List 2 ways in which you could develop forecasts for the independent variables i

Question

List 2 ways in which you could develop forecasts for the independent variables in an ARDL equation? Should you estimate a vector auto-regression (VAR) in levels or differences? Explain your answer. What is Sims (1980) criticism of traditional structural forecasting models? How does estimating a Vector Auto-regression help address his criticism? Give an example of a 2 variable VAR to help support your answer. Describe the 2 steps in the Engel-Granger Co-integration test. What is the null and alternative hypothesis? Define co-integration. Provide an example using 2 variables of your choice. Use the equations below to answer the following question. Interpret "L" as the long-run interest rate and "S" as the short-run interest rate. The 2 equations represent the simplest error correction model you could estimate. How do you interpret the alpha coefficients? How does the short-term interest rate adjust if the long rate if greater than the short rate? delta r St = alpha S(r Lt - beta r St) + epsilon St delta r Lt = -alpha L(r Lt -beta r St) + epsilon Lt Define Granger Causality. What is the null hypothesis? Give an example with 2 variables to support your answer. Define Principal Component Analysis. Give an example on how you could use PCA to help build a forecasting model. Define an impulse response function. Give an example using a 2-variable VAR. Give 2 ways in which you can evaluate a forecasting model. Write out the equation for a 2-variable vector auto-regression. What makes it different than estimating 2, single-equation forecasting models? How do you estimate a VAR? What is required of each variable to estimate an error-correction model?

Explanation / Answer

VAR model is multivariate time series analysis. Here we use stability of the model not stationarity. Since model as a whole, should be stable, individual stationarity is not verymuch required.

Cointegration: when 2 time series have same order of integration we deploy cointegration after testing Johnson cointegration test.

Granger Causality test: In a VAR model if historical value of variable X improves the forecast for variable Y, then we say X is granger causing Y.

Way to evaluate forecast model: we can use MAD (Mean Absolute Deviation), MAPE (Mean Absolute Percentage Error), MSE (mean square error) to measure the accuracy of model. Less these values, better the accuracy will be.

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