neural network. Average approach In this approach, the predictions of all future values are equal to the mean of the past data. This approach can be used with any sort of data where past data is available. In time series notation: where is the past data. Although the time series notation has been used here, the average approach can also be used for cross-sectional data (when we are predicting unobserved values; values that are not included in the data set). Then, the prediction for unobserved values is the average of the observed values. Naïve approach Naïve forecasts are the most cost-effective forecasting model, and provide a benchmark against which more sophisticated models can be compared. This forecasting method is only suitable for time series data. Using the naïve approach, forecasts are produced that are equal to the last observed value. This method works quite well for economic and financial time series, which often have patterns that are difficult to reliably and accurately predict. If the time series is believed to have seasonality, the seasonal naïve approach may be more appropriate where the forecasts are equal to the value from last season. In time series notation: Drift method A variation on the naïve method is to allow the forecasts to increase or decrease over time, where the amount of change over time (called the drift) is set to be the average change seen in the historical data. So the forecast for time is given by This is equivalent to drawing a line between the first and last observation, and extrapolating it into the future. Seasonal naïve approach The seasonal naïve method accounts for seasonality by setting each prediction to be equal to the last observed value of the same season. For example, the prediction value for all subsequent months of April will be equal to the previous value observed for April. The forecast for time is where =seasonal period and is the smallest integer greater than . The seasonal naïve method is particularly useful for data that has a very high level of seasonality. Time series methods Time series methods use historical data as the basis of estimating future outcomes. They are based on the assumption that past demand history is a good indicator of future demand. Moving average Weighted moving average Exponential smoothing Autoregressive moving average (ARMA) (forecasts depend on past values of the variable being forecast and on past