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Which of the following is a limitation of ARCH models (select all correct responses):  

When the p-value of the Ljung-Box test performed on the squared residuals is lower than 0.05, we reject the null hypothesis of uncorrelated variance with a 95% confidence level. 

A hypothesis test is used to assess the significance of individual coefficients in a regression model by comparing the estimated parameter to its hypothesized value. Which of the options below is the correct test? 

Assume we have a multivariate time series with n individual time series. If the AR(2) applied to each of the n time series in the multivariate time series is causal, we can infer that:  

The BIC criterion is preferred  in the order selection in both  ARMA-GARCH and VAR models when the objective is prediction since it selects less complex models (lesser overfitting).

In a stationary multivariate time series, the individual variances of each time series and cross-variances between different series must remain constant over time.

The ARCH model assumes positive and negative shocks have the same effect on volatility because it depends on the log of the previous shocks 

In the reading, “What educated citizens should know about statistics and probability”, Utts argues that several statistical concepts are commonly misunderstood by both the public and even researchers themselves. Choose one of the seven topics mentioned in the article that the author identifies as a source of confusion and describe it in your own words. Then, discuss a potential consequence of this misunderstanding (within a specific scientific discipline or society more broadly). How might scientists (and lifelong students of science like you) be able to reduce misunderstandings of the topic you chose? 

In the reading, “Striving for transparent and credible research: practical guidelines for behavioral ecologists”, Ihle and her co-authors make several concrete recommendations that they think will help improve the credibility of behavioral ecology research (and science more broadly). Describe one of these recommendations in your own words, including how and why they think it will improve the credibility of science. (Optional: you can also add your opinion here about whether or not this recommendation will be effective and why).  

Tonya knows that people seeing the billboard advertising her real estate firm will be busy driving or talking or otherwise be distracted. Instead of outlining thoughtful reasons for why people should call her firm, she decides to limit the billboard to a picture of a beautiful house with an attractive, happy family standing out front. In the terminology of researchers Petty and Cacioppo, which route will the information on the billboard target?