数学代写｜Practice Questions for Part 1

这是一篇英国的计量经济**数学代写**

**Question 1**A friend of yours (who has not taken BEEM012!) wants to check that their time series data doesn’t violate the stationarity assumption.

They compute the variance at difffferent time periods and are confifident that var(*Y**t*) = var(*Y**t*+*s*) for any *t *and *s*, and based on this information alone decide that their time series is stationary.

Explain why or why not.

**Question 2**For OLS regressions, we can use the Central Limit Theorem to construct our confifidence interval. Why can’t we always do this for forecast intervals with Time Series? Refer to the composition of forecasting errors in your explanation.

**Question 3**Explain how you would use a Granger causality test to test whether the two lags of*X**t*are jointly statistically signifificant in the following

ADL(2,2) model:

*Y**t *= *β*0 + *β*1*Y**t**−*1 + *β*2*Y**t**−*2 + *δ*1*X**t**−*1 + *δ*2*X**t**−*2 + *u**t *

Make sure to explain your null hypothesis in terms of these coeffiffifficients. Explain what regression model or models you estimate, and how you construct your test statistic.

**Question 4**Write down the formula for the Mean Squared Forecast Error for an AR(2) model. Refer to the terms of this model to explain in words the costs and benefifits from including additional lags in an autoregression model.

Explain which term captures the costs of including more lags, and which term captures the benefifits of additional lagged regressors.

*p **AIC*(*p*)

1 1.432

2 1.426

3 1.391

4 1.445

5 1.552

Write down the autoregression model you would choose as a result.

**Question 5**If you run the following model, what test can you perform?

∆*Y**t *= *β*0 + *δY**t**−*1 *− **β*2∆*Y**t**−*1 + *u**t *

*δ*equal to, in terms of the parameters of an AR(2)?

**Question 6**Explain the concept of a*spurious regression*with regards to a time series. What form of*nonstationarity*that we have covered is most likely to cause this problem?

**Question 7**What test would you use to test for a break in an AR(2) process?

Write down the model you would estimate, the null hypothesis and the type of test you would run.

*Y**t**−*2 increases by 1, how much of a change in*Y**t*would this lead you to predict?

**Question 8**Look at the plot of a time series in Fig 1. Based on the behaviour of this time series, what problem might be present? Explain (just give the name) how you would formally test for this problem? If this problem is present, how would you fifix it?

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