Reference no: EM131273334 , Length: 4

1. The Excel file CFE5305A22016Q1.xls contains monthly UK house price from Jan- uary 1991 to May 2007.

(a) State the null and alternative hypothesis for a unit root test.

(b) Perform an augmented Dickey-Fuller (ADF) Unit-Root test with up to 12 lags of the dependent variable, in a regression equation on the raw data series with a constant but no trend in the test equation, with the Schwarz criterion being the default. Comment on results for the raw house price series.

In Eviews click on the View button on the button bar above the spread- sheet and then Unit Root Test choose the following options: (1) Test Type Augmented Dickey-Fuller (2) Test for Unit Root in Levels (3) Include in test equation Intercept (4) Maximum lags 12 and click OK.

(c) repeat all of the above steps for the first difference of the house price series (use the First Difference option in the unit root testing window). Comment on the results.

2. The Excel file CFE5305A22016Q2.xls contains the monthly SP500 spot and futures series from 2/2002 to 7/2007. The data were obtained from yahoo finance. As a Financial Engineer you have been tasked to examine the SP500 spot and futures series for cointegration using EViews. If the two series are cointegrated, this means that the spot and futures prices have a long-term relationship, which prevents them from wandering apart without bound. To test for cointegration using the Engle- Granger approach, the residuals of a regression of the spot price on the futures price are examined. Create two new variables, for the log of the spot series and the log of the futures series, and call them lspot and lfutures respectively. Then generate a new equation object and run the regression:

LSPOT C LFUTURES

Note again that it is not valid to examine anything other than the coefficient values in this regression. The residuals of this regression are found in the object called RESID. Generate a new series (STATRESIDS) that will keep these residuals in an object for later use:

STATRESIDS = RESID

(a) Perform the Augmented Dickey-Fuller (ADF) Test on the residual series STA- TRESIDS. Assuming again that up to 12 lags are permitted, and that a constant but not a trend are employed in a regression on the levels of the series.

(b) Compare the test statistic and the critical values, at the 5% level and even at the 1% level and decide whether the null hypothesis of a unit root in the test regression residuals is accepted or rejected. Are the two series are cointe- grated?

3. As a consultant you been been asked to estimate a VAR(p) in order to examine whether there are lead-lag relationships for the returns to three exchange rates against the US dollar - the euro, the British pound and the Japanese yen. The data are daily and run from 7 July 2002 to 7 July 2007, giving a total of 1,827 observations. The data are contained in the Excel file CFE5305A22016Q3.xls. First Create a new workfile, called CFE5305A22016Q3.wf1, and import the three currency series. Construct a set of continuously compounded percentage returns called reur, rgbp and rjpy. VAR estimation in EViews can be accomplished by clicking on the Quick menu and then Estimate VAR. In the Endogenous variables box, type the three variable names, reur rgbp rjpy. In the Exogenous box, leave the default C and in the Lag Interval box, enter 1 2 to estimate a VAR(2), just as an example. The output appears in a neatly organised table, with one column for each equation in the first and second panels, and a single column of statistics that describes the system as a whole in the third. So values of the information criteria are given separately for each equation in the second panel and jointly for the model as a whole in the third.

(a) The first step in the construction of any VAR model, once the variables that will enter the VAR have been decided, will be to determine the appropriate lag length. This can be achieved in a variety of ways, but one of the easiest is to employ a multivariate information criterion. In EViews, this can be done easily from the EViews VAR output we have by clicking View/Lag Structure/Lag Length Criteria. You will be invited to specify the maximum number of lags to entertain including in the model, and for this example, arbitrarily select 10.

Comment on the values of various information criteria and other methods for determining the lag order. In this case, the Schwartz, Hannan-Quinn and Akaikes criterion. Which VAR model do you select and why?

(b) Run a Granger causality test by clicking View/Lag Structure/Granger Causal- ity/Block Exogeneity Tests. Comment on the results.

(c) Obtain the impulse responses for the estimated model and comment. Simply click the Impulse on the button bar above the VAR object. EViews will offer to estimate and plot all of the responses to separate shocks of all of the variables in the order that the variables were listed in the estimation window, using ten steps and confidence intervals generated using analytic formulae.

(d) Plot the variance decompositions by clicking on View and then Variance De- composition. Comment on your results.

The ordering of the variables has an effect on the impulse responses and vari- ance decompositions, and when, as in this case, theory does not suggest an obvious ordering of the series, some sensitivity analysis should be undertaken. This can be achieved by clicking on the Impulse Definition tab when the window that creates the impulses is open. A window entitled Ordering for Cholesky should be apparent, and it would be possible to reverse the order of variables or to select any other order desired. For the variance decomposi- tions, the Ordering for Cholesky box is observed in the window for creating the decompositions without having to select another tab.

Notes: Impulse responses and variance decompositions

Block F-tests and an examination of causality in a VAR will suggest which of the variables in the model have statistically significant impacts on the future values of each of the variables in the system. But F-test results will not, by construction, be able to explain the sign of the relationship or how long these effects require to take place. That is, F-test results will not reveal whether changes in the value of a given variable have a positive or negative effect on other variables in the system, or how long it would take for the effect of that variable to work through the system. Such information will, however, be given by an examination of the VARs impulse responses and variance decom- positions. Impulse responses trace out the responsiveness of the dependent variables in the VAR to shocks to each of the variables. So, for each variable from each equation separately, a unit shock is applied to the error, and the effects upon the VAR system over time are noted. Thus, if there are g vari- ables in a system, a total of g2 impulse responses could be generated. The way that this is achieved in practice is by expressing the VAR model as a VMA - that is, the vector autoregressive model is written as a vector moving average. Provided that the system is stable, the shock should gradually die away. VAR system dynamics. They give the proportion of the movements in the dependent variables that are due to their own shocks, versus shocks to the other variables. A shock to the ith variable will directly affect that variable of course, but it will also be transmitted to all of the other variables

in the system through the dynamic structure of the VAR. Variance decom- positions determine how much of the s-step-ahead forecast error variance of a given variable is explained by innovations to each explanatory variable for s = 1, 2, ... In practice, it is usually observed that own series shocks explain most of the (forecast) error variance of the series in a VAR. To some extent, impulse responses and variance decompositions offer very similar information.

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