Consider the monthly simple returns of GE stock from January 1926 to December 2008. Use the last three years of data for forecasting evaluation.

(a) Using lagged returns \(r_{t-1}, r_{t-2}, r_{t-3}\) as input, build a 3-2-1 feed-forward network to forecast 1 -step-ahead returns. Calculate the mean squared error of forecasts.

(b) Again, use lagged returns \(r_{t-1}, r_{t-2}, r_{t-3}\) and their signs (directions) to build a 6-5-1 feed-forward network to forecast the 1-step ahead direction of GE stock price movement with 1 denoting upward movement. Calculate the mean squared error of forecasts.

Let \(\mathrm{rtn}\) denote a time series in \(\mathrm{R}\) or \(\mathrm{S}\)-Plus. To create a direction variable for \(r t n\), use the command

\[ \text { drtn }=\text { ifelse }(r t n>0,1,0) \]