Solution

Holt-Winters Exponential Smoothing is a forecasting method that is specifically designed for time series data that exhibits both trend and seasonality. It extends the simple exponential smoothing method by incorporating components for trend and seasonality. The model uses weighted averages of past data points and adjusts for both the long-term trend and seasonal variations. It is particularly useful in situations where data has both trend (a long-term increase or decrease) and seasonality (periodic fluctuations). This method is ideal for situations where both of these components need to be accounted for in forecasting future values. Why Other Options Are Incorrect: • A: Simple moving averages smooth out short-term fluctuations but do not account for trend or seasonality, making it unsuitable for data with these characteristics. • B: Exponential smoothing (without trend or seasonality components) works best for data with no clear trend or seasonality, which makes it less appropriate for data exhibiting both. • C: ARIMA (AutoRegressive Integrated Moving Average) can handle trends but does not explicitly model seasonality unless specifically adapted (e.g., SARIMA), so it is less ideal than Holt-Winters for seasonal data. • E: Linear regression is used for modeling relationships between variables and can model a trend, but it does not account for seasonality or provide a smoothing mechanism, making it less appropriate for time series forecasting.