For this project, you will work any with dataset you like, however, it must contain at least 2 predictors and two response variables (y1t and y2t) which you will aim to predict. The response variables need to exhibit some shared dynamics since we will also consider a VAR model fit. Your task will be to find the best fit model by following the steps outlined below.
1. Provide a descriptive analysis of your variables. This should include histograms and fitted distributions, correlation plot, boxplots, scatterplots, and statistical summaries (e.g., the five-number summary). All figures must include comments.
2. Show the tsdisplay plot for each variable and comment on the stationarity, ACF, and PACF results.
3. Fit two AR(p) models to each variable, and evaluate the model performance as follows: • Plot and comment on the ACF and PACF of the residuals.
Evaluate the training/testing performance by splitting the data into 2/3 training and 1/3 testing, and computing the MSE for each subset. Comment on which model is better. Make sure to also look at AIC and/or BIC.
Compute and plot a 10-step-ahead forecast for each model.
4. For this question, you need to identify an appropriate preditor(s) for your two series. Fit two ARDL(p,q) models to each variable, and evaluate the model performance as follows:
Plot and comment on the ACF and PACF of the residuals.
• Evaluate the training/testing performance by splitting the data into 2/3 training and 1/3 testing, and computing the MSE for each subset. Comment on which model is better. Make sure to also look at AIC and/or BIC.
Compute and plot a 10-step-ahead forecast for each model.
5. Fit a VAR(p) model to your data (y1t and y2t), and evaluate the model performance as follows:
Plot the CCF and comment on the results.
• Perform a Granger-Causality test, and discuss whether it is possible to identify any causality between the variables.
Plot the IRFs and comment on the plots.
Show the plot that includes the data, fitted values, ACF, and PACF all in one figure. Comment on the results.
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Evaluate the training/testing performance by splitting the data into 2/3 training and 1/3 testing, and computing the MSE for each subset. Comment on which model is better (e.g., the one for y1t or for y2t). Make sure to also look at AIC and/or BIC.
• Compute and plot an n-step-ahead forecast for each model. You can choose the number of steps-ahead.
Plot and discuss the FEVD plot.
6. Provide a short (1 paragraph) summary of your overall conclusions/findings, and discuss which model is your preferred one.
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