Your assignment will be assigned a grade as follows:
- (Weight: 50%) Interpretation and Understanding of Econometric Tools Part of your grade will be based on whether you correctly use and interpret the tools of Time Series Econometrics that we learned. This means that you use the appropriate models for the given task, that you interpret results correctly, using the proper critical values for inference as well as interpreting null hypotheses correctly. This also depends on whether you explain why you use difffferent tools, and the problems these are selected to deal with.
- (Weight: 25%) Programming and R Code Part of your grade will depend on correctly using R to implement the tasks you are assigned and whether your R code correctly implements the work that you describe in the write-up of your assignmnet. Marks will be given for R code that is correct,and with comments to clarify you understand the tools you are using.
- (Weight: 25%) Economic Analysis and Discussion This part of your grade will depend on the economic analysis of your results and the depth of your discussion. Marks will be given for the economic content of your analysis and your interpretation of the economic reasoning of your results.
Assignment Outputs to Submit
- A PDF write-up of the results of your analysis, including graphs and tables.
See the outline of the analysis tasks to complete below for details on exactly what tables & graphs you need to complete. Include your R code at the end of the document. You can write this document in Word or you can use LATEX. There are additional videos on the assignment page about exporting tables and using LATEX.
Word Count: Maximum 2,500 words, excluding R code, tables and fifigures.
1 Analysis Tasks to Complete
1.1 Descriptive Analysis – Week 1 Exercises
Before running regressions, we will fifirst examine our data and use some simple tools to look at the time series.
1.1.1 Data Description
First, write a very brief (just a few sentences) description of the outcome variable you are interested in analysing. Next write a brief description of your primary explanatory variable, and the rough research question.
1.1.2 Time Series Plots
Next, plot your Yt time series., and give a few sentences of description. Do there appear to be signifificant outliers in this time series? Either exclude them if they are near the beginning or end of your time series, and if not, make note of this outlier and make sure to take it into account in your analysis.
1.2 Autoregression Analysis of a Time Series
1.2.1 Estimate an Autoregression Model
- First, run an AR(1) regression of your outcome variable. Then use the Bayes Information Criterion to select the appropriate lag length for your model,setting a maximum of four lags. Write down the four values of the BIC(p) you calculate, and explain which model length you end up selecting. Now,estimate this model. (See Week 1 & 2 Exercises)
- Next, test for violations of our key Time Series Assumptions: (See Week 3 Exercises)
– Use the appropriate model to test for a unit root process. Does economic theory suggest that your time series should exhibit a roughly linear time trend? Justify your answer brieflfly, and explain what this means for the model you use for this test and the hypotheses you test. Write a brief explanation of the result, and what this means for your time series. If you conclude your time series has a unit root, perform the necessary transformation, use the BIC again on your transformed time series and add this revised AR(p) model to your table.
– Use the appropriate test for a break in your time series where you don’t know the exact date of the break. Write a brief explanation of the result, and what this means for your time series. If you conclude your time series has a break and you identify the likely break date, make the necessary adjustment to your model and add this model to your table.
- Report estimated coeffiffifficients from both the AR(1) and AR(p) models in a table, along with the coeffiffifficients from your modifified model in the case that your time series either has a break or a unit root.
- Is the coeffiffifficient on Yt−1 in your AR(1) signifificant? Write a brief explanation of whether it is statistically signifificant, and an additional brief interpretation of the economics of this result. How about the coeffiffifficient Yt−1 in your AR(p) model – is it similar? Discuss the implication of these results, and the persistence of shocks. If you correct for a trend or a break, discuss how your analysis of the non-transformed time series might be misleading.
1.2.2 Estimate an Autoregressive Distributed Lag Model – Week 2 Exercises
- Now we are going to introduce a second variable Xt . First, estimate an ADL(1,1) model. If you found your Yt had a unit root above, then continue
1.2.3 Check Out-Of-Sample Forecast Performance – Week 4 Exercises
- Using the Pseudo Out-Of-Sample forecasting method, with your ADL(1,1) model and with the fifinal 25% of your sample as your excluded sample, and compare the within-sample SER (from the regression including none of your excluded observations) and the out-of sample fifit using your estimate of the Root Mean Squared Forecast Error.
- Compare the size of the SER to the size of your RMSFE. Which is larger?
Does this suggest your forecast errors are larger, smaller, or the same as your within-sample errors? Is your model capable of predicting out-of-sample?
1.3 Dynamic Causal Effffects – Week 5 Exercises
- Use GLS to estimate the dynamic multipliers for a distributed lag model regressing Yt on Xt and lags. For simplicity, use a Distributed Lag model where r = 3, which means you will include Xt as well as the lag Xt−1 and Xt−2, and an AR(1) error term, meaning that you model the error term just as in lecture using φ1. Now, estimate these dynamic multipliers using the Cohcrane-Orcutt method (not the Iterated Cochrane-Orcutt!).
- Discuss the results above, beginning with a short discussion of whether it is reasonable to assume strict exogeneity or exogeneity and give an example of something that would mean we can only assume exogeneity but not strict exogeneity. For example, in lecture we considered crop prices as our outcome Yt and climate shocks as our Xt . If people potentially stockpile crops today based on anticipated climate shocks tomorrow then this would violate strict exogeneity. Give an example of the issues with assuming strict exogeneity in your setting. The important thing here is showing you understand the conditions, so you can use a slightly unrealistic example here, as long as you show you understand how to think of the exogeneity conditions in your context. Next, discuss the implications of the dynamic multipliers you estimate. Which dynamic multiplier of Xt is strongest? Does the effffect increase,decrease, or stay the same over time?
1.4 Multiperiod Forecasts – Week 7 Exercises
Using both methods that we have learned for multiperiod forecasting, forecast the next ten periods of your time series past the end of your data using your ADL(p,p) model above. What is the forecasted value in ten periods time? How do the two forecasts diffffer?
1.5 Cointegration – Week 8 Exercises
- Use the two-stage test for cointegration to test if your Yt and Xt are cointegrated. You can use the same Xt as above, or you can choose a difffferent Xt if you think they are more likely to be cointegrated and, therefore, a more interesting exercise. (Note: even if it isn’t sensible to test for cointegration here, conduct the test anyways, and interpret the result accordingly, and explain why it isn’t appropriate to test for cointegration of these time series)
- Discuss the results from the above analysis. First of all, discuss whether it makes sense in this case to test for cointegration.
1.6 Volatility Clustering Analysis – Week 9 Exercises
- Next, analyse whether the volatility of your time series is clustered, that is,whether your time series exhibits greater variance at some times than others.
Estimate an ARMA(1,1)-GARCH(1,1) model on your data.
- Report estimated coeffiffifficients from this model in a table. Are any of the coeffiffifficients signifificant? What does this mean about whether your time series display conditional heteroskedasticity? Give a very brief interpretation of the economics of this result: will a period of high volatility tend to be long-lived,or will it be brief?
Finally, write a brief paragraph summarizing your fifindings. Again, this should just be a brief summary of any of the results that give additional economic insights relating to your outcome variable Yt or the relationship between Yt and Xt .
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