Exponential smoothing method is the forecasting method that takes a fraction of forecast error into account for the next period forecast.

Exponential smoothing is a widely used time series forecasting method that calculates the weighted average of past observations to predict future values. It is based on the assumption that recent data points are more relevant than older ones, and it assigns exponentially decreasing weights to past observations.

Here's how the exponential smoothing method works:

1. Initialization: The method starts with an initial forecast for the first period, usually based on historical data or expert judgment.

2. Calculation: The forecast for each subsequent period is calculated using the following formula:
Forecast = α * Actual + (1 - α) * Previous Forecast
where α is the smoothing parameter (also known as the smoothing constant) that determines the weight given to the most recent observation. It ranges between 0 and 1, with higher values giving more weight to recent data.

3. Updating: After calculating the forecast for a period, the actual value for that period becomes available. The forecast error, which is the difference between the actual value and the forecast, is then calculated.

4. Adjustment: The forecast for the next period is adjusted by taking a fraction of the forecast error into account. This is done by multiplying the forecast error by a factor (1 - α) and adding it to the previous forecast.

The key advantage of exponential smoothing is its simplicity and flexibility. It allows for the incorporation of new data points as they become available, providing updated forecasts that adapt to changing patterns in the data. The smoothing parameter α can be adjusted to give more or less weight to recent observations, depending on the level of noise or volatility in the data.

By considering a fraction of the forecast error for the next period forecast, the exponential smoothing method can capture changes in trend or seasonality more effectively than other forecasting methods such as simple average or moving average. This makes it a popular choice for short-term forecasting applications where recent data is more relevant.