Question 1

The unknown parameters of a Markov switching model are usually estimated using:&#10;A) Maximum likelihood&#10;B) Instrumental variables&#10;C) Indirect least squares&#10;D) Ordinary least squares

Accepted Answer

Maximum likelihood estimation is commonly used for estimating the unknown parameters in a Markov switching model because it can effectively handle the model's complexity and non-linearity.

Question 2

Which of these equations is a self-exciting threshold autoregressive model?&#10;A) if     if    &#10;B) if     if    &#10;C) if     if    &#10;D) if     if

Accepted Answer

if     if

Question 3

Threshold autoregressive and Markov switching models:&#10;A) Allow us to potentially capture regime switches in a dependent variable&#10;B) Forecast correlations of two distinct series&#10;C) Maximise the threshold of autoregressive models&#10;D) All of the above

Accepted Answer

Threshold autoregressive and Markov switching models are specifically designed to capture regime switches in a dependent variable, allowing for different behaviors or states in the data. They do not inherently forecast correlations between two series or maximize the threshold of autoregressive models.

Question 4

The key difference between threshold autoregressive and Markov switching models is that:&#10;A) The latter can be estimated using ordinary least squares while the latter is estimated using indirect least squares estimation technique&#10;B) Under the latter, the state variable is assumed to be known and observable, while it is latent under the former&#10;C) Under the former, the state variable is assumed to be known and observable, while it is latent under the latter&#10;D) None of the above

Accepted Answer

Threshold autoregressive models assume the state variable is observable and switches according to the level of an observable variable, whereas Markov switching models assume the state is unobservable and follows a Markov process.

Question 5

To check for seasonality (day-of-the-week effect) in stock returns of South Korea, Malaysia, the Philippines, Taiwan and Thailand, Brooks and Persand (2001) regress daily returns in each of these countries' stock market on five dummy variables D1 to D5 representing each day of the week i.e. D1 for Mondays, D2 for Tuesdays, D3 for Wednesdays, D4 for Thursdays and D5 for Fridays: Their results were:
Which market(s) did not display any evidence of day-of-the-week effect?

A) Thailand, Malaysia and Taiwan
B) Philippines only
C) South Korea only
D) South Korea and Philippines

Accepted Answer

South Korea and Philippines did not show evidence of the day-of-the-week effect, meaning that there was no consistent pattern of returns based on the day of the week in these markets.

Question 6

A Markov process can be written mathematically as:&#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of A Markov process can be written mathematically...

Question 7

To compare the goodness of fit of Markov switching and threshold autoregressive models with linear models, one can compare the residual sums of squares of the two types of models using an F-test. Is the statement true?

A) Yes
B) No
C) If the autoregressive model is restricted
D) Cannot say without knowing the number of regimes in the regime switching models

Accepted Answer

The statement is false because an F-test is not appropriate for comparing non-nested models like Markov switching or threshold autoregressive models with linear models. These models have different structures and assumptions, making direct comparison using residual sums of squares and an F-test not valid.

Question 8

Suppose that a researcher wishes to test for calendar (seasonal) effects using a dummy variables approach. Which of the following regressions could be used to examine this?
(I) A regression containing intercept dummies
(ii) A regression containing slope dummies
(iii) A regression containing intercept and slope dummies
(iv) A regression containing a dummy variable taking the value 1 for one observation and zero for all others

A) (ii) and (iv) only
B) (i) and (iii) only
C) (i), (ii), and (iii) only
D) (i), (ii), (iii), and (iv).

Accepted Answer

Intercept dummies can capture the average seasonal effect, slope dummies can capture how the effect of another variable changes with the season, and a combination of both can provide a more detailed seasonal analysis. Option (iv) is not suitable for seasonal effects as it only differentiates one observation from all others, not capturing any seasonal pattern.

Question 9

If a series possesses the &#34;Markov property&#34;, what would this imply?&#10;(I) The series is path-dependent&#10;(ii) All that is required to produce forecasts for the series is the current value of the series plus a transition probability matrix&#10;(iii) The state-determining variable must be observable&#10;(iv) The series can be classified as to whether it is in one regime or another regime, but it can only be in one regime at any one time&#10;A) (ii) only&#10;B) (i) and (ii) only&#10;C) (i), (ii), and (iii) only&#10;D) (i), (ii), (iii), and (iv)

Accepted Answer

The Markov property implies that the future state of a process depends only on the current state, not on the sequence of events that preceded it. This means that to forecast future states, only the current state and a transition probability matrix are needed, making choice (ii) correct. Choices (i), (iii), and (iv) do not accurately describe the Markov property.

Deck 2: Mathematical and Statistical Foundations