run timeseries models and compare in R

Make an ARMA(4,3)-EGARCH(1,1) model considering forward selection procedure.

Select the model using Occam’s razor approach, looking for the simplest possible model (i.e. the smallest number of parameters) that has significant parameters but that also provides a very good fit to the data. The model with superior AIC and BIC goodness-of-fit is preferred

For the GBM model, after discretizing at monthly frequency, we use three methods to estimate the parameters from historical data, the maximum likelihood estimation (MLE), method of moments (MM) and generalised method of moments (GMM).

There could be other ARMA-GARCH type models that may provide a better fit than the model we have identified.

Forecasting : house price prediction must have good prediction power atleast short and medium horizon. Report some measure of accuracy RMSE, MAE nd the Diebold-Mariano test (for comparing GBM model under different estimation methods with the selected ARMA-EGARCH model, based on the out-of-sample data for monthly Nationwide index.

The test statistic is compared with critical values of standard normal distribution N(0, 1). If we fail to reject the null, i.e. the p-value is between 0.05 and 0.95 at 90% confidence level, then the two models compared produced similar forecasts. Otherwise, the model in the direction of the statistic (1 if negative, 2 if positive) will give better forecasts. For the short forecasting horizon of two years ARMA(4,3)-EGARCH(1,1) model produces similar forecasts with the GBM specification, under any of the three parameter estimation method.

Do the analysis for a five year out-of-sample period, with both monthly and quarterly data, the latter going back to 1952, the same analysis for the forecasting error for the out-of-sample Nationwide monthly time series with five years out of sample.

Produce appropriate graphs showing model forecasts.

Machine Learning (ML)

Projektin tunnus: #29780012

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