In forecasting, which method is most appropriate when the time series data exhibits both trend and seasonality?

When time series data exhibits both trend and seasonality , a simple exponential smoothing model would not be sufficient, as it only considers smoothing over time without accounting for the trend. The most appropriate method in this case would be Exponential Smoothing with Trend Adjustment , often referred to as Holt’s Linear Trend Model. This method accounts for both the trend and seasonality by smoothing the data while adjusting for the increasing or decreasing trend. ARIMA could also be useful but requires stationarity, which might not be the case with seasonal data unless seasonal ARIMA is used. Simple moving average and simple exponential smoothing do not consider trend or seasonality, so they are less appropriate in this scenario. Why other options are wrong: a) Simple Moving Average : This method averages over a specified period but doesn't account for trend or seasonality, making it less suitable for data exhibiting these components. b) ARIMA : While ARIMA models are powerful, they require data to be stationary. Seasonal ARIMA (SARIMA) can handle seasonality, but ARIMA itself doesn’t address both trend and seasonality. d) Simple Exponential Smoothing : This method does not handle trend or seasonality; it’s best used for data without either. e) Linear Regression : While linear regression models trends, it doesn't handle seasonal fluctuations, making it inappropriate for data with both trend and seasonality.