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:
- How is the naive forecasting method generally applied in time series data?
- What other forecasting accuracy measures can be computed besides MAE?
- How does MAE compare with measures like RMSE or MAPE for assessing accuracy?
- How can this forecasting method be improved for better accuracy?
- 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
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