计量经济学Test bank questions Chapter 5

Multiple Choice Test Bank Questions No Feedback

–

Chapter 5

Correct answers denoted by an asterisk.

1. Consider the following model estimated for a time series

y

t

= 0.3 + 0.5

y

t

-1

- 0.4

?

t-

1

+

?

t

where

?

t

is a zero mean error process.

What is the (unconditional) mean of the series,

y

t

?

(a) * 0.6

(b) 0.3

(c) 0.0

(d) 0.4

2. Consider the following single exponential smoothing model:

S

t

=

?

X

t

+

(1-

?

)

S

t

-1

You are given the following data:

?

=0.1,

X

t

=0.5,

S

t-

1

=0.2

?

If we believe that the true DGP can be approximated by the exponential smoothing model,

what would be an appropriate 2-step ahead forecast for

X

? (i.e. a forecast of

X

t+

2

made at

time

t

)

(a) 0.2

(b) * 0.23

(c) 0.5

(d)

There

is

insufficient

information

given

in

the question to

form

more than a one

step

ahead forecast.

3. Consider the following MA(3) process.

y

t

= 0.1 + 0.4

u

t

-1

+ 0. 2

u

t

-2

–

0.1

u

t

-3

+

u

t

What

is

the

optimal

forecast

for

y

t

,

3

steps

into

the

future

(i.e.

for

time

t

+2

if

all

information until time

t

-1 is available), if you have the following data?

u

t

-1

= 0.3;

u

t

-2

= -0.6;

u

t

-3

= -0.3

(a)

0.4

(b)

0.0

(c)

* 0.07

(d)

–

0.1

4.

Which

of

the

following

sets

of

characteristics

would

usually

best

describe

an

autoregressive process of order 3 (i.e. an AR(3))?

(a) * A slowly decaying acf, and a pacf with 3 significant spikes

(b) A slowly decaying pacf and an acf with 3 significant spikes

(c) A slowly decaying acf and pacf

(d) An acf and a pacf with 3 significant spikes

5. A process,

x

t

, which has a constant

mean and variance, and

zero autocovariance for all

non-zero lags is best described as

(a) * A white noise process

(b) A covariance stationary process

(c) An autocorrelated process

(d) A moving average process

6. Which of the

following conditions

must

hold

for the autoregressive part of an

ARMA

model to be stationary?

(a) * All roots of the characteristic equation must lie outside the unit circle

(b) All roots of the characteristic equation must lie inside the unit circle

(c) All roots must be smaller than unity

(d) At least one of the roots must be bigger than one in absolute value.

7. Which of the following statements are true concerning time- series forecasting?

(i) All time-series forecasting methods are essentially extrapolative.

(ii)

Forecasting

models

are

prone

to

perform

poorly

following

a

structural

break

in

a

series.

(iii) Forecasting accuracy often declines with prediction horizon.

(iv)

The

mean

squared

errors

of

forecasts

are

usually

very

highly

correlated

with

the

profitability of employing those forecasts in a trading strategy.

(a) (i), (ii), (iii), and (iv)

(b) * (i), (ii) and (iii) only

(c) (ii), (iii) only

(d) (ii) and (iv) only

8. If a series,

y

t

,

follows a random walk (with

no drift),

what

is the optimal 1-step ahead

forecast for

y

?

(a)

* The current value of

y

.

(b)

Zero.

(c)

The historical unweighted average of

y

.

(d)

An exponentially weighted average of previous values of

y

.

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 autocorrelation function at lag 1?

(a)

0.4

(b)

1

(c)

*0.34

(d)

It is not possible to determine the value of the autocovariances without knowing the

disturbance variance.

10. Which of the following statements are true?

(i)

An MA(q) can be expressed as an AR(infinity) if it is invertible