Introductory Econometrics For Finance 2nd Edition Chris Brooks - Solutions

Consider the following simultaneous equations system y1t = α0 + α1 y2t + α2 y3t + α3X1t + α4X2t + u1t (6.94)y2t = β0 + β1 y3t + β2X1t + β3X3t + u2t (6.95)y3t = γ0 + γ1 y1t + γ2X2t + γ3X3t + u3t(a) Derive the reduced form equations corresponding to (6.94)–(6.96).(b) What do you
Construct simultaneous equations models and VARs in EViews AppendixLO1
Conduct Granger causality tests AppendixLO1
Estimate optimal lag lengths, impulse responses and variance decompositions AppendixLO1
Determine whether an equation from a system is identified AppendixLO1
Explain the relative advantages and disadvantages of VAR modelling AppendixLO1
Describe several methods for estimating simultaneous equations models AppendixLO1
Derive the reduced form equations from a structural model AppendixLO1
Discuss the cause, consequence and solution to simultaneous equations bias AppendixLO1
Compare and contrast single equation and systems-based approaches to building models AppendixLO1
Select two of the stock series from the ‘CAPM.XLS’ Excel file, construct a set of continuously compounded returns, and then perform a time-series analysis of these returns. The analysis should include(a) An examination of the autocorrelation and partial autocorrelation functions.(b) An
(a) Briefly explain any difference you perceive between the characteristics of macroeconomic and financial data. Which of these features suggest the use of different econometric tools for each class of data?(b) Consider the following autocorrelation and partial autocorrelation coefficients
(a) Explain what stylised shapes would be expected for the autocorrelation and partial autocorrelation functions for the following stochastic processes:● white noise● an AR(2)● an MA(1)● an ARMA (2,1).Univariate time series modelling and forecasting 263 (b) Consider the following ARMA
You have estimated the following ARMA(1,1) model for some time series data yt = 0.036 + 0.69yt−1 + 0.42ut−1 + ut Suppose that you have data for time to t−1, i.e. you know that yt−1 = 3.4, and ˆut−1 = −1.3(a) Obtain forecasts for the series y for times t, t +1, and t +2 using the
(a) You obtain the following sample autocorrelations and partial autocorrelations for a sample of 100 observations from actual data:Lag 1 2 3 4 5 6 7 8 acf 0.420 0.104 0.032 −0.206 −0.138 0.042 −0.018 0.074 pacf 0.632 0.381 0.268 0.199 0.205 0.101 0.096 0.082 Can you identify the most
‘Given that the objective of any econometric modelling exercise is to find the model that most closely ‘fits’ the data, then adding more lags to an ARMA model will almost invariably lead to a better fit. Therefore a large model is best because it will fit the data more closely.’Comment on
How could you determine whether the order you suggested for question 6 was in fact appropriate?AppendixLO1
A researcher is trying to determine the appropriate order of an ARMA model to describe some actual data, with 200 observations available.She has the following figures for the log of the estimated residual variance (i.e. log ( ˆ σ2)) for various candidate models. She has assumed that an order
You obtain the following estimates for an AR(2) model of some returns data yt = 0.803yt−1 + 0.682yt−2 + ut where ut is a white noise error process. By examining the characteristic equation, check the estimated model for stationarity.AppendixLO1
(a) Describe the steps that Box and Jenkins (1976) suggested should be involved in constructing an ARMA model.(b) What particular aspect of this methodology has been the subject of criticism and why?(c) Describe an alternative procedure that could be used for this aspect.AppendixLO1
Consider the following three models that a researcher suggests might be a reasonable model of stock market prices yt = yt−1 + ut (5.190)yt = 0.5yt−1 + ut (5.191)yt = 0.8ut−1 + ut (5.192)(a) What classes of models are these examples of?(b) What would the autocorrelation function for each of
Why might ARMA models be considered particularly useful for financial time series? Explain, without using any equations or mathematical notation, the difference between AR, MA and ARMA processes.AppendixLO1
What are the differences between autoregressive and moving average models?AppendixLO1
Estimate time series models and produce forecasts from them in EViews AppendixLO1
Evaluate the accuracy of predictions using various metrics AppendixLO1
Produce forecasts for ARMA and exponential smoothing models AppendixLO1
Identify the appropriate time series model for a given data series AppendixLO1
Explain the defining characteristics of various types of stochastic processes AppendixLO1
Find a further example of where panel regression models have been used in the academic finance literature and do the following:● Explain why the panel approach was used.● Was a fixed effects or random effects model chosen and why?● What were the main results of the study and is any indication
(a) Explain how fixed effects models are equivalent to an ordinary least squares regression with dummy variables.(b) How does the random effects model capture cross-sectional heterogeneity in the intercept term?(c) What are the relative advantages and disadvantages of the fixed versus random
(a) What are the advantages of constructing a panel of data, if one is available, rather than using pooled data?(b) What is meant by the term ‘seemingly unrelated regression’? Give examples from finance of where such an approach may be used.(c) Distinguish between balanced and unbalanced
Construct and estimate panel models in EViews AppendixLO1
Contrast the fixed effect and random effect approaches to panel model specification, determining which is the more appropriate in particular cases AppendixLO1
Explain the intuition behind seemingly unrelated regressions and propose examples of where they may be usefully employed AppendixLO1
