Solution

Time series decomposition involves breaking down a time series into three main components: trend, seasonality, and residuals (also called irregular components). The trend represents the long-term movement of the data, the seasonality captures periodic fluctuations, and the residuals account for random noise or irregular fluctuations that cannot be explained by trend or seasonality. Decomposition is crucial for understanding the underlying structure of the data, and these components can then be modeled separately to improve forecasting accuracy. Time series decomposition is essential for isolating the patterns within data, especially for seasonal data, to apply appropriate forecasting techniques like ARIMA or exponential smoothing. The other options are incorrect because: • Option 1 (ARIMA modeling) is not a decomposition method. ARIMA is a time series forecasting model that can handle trends and seasonality but doesn't break the series into components. • Option 2 (Exponential smoothing) is a forecasting method, not a decomposition technique. • Option 4 (Autoregressive process) refers to a type of model used in time series analysis to capture dependencies in the data, not decomposition. • Option 5 (Fourier transformation) is a technique used for frequency analysis, not decomposition of time series data into trend, seasonality, and residuals.