this is the final question for time series econometrics.1. Is GARCH conditional variance...

Question

this is the final question for time series econometrics.
1.

Is GARCH conditional variance specification that was introduced earlier, say, for the i^th return,

Still appealing in the multivariate case? Why or why not?

Consider the following specification for the conditional covariance between i^th and j^th return:

Is it appealing? Why or why not?

Consider a fully general multivariate volatility model, in which every conditional variance and covariance may depend on lags of every conditional variance and covariance, as well as every squared return and cross product of returns. What are the strengths and weaknesses of such a model? Would it be useful for modeling, say, a set of 500 returns? If not, how might you proceed?

Research into the Philips curve is concerned with providing empirical evidence of a tradeoff between inflation and unemployment. Can an economy experience lower unemployment rate if it is prepared to accept higher inflation? The data set contains the changes in unemployment rate (DU) and the changes in inflation (DP) for the United States for the sample period 1976:07 to 2005:06. A VAR model was estimated as follow:

Is there evidence of an inverse relationship between the change in the unemployment rate (DU) and the change in inflation rate (DP)?
What is the response of DP at time t+1 following a unit shock to DU at time t?
What is the response of DU at time t+2?

The quantity theory of money states that there is a direct relationship between the quantity of money in the economy and the aggregate price level. Put simply, if the quantity of money doubles, then the price level should also double. A VEC model is estimated for the Canadian data between 1971:1 and 2015:4

Identify the cointegrating relationship between P and M. Is the quantity theory of money supported?
Identify the error-correction coefficients. Is the system stable?
The above results were estimated using a system approach. Derive the cointegrating residuals and given the following unit root test result, can you confirm that the series is indeed I(0) variable?

a. Clearly explain the difference between one-step ahead, filtered, and smoothed regime probabilities. Is it correct to state that we should always use smoothed instead of filtered probabilities to identify phrases of business cycle? Why or Why not?

b. Derive the smoothed probabilities using information up to t+1. (following the same methodology we discussed in the lab)

To investigate the wealth effect on consumption, a researcher has estimated the following first-order Markov Switching Model with two regimes.

(10 marks) Given Eviews outputs below, interpret the coefficients and transition probabilities.Are the models adequate in terms of diagnostic statistics?

Dependent Variable: CONSUMPTION
Method: Markov Switching Regression (BFGS / Marquardt steps)
Date: 04/10/16 Time: 23:23
Sample: 1960M01 2014M03
Included observations: 219
Number of states: 2
Initial probabilities obtained from ergodic solution
Standard errors & covariance computed using observed Hessian
Random search: 25 starting values with 10 iterations using 1 standard
deviation (rng=kn, seed= XXXXXXXXXX)
Convergence achieved after 26 iterations
Variable	Coefficient	Std. Error	z-Statistic	Prob.
Regime 1
C	XXXXXXXXXX	XXXXXXXXXX	XXXXXXXXXX	0.0000
WEALTH	XXXXXXXXXX	XXXXXXXXXX	XXXXXXXXXX	0.0000
LOG(SIGMA)	XXXXXXXXXX	XXXXXXXXXX	XXXXXXXXXX	0.0000
Regime 2
C	XXXXXXXXXX	XXXXXXXXXX	XXXXXXXXXX	0.0023
WEALTH	XXXXXXXXXX	XXXXXXXXXX	XXXXXXXXXX	0.0000
LOG(SIGMA)	XXXXXXXXXX	XXXXXXXXXX	XXXXXXXXXX	0.0000
Transition Matrix Parameters
P11-C	XXXXXXXXXX	XXXXXXXXXX	XXXXXXXXXX	0.0000
P21-C	XXXXXXXXXX	XXXXXXXXXX	XXXXXXXXXX	0.0000
Mean dependent var	XXXXXXXXXX	S.D. dependent var	XXXXXXXXXX
S.E. of regression	XXXXXXXXXX	Sum squared resid	XXXXXXXXXX
Durbin-Watson stat	XXXXXXXXXX	Log likelihood	XXXXXXXXXX
Akaike info criterion	XXXXXXXXXX	Schwarz criterion	XXXXXXXXXX
Hannan-Quinn criter.	XXXXXXXXXX

Equation: MODEL1
Date: 04/10/16 Time: 23:24
Transition summary: Constant Markov transition
probabilities and expected durations
Sample: 1960M01 2014M03
Included observations: 219
Constant transition probabilities:
P(i, k) = P(s(t) = k \| s(t-1) = i)
(row = i / column = j)
1	2
1	XXXXXXXXXX	XXXXXXXXXX
2	XXXXXXXXXX	XXXXXXXXXX
Constant expected durations:
1	2
XXXXXXXXXX	XXXXXXXXXX

What are the unconditional probabilities of regime 1 and 2? Using the one-step ahead (onestep1 and onestep2) and filtered (filtered1 and filtered2) regime probabilities, construct a one-step ahead forecast for consumption in the 2014Q4. What is your best forecast for 2015Q4 if wealth will be around 12.3?

Comparing to the estimated results for a three-regime model below, which model will you choose to forecast consumption?

Can you perform a Likelihood Ratio (LR) test in this case with the null hypothesis of two-regime model against the alternative hypothesis of a three-regime model? Why or Why not?

David · Accepted Answer

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this is the final question for time series econometrics. 1. Is GARCH conditional variance specification that was introduced earlier, say, for the i th return, Still appealing in the multivariate case?...