Learning Goal: I’m working on a r multi-part question and need support to help me learn.

• In a regression model, if the errors are not normally distributed, you try to fix it. If you fail to do so, how can you argue in favor of ignoring non-normality?
• Name two ways of dealing with outliers in regression-based models.
• How do you deal fix a regression with autocorrelated and heteroskedastic residuals?
• If two series are non-stationary, can we regress them on each other? Explain why or why not.
• Explain what co-integration is, and name two ways of testing for it.
• Describe the methodology of an Engle Granger test for cointegration and why it is called a two-step test.
• For series to be modeled using a Vector Autoregressive Model (VAR), they must be stationary at level [I(0)]. When can the series to be modeled using Vector Error Correction Model (VECM)?
• How do you determine the order of a VAR model? And a VECM?
• How do you determine whether a VAR or VECM model is stable?
• There are two types of coefficients in a VECM model of order greater than zero (and in any error correction model in general). What are they, and to which coefficients does the VECM order refer?
• Explain the use of impulse response functions and variance decomposition while modeling VAR and VECM.
• When can two series be modeled using an ARDL model?
• Describe how we check for co-integration in an ARDL model?
• In an error correction model, what is the role of the error correction term and what should be its characteristics for it to be valid?
• In a model that seeks to capture both the long-term relationship and short-term dynamics between the different variables, does an invalid error correction term void the whole model or only a part of it? Explain.
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• John is tasked with writing a report on the state of the economy and where it is heading. John thinks that the current state of the stock market is useful in predicting the future state of the economy, but his opinion is not enough, and he needs to determine it empirically. He comes to you and asks to help him in empirically determining whether a relationship exists between the stock market and the state of the economy, and, if it does, what is the empirical directionality of this relationship, or, in layman’s terms, whether the stock market is a leading indicator or lagging indicator. Your mission, should you choose to accept it, is to create the best model capturing the relationship between GDP and the Wilkshire 5000 as a market proxy, and determine not only whether such relationship exists, but also the empirical directionality of such relationship should it exist, to see whether the stock market is any good at predicting whether we are heading towards a recession. To that end, John provides you with the Wilkshire 5000 daily data since 1989, and nominal GDP seasonally adjusted quarterly data between since 1947. You refuse to accept it, since you only trust the data you gather yourself. So John gives you the following instructions: 1- Get the data from Fred and Yahoo Finance using R. Group the data in a dataframe of quarterly observations, and programmatically save the dataframe to an excel file so you can import it into E-Views where you will do the modelling. You can use the raw data or a transformation of it (log-level, difference / returns / growth, log difference / log-returns / log-growth, you can add dummies, do whatever you deem fit) to write an empirical report. (15 pts) 2- Answers to the following questions: Are the series stationary, and what is the order of integration of each series (I(0), I(1), or I(2))? Do we need to test them for cointegration and why? Which is best for modeling them: Simple Regression, VAR at levels, VAR differences, VECM, or ARDL, and why? (5 pts). 3- Assuming you decide that error correction modeling is the way to go, you would run a VECM and an ARDL and choose between them. The criteria you must consider for choosing the best model are the breadth of time coverage, model and coefficient stability, “cleanliness” of the residuals (uncorrelated, normal, and homoscedastic), and whether the model is well-specified (RAMSEY RESET test) and captures long- and short-run dynamics. (30 points). 4- Analyze the two error-correction models and use the know-how you acquired in this class to identify whether there is a relationship between the market and the economy, identify its characteristics and study its directionality. (20 points) 5- Your submission consists of (1) one pdf file containing the modeling and analysis with the necessary E-Views output, and (2) an R file containing the code used to compile and pre-process the data.