Describe the key features of panel data and outline the advantages and disadvantages of working with panels rather than other structures AppendixLO1
Determine a sensible structure for the dissertation AppendixLO1
Find appropriate sources of literature and data AppendixLO1
Choose a suitable topic for an empirical research project in finance AppendixLO1
A barrier option is a path-dependent option whose payoff depends on whether the underlying asset price traverses a barrier. A knock-out call is a call option that ceases to exist when the underlying price falls below a given barrier level H. Thus the payoff is given by max[0, ST − K] ifSt > H ∀
(a) Consider the following AR(1) model yt = φyt−1 + ut (12.31)Design a simulation experiment (with code for EViews) to determine the effect of increasing the value of φ from 0 to 1 on the distribution of the t-ratios.(b) Consider again the AR(1) model of (12.31). As stated in chapter 4, the
A researcher tells you that she thinks the properties of the Ljung–Box test (i.e. the size and power) will be adversely affected by ARCH in the data. Design a simulations experiment to test this proposition.AppendixLO1
(a) Present two examples in finance and two in econometrics (ideally other than those listed in this chapter!) of situations where a simulation approach would be desirable. Explain in each case why simulations are useful.(b) Distinguish between pure simulation methods and bootstrapping.What are the
Implement a simulation analysis in EViews AppendixLO1
Describe the various techniques available for reducing Monte Carlo sampling variability AppendixLO1
Explain the difference between pure simulation and bootstrapping AppendixLO1
Design simulation frameworks to solve a variety of problems in finance AppendixLO1
Re-open the ‘fail xls’ spreadsheet for modelling the probability of MSc failure and do the following:(a) Take the country code series and construct separate dummy variables for each country. Re-run the probit and logit regression above with all of the other variables plus the country dummy
(a) Explain the difference between a censored variable and a truncated variable as the terms are used in econometrics.(b) Give examples from finance (other than those already described in this book) of situations where you might meet each of the types of variable described in part (a) of this
(a) Describe the intuition behind the maximum likelihood estimation technique used for limited dependent variable models.(b) Why do we need to exercise caution when interpreting the coefficients of a probit or logit model?(c) How can we measure whether a logit model that we have estimated fits the
Compare and contrast the probit and logit specifications for binary choice variables.AppendixLO1
Explain why the linear probability model is inadequate as a specification for limited dependent variable estimation.AppendixLO1
Estimate limited dependent variable models using maximum likelihood in EViews AppendixLO1
Deal appropriately with censored and truncated dependent variables AppendixLO1
Distinguish between the binomial and multinomial cases AppendixLO1
Interpret and evaluate logit and probit models AppendixLO1
Compare between different types of limited dependent variables and select the appropriate model AppendixLO1
(a) Re-open the exchange rate returns series and test them for day-of-the-week effects.(b) Re-open the house price changes series and determine whether there is any evidence of seasonality.AppendixLO1
A researcher suggests that the volatility dynamics of a set of daily equity returns are different:● on Mondays relative to other days of the week● if the previous day’s return volatility was bigger than 0.1% relative to when the previous day’s return volatility was less than 0.1%.Describe
(a) What is a switching model? Describe briefly and distinguish between threshold autoregressive models and Markov switching models. How would you decide which of the two model classes is more appropriate for a particular application?(b) Describe the following terms as they are used in the context
A researcher is attempting to form an econometric model to explain daily movements of stock returns. A colleague suggests that she might want to see whether her data are influenced by daily seasonality.(a) How might she go about doing this?(b) The researcher estimates a model with the dependent
Describe the intuition behind the estimation of regime switching models AppendixLO1
Compare and contrast Markov switching and threshold autoregressive models AppendixLO1
Specify and explain the logic behind Markov switching models AppendixLO1
Motivate the use of regime switching models in financial econometrics AppendixLO1
Use intercept and slope dummy variables to allow for seasonal behaviour in time series AppendixLO1
In EViews, open the ‘currencies.wf1’ file that will be discussed in detail in the following chapter. Determine whether the exchange rate series (in their raw levels forms) are non-stationary. If that is the case, test for cointegration between them using both the Engle–Granger and Johansen
Compare and contrast the Engle–Granger and Johansen methodologies for testing for cointegration and modelling cointegrated systems. Which, in your view, represents the superior approach and why?AppendixLO1
(a) Suppose that a researcher has a set of three variables, yt (t = 1, . . . , T ), i.e. yt denotes a p-variate, or p × 1 vector, that she wishes to test for the existence of cointegrating relationships using the Johansen procedure.What is the implication of finding that the rank of the
(a) Briefly outline Johansen’s methodology for testing for cointegration between a set of variables in the context of a VAR.(b) A researcher uses the Johansen procedure and obtains the following test statistics (and critical values):r λmax 95% critical value 0 38.962 33.178 1 29.148 27.169 2
