Chapter 5
1 | Which of the following is a typical characteristic of financial asset return time-series?
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2 | Which of the following is a DISADVANTAGE of using pure time-series models (relative to structural models)?
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3 | Which of the following conditions are necessary for a series to be classifiable as a weakly stationary process? (i) It must have a constant mean (ii) It must have a constant variance (iii) It must have constant autocovariances for given lags (iv) It must have a constant probability distribution
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4 | A white noise process will have (i) A zero mean (ii) A constant variance (iii) Autocovariances that are constant (iv) Autocovariances that are zero except at lag zero
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5 | Consider the following sample autocorrelation estimates obtained using 250 data points: 1) Lag 1 2 3 2) Coefficient 0.2 -0.15 -0.1 3) Assuming that the coefficients are approximately normally distributed, which of the coefficients are statistically significant at the 5% level?
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6 | Consider again the autocorrelation coefficients described in question 5. The value of the Box-Pierce Q-statistic is
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7 | Which of the following statements is INCORRECT concerning a comparison of the Box-Pierce Q and the Ljung-Box Q* statistics for linear dependence in time series?
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8 | Consider the following MA(3) process yt = μ + Εt + θ1Εt-1 + θ2Εt-2 + θ3Εt-3 , where σt is a zero mean white noise process with variance σ2. Which of the following statements are true? i) The process yt has zero mean ii) The autocorrelation function will have a zero value at lag 5 iii) The process yt has variance σ2 iv) The autocorrelation function will have a value of one at lag 0
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9 | Consider a series that follows an MA(1) with zero mean and a moving average coefficient of 0.4. What is the value of the autocovariance at lag 1?
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10 | For an autoregressive process to be considered stationary
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11 | Consider the following AR(2) process: yt = 1.5 yt-1 - 0.5 yt-2 + ut This is a
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12 | Consider the following AR(1) model with the disturbances having zero mean and unit variance yt = 0.2 + 0.4 yt-1 + ut The (unconditional) mean of y will be given by
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13 | The (unconditional) variance of the AR(1) process for y given in question 12 will be
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14 | The value of the autocovariance function at lag 3 for the AR(1) model given in question 12 will be
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15 | The value of the autocorrelation function at lag 3 for the AR(1) model given in question 12 will be
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16 | Which of the following statements are true concerning the autocorrelation function (acf) and partial autocorrelation function (pacf)? i) The acf and pacf will always be identical at lag one whatever the model ii) The pacf for an MA(q) model will in general be non-zero beyond lag q iii) The pacf for an AR(p) model will be zero beyond lag p iv) The acf and pacf will be the same at lag two for an MA(1) model
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17 | An ARMA(p,q) (p, q are integers bigger than zero) model will have
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18 | The pacf is necessary for distinguishing between
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19 | The characteristic roots of the MA process yt = -3ut-1 + ut-2 + ut are
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20 | Consider the picture below and suggest the model from the following list that best characterises the process:
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21 | Consider the picture below and suggest the model from the following list that best characterises the process:
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22 | Which of the following statements are true concerning the acf and pacf? (i) The acf and pacf are often hard to interpret in practice (ii) The acf and pacf can be difficult to calculate for some data sets (iii) Information criteria represent an alternative approach to model order determination (iv) If applied correctly, the acf and pacf will always deliver unique model selections
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23 | Which of the following statements are true concerning the Box-Jenkins approach to diagnostic testing for ARMA models? (i) The tests will show whether the identified model is either too large or too small (ii) The tests involve checking the model residuals for autocorrelation, heteroscedasticity, and non-normality (iii) If the model suggested at the identification stage is appropriate, the acf and pacf for the residuals should show no additional structure (iv) If the model suggested at the identification stage is appropriate, the coefficients on the additional variables under the overfitting approach will be statistically insignificant
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24 | Which of the following statements are true concerning information criteria? (i) Adjusted R-squared is an information criterion (ii) If the residual sum of squares falls when an additional term is added, the value of the information criterion will fall (iii) Akaike's information criterion always leads to model orders that are at least as large as those of Schwarz's information criterion (iv) Akaike's information criterion is consistent
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25 | Consider the following ARMA(2,1) equation (with standard errors in parentheses) that has been estimated as part of the Box-Jenkins overfitting strategy for testing the adequacy of the chosen AR(1) mmodel. Which model do you think, given these results, is the most appropriate for the data?
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26 | Which of the following statements are true concerning the class of ARIMA(p,d,q) models? (i) The "I" stands for independent (ii) An ARIMA(p,1,q) model estimated on a series of logs of prices is equivalent to an ARIMA(p,0,q) model estimated on a set of continuously compounded returns (iii) It is plausible for financial time series that the optimal value of d could be 2 or 3. (iv) The estimation of ARIMA models is incompatible with the notion of cointegration
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27 | Which of the following statements is true concerning forecasting in econometrics?
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28 | If a series, y, follows a random walk, what is the optimal one-step ahead forecast of y?
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29 | If a series, y, follows a random walk with drift b, what is the optimal one-step ahead forecast of the change in y?
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30 | An "ex ante" forecasting model is one which
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31 | Consider the following MA(2) model yt = 0.3 + 0.5ut-1 - 0.4ut-2 + ut What is the optimal two-step ahead forecast from this model, made at time t, if the values of the residuals from the model at time t and t-1 were 0.6 and -0.1 respectively and the values of the actual series y at time t-1 was -0.4?
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32 | What is the optimal three-step ahead forecast from the MA(2) model given in question 31?
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33 | Which one of the following statements is true concerning alternative forecast accuracy measures?
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34 | Which one of the following factors is likely to lead to a relatively high degree of out-of-sample forecast accuracy?
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