Reference no: EM132630213
Task a. [Pre-analysis] Provide the data visualisations (time series plot, box plot, histogram, and ACF plot) and the descriptive statistics of log (Yt) and Δlog (Yt). What can you spot from various plots? What is the meaning of the descriptive statistics?
Task b. [Unit root/stationatity tests' Perform ADF test, PP test, and KP55 test on log (Yt) and Δlog (Yt). You can use AIC to select the best lag length for the ADF test and use "short" lag length for the PP and KPSS test
Task c. [Model selection] Select the best ARMA(p, q) model for Δlog (Yt) by AlC. Please set the maximum orders as 5, i.e. p, q ≤ 5.
Task d. [Model diaffnustics] Perform model diagnostics for the residuals from the best selected model. To be specific, carry out the time series plot, ACF plot, and Ljung-Box test on the residuals. For the Ljung-Box test, please set the lag lengths as 20, 30, and 50. Comment on the results of the model diagnostics.
Task e. [Forecasting] Choose the best model based on the data in the in-sample period and make forecasting for the out-of-sample period. Plot the predicted values from the best model versus the true values. Calculate the forecasting performance (MSE, MAE, MAPE, and %correct sign) of the best model.
Task f. [Rolling-window Forecasting] The idea of rolling-window forecasting is to iteratively make one-step-ahead prediction using the most recent w data observations, which is referred to as the window of data. In practice, we have one new monthly observation coming in each month. Thus, it is potentially helpful for forecasting if can we include the newest observation (whenever it becomes available) and exclude the oldest observation (since it become less relevant), For this rolling-window for task„ you need to update the best model (and its parameters) in each window and then only make one-step-ahead prediction. For each time-point t in the out-of-sample period, you need to use the most recent w observations (i.e. from t - w to - 1) to make prediction for the value at time-point t in this task, please set the window length w = 503. To be fully clear:
• use data from Feb 1971 to Dec 2012 to select the best model, estimated the model, and make the prediction for Jan 2013 on
• use data from Mar 1971 to Jan 2013 to select the best model, estimated the model, and make the prediction for Feb 2013 only
• use data from Mar l478 to Jan 2020 to select the best model, estimated the model, and make the prediction for Feb 2020 only.