Runtun Waktu 2

Which of the following is a DISADVANTAGE of using pure time-series models (relative to structural models)?

• They are not theoretically motivated

• They cannot produce forecasts easily

• They cannot be used for very high frequency data

• It is difficult to determine the appropriate explanatory variables for use in pure time-series models

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?

• 1 only

• 1 and 2 only

• 1, 2 and 3 only

• It is not possible to determine the statistical significance since no standard errors have been given

Consider the following sample autocorrelation estimates obtained using 250 data points:

1) Lag 1 2 3

2) Coefficient 0.2 -0.15 -0.1

The value of the Box-Pierce Q-statistic is

• 0.12

• 37.50

• 18.12

• 18.09

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?

• Asymptotically, the values of the two test statistics will be equal

• The Q test has better small-sample properties than the Q*

• The Q test is sometimes over-sized for small samples

• As the sample size tends towards infinity, both tests will show a tendency to always reject the null hypothesis of zero autocorrelation coefficients.

Consider the following MA(3) process

y_t = μ + Ε_t + θ₁Ε_t-1 + θ₂Ε_t-2 + θ₃Ε_t-3 , where σ_t is a zero mean white noise process with variance σ².

Which of the following statements are true?

i) The process y_t has zero mean

ii) The autocorrelation function will have a zero value at lag 5

iii) The process y_t has variance σ²

iv) The autocorrelation function will have a value of one at lag 0

• (ii) and (iv) only

• (i) and (iii) only

• (i), (ii), and (iii) only

• (i), (ii), (iii), and (iv)

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?

• 0.4

• 1

• 0.34

• It is not possible to determine the value of the autocovariances without knowing the disturbance variance.

Consider the following AR(2) process:

y_t = 1.5 y_t-1 - 0.5 y_t-2 + u_t

This is a

• Stationary process

• Unit root process

• Explosive process

• Stationary and unit root process

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

• (ii) and (iv) only

• (i) and (iii) only

• (i), (ii), and (iii) only

• (i), (ii), (iii), and (iv)

An ARMA(p,q) (p, q are integers bigger than zero) model will have

• An acf and pacf that both decline geometrically

• An acf that declines geometrically and a pacf that is zero after p lags

• An acf that declines geometrically and a pacf that is zero after q lags

• An acf that is zero after p lags and a pacf that is zero after q lags

The pacf is necessary for distinguishing between

• An AR and an MA model

• An AR and an ARMA model

• An MA and an ARMA model

• Different models from within the ARMA family