Can historical averages be used for both short-term and long-term forecasting

Short-Term Forecasting

Historical averages are particularly useful for short-term forecasting, which involves predicting future values over a relatively short period (e.g., next few days or weeks). In this context, historical averages can provide a robust and simple method for smoothing out noise and identifying trends. They are effective for capturing short-term patterns and can be used to make predictions based on recent data points.

Long-Term Forecasting

Historical averages can also be used for long-term forecasting, but their effectiveness is generally lower compared to more complex models. Long-term forecasting involves predicting future values over a longer period (e.g., months or years), where the underlying patterns and trends may change significantly. In such cases, historical averages may not capture these changes effectively, leading to less accurate predictions.

Limitations of Historical Averages for Long-Term Forecasting

1. Assumes Stationarity: Historical averages assume that the time series is stationary, meaning its statistical properties do not change over time. If the series is non-stationary, historical averages may not be effective for long-term forecasting.

2. Does Not Capture Trends: Historical averages do not capture long-term trends or seasonality in the data, which can lead to poor performance if these patterns are significant.

3. May Not Be Robust to Changes: Historical averages may not be robust to changes in the underlying patterns or external factors that affect the time series.

Conclusion

Historical averages can be used for both short-term and long-term forecasting, but their effectiveness varies depending on the context and data. For short-term forecasting, historical averages are a simple and effective method. However, for long-term forecasting, more complex models like ARIMA, exponential smoothing, and machine learning methods are generally more effective in capturing long-term trends and patterns.

Example Code for Historical Averages

Here is an example of how you can use historical averages for short-term and long-term forecasting in Python using the Darts library:

python
import darts
from darts import TimeSeries

# Load and preprocess data
df = pd.read_csv('your_data.csv')
train_series = TimeSeries.from_dataframe(df, time_col='timestamp', value_cols='target')
test_series = train_series.split_before(0.8)

# Calculate historical mean
historical_mean = train_series.mean()

# Evaluate the historical mean baseline for short-term forecasting
short_term_mape = mape(historical_mean, test_series)
print("Short-Term Historical Mean MAPE:", short_term_mape)

# Evaluate the historical mean baseline for long-term forecasting
long_term_mape = mape(historical_mean, test_series)
print("Long-Term Historical Mean MAPE:", long_term_mape)

This code calculates the historical mean for both short-term and long-term forecasting and evaluates their performance using the Mean Absolute Percentage Error (MAPE) metric.