(a) Consider a series of values for the spot and futures prices of a given commodity. In the context of these series, explain the concept of cointegration. Discuss how a researcher might test for cointegration between the variables using the Engle–Granger approach. Explain also the steps involved
Using the same regression as for question 2, but on a different set of data, the researcher now obtains the estimate ˆψ = −0.52 with standard error = 0.16.(a) Perform the test.(b) What is the conclusion, and what should be the next step?(c) Another researcher suggests that there may be a
A researcher wants to test the order of integration of some time series data. He decides to use the DF test. He estimates a regression of the formyt = μ + ψyt−1 + ut and obtains the estimate ˆψ = −0.02 with standard error = 0.31.(a) What are the null and alternative hypotheses for this
(a) What kinds of variables are likely to be non-stationary? How can such variables be made stationary?(b) Why is it in general important to test for non-stationarity in time series data before attempting to build an empirical model?(c) Define the following terms and describe the processes that
Construct models for long-run relationships between variables in EViews AppendixLO1
Describe how to test hypotheses in the Johansen framework AppendixLO1
Explain the intuition behind Johansen’s test for cointegration AppendixLO1
Estimate error correction and vector error correction models AppendixLO1
Examine whether systems of variables are cointegrated AppendixLO1
Highlight the problems that may occur if non-stationary data are used in their levels form AppendixLO1
What are the units of R2?AppendixLO1
Re-open the Macro file and apply the same APT-type model to some of the other time-series of stock returns contained in the CAPM-file.(a) Run the stepwise procedure in each case. Is the same sub-set of variables selected for each stock? Can you rationalise the differences between the series
Re-open the CAPM Eviews file and estimate CAPM betas for each of the other stocks in the file.(a) Which of the stocks, on the basis of the parameter estimates you obtain, would you class as defensive stocks and which as aggressive stocks? Explain your answer.(b) Is the CAPM able to provide any
A researcher estimates the following two econometric models yt = β1 + β2x2t + β3x3t + ut (3.56)yt = β1 + β2x2t + β3x3t + β4x4t + vt (3.57)where ut and vt are iid disturbances and x3t is an irrelevant variable which does not enter into the data generating process for yt . Will the value of
A researcher estimates the following econometric models including a lagged dependent variable yt = β1 + β2x2t + β3x3t + β4 yt−1 + ut (3.54)yt = γ1 + γ2x2t + γ3x3t + γ4 yt−1 + vt (3.55)where ut and vt are iid disturbances.Will these models have the same value of (a) The residual sum of
You estimate a regression of the form given by (3.52) below in order to evaluate the effect of various firm-specific factors on the returns of a sample of firms. You run a cross-sectional regression with 200 firms ri = β0 + β1Si + β2MBi + β3PEi + β4BETAi + ui (3.52)where: ri is the percentage
You decide to investigate the relationship given in the null hypothesis of question 2, part (c). What would constitute the restricted regression?The regressions are carried out on a sample of 96 quarterly observations, and the residual sums of squares for the restricted and unrestricted regressions
Which would you expect to be bigger – the unrestricted residual sum of squares or the restricted residual sum of squares, and why?AppendixLO1
Which of the above null hypotheses constitutes ‘THE’ regression F-statistic in the context of (3.51)? Why is this null hypothesis always of interest whatever the regression relationship under study?What exactly would constitute the alternative hypothesis in this case?AppendixLO1
Which of the following hypotheses about the coefficients can be tested using a t-test? Which of them can be tested using an F-test? In each case, state the number of restrictions.(a) H0 : β3 = 2(b) H0 : β3 + β4 = 1(c) H0 : β3 + β4 = 1 and β5 = 1 (d) H0 : β2 = 0 and β3 = 0 and β4 = 0 and
By using examples from the relevant statistical tables, explain the relationship between the t- and the F-distributions.For questions 2–5, assume that the econometric model is of the form yt = β1 + β2x2t + β3x3t + β4x4t + β5x5t + ut (3.51)AppendixLO1
Estimate multiple regression models and test multiple hypotheses in EViews AppendixLO1
Derive the OLS parameter and standard error estimators using matrix algebra AppendixLO1
Form a restricted regression AppendixLO1
Determine how well a model fits the data AppendixLO1
Test multiple hypotheses using an F-test AppendixLO1
Construct models with more than one explanatory variable AppendixLO1
Using EViews, select one of the other stock series from the ‘capm.wk1’file and estimate a CAPM beta for that stock. Test the null hypothesis that the true beta is one and also test the null hypothesis that the true alpha (intercept) is zero. What are your conclusions?AppendixLO1
Are hypotheses tested concerning the actual values of the coefficients(i.e. β) or their estimated values (i.e. βˆ) and why?AppendixLO1
Form and interpret a 95% and a 99% confidence interval for beta using the figures given in question 7.AppendixLO1
The analyst also tells you that shares in Chris Mining PLC have no systematic risk, in other words that the returns on its shares are completely unrelated to movements in the market. The value of beta and its standard error are calculated to be 0.214 and 0.186, respectively. The model is estimated

Showing 300 - 400 of 618

Introductory Econometrics For Finance 2nd Edition Chris Brooks - Solutions

Step by Step Answers