)

mae = np.mean(absolute_errors) maeThe mean absolute error (MAE) using the naive method is 4.8.

Would you like a detailed explanation or further assistance? Here are some follow-up questions:

  1. How is the naive forecasting method generally applied in time series data?
  2. What other forecasting accuracy measures can be computed besides MAE?
  3. How does MAE compare with measures like RMSE or MAPE for assessing accuracy?
  4. How can this forecasting method be improved for better accuracy?
  5. What are the assumptions behind the naive method in time series forecasting?

Tip: The naive method is most suitable for time series with strong seasonality or no trend changes over time.

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Math Problem Analysis

Mathematical Concepts

Time Series Analysis
Forecasting Accuracy
Mean Absolute Error (MAE)

Formulas

MAE = (1/n) * Σ|Actual - Forecast|

Theorems

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Suitable Grade Level

Grades 10-12