Ch7 ARIMA Forecasting Models Exam Prep

Forecasting and Predictive Analytics with Forecast X, 7e (Keating)

Chapter 7 Explanatory Models 3. ARIMA (Box-Jenkins) Forecasting Models

1) Why are ARIMA (Box-Jenkins) models often referred to as "black boxes"?

A) They ignore causal variables.

B) They use regression analysis in non-standard ways.

C) They evaluate forecast accuracy different from regression models.

D) They are difficult to understand.

E) All of the options are correct.

2) Which of the following is not a potential advantage to using ARIMA models to generate forecasts?

A) They are useful when a set of explanatory variables cannot be identified.

B) They are useful when the only data available are the variable to be forecast.

C) They determine a great deal of information about a time series.

D) They are especially useful for long-term forecasts.

E) All of the options are correct.

3) Which of the following is not a reason for the widespread popularity of ARIMA-type forecasting models?

A) They require less data.

B) They are quite accurate.

C) They allow forecasts with little modeling based on economic theory.

D) They generate especially good short-term forecasts.

E) None of the options are correct.

4) What is a key difference between ARIMA-type models and multiple regression models?

A) The dependent variable

B) Attention to data trend and seasonality

C) Attention to serial correlation

D) Use of explanatory variables

E) None of the options are correct.

5) In the model selection process for ARIMA-type models, the ultimate goal is to find an underlying model that

A) explains the dependent variable.

B) leads to non-random errors.

C) produces white noise forecast errors.

D) models the nonlinear components in a time series.

E) None of the options are correct.

6) If it is found that the forecast errors from an ARIMA-type model exhibit serial correlation, the model

A) is not an adequate forecasting model.

B) is a candidate for adding another explanatory variable.

C) almost surely contains seasonality.

D) is a candidate for Cochrane-Orcutt regression.

E) All of the options are correct.

7) The choice of models in the "black box" of the ARIMA model methodology does not refer to

A) autoregressive models.

B) moving average models.

C) causal models.

D) mixed autoregressive-moving-average models.

E) All of the options are correct.

8) "White noise" refers to model forecast errors that are

A) normally distributed with a mean of one.

B) non-normal.

C) serially independent.

D) heteroscedastic.

E) None of the options are correct.

9) The ARIMA model selection process seeks to find that underlying model which removes

A) all deterministic components from the data.

B) data trend.

C) data seasonality.

D) any serial correlation in the data.

E) All of the options are correct.

10) Which of the following models is not considered as a potential correct "black box" addition in Box-Jenkins modeling?

A) MA(1) models

B) Exponential smoothing models

C) Time-trend regression models

D) Autoregressive models

E) None of the options are correct.

11) Moving-average (or MA type) ARIMA models are best described as

A) simple averages.

B) non-weighted averages.

C) weighted averages of white noise series.

D) weighted averages of non-normal random variates.

E) None of the options are correct.

12) Autocorrelation and partial autocorrelation functions differ in

A) what series is being analyzed.

B) their length.

C) diagnostic ability to identify ARIMA models.

D) what is being held constant in the observed correlogram.

E) All of the options are correct.

13) For a moving-average solution to a forecasting problem, the autocorrelation plot should _______ and the partial autocorrelation plot should _______.

A) slowly approach zero; slowly approach zero

B) dramatically approach zero; exponentially approach one

C) slowly approach one; and cyclically approach zero

D) dramatically cut off to zero; decline to zero whether monotonically or in a wavelike manner

E) None of the options are correct.

14) The autocorrelation function correlogram should show spikes close to _______ lags if a moving-average type model generates the true data.

A) one

B) two

C) three

D) four

E) All of the options are correct.

15) Which of the following patterns of the partial autocorrelation function correlogram is inconsistent with an underlying moving-average data process?

A) Exponentially declining to zero

B) Cyclically declining to zero

C) Positive at first, then negative and increasing to zero

D) Negative at first, then positive and declining to zero

E) None of the options are correct.

16) The autocorrelation function of a time series shows coefficients significantly different from zero at lags 1 through 4. The partial autocorrelation function shows one spike and monotonically increases to zero as lag length increases. Such a series can be modeled as a _______ model.

A) MA(1)

B) MA(2)

C) MA(3)

D) MA(4)

E) None of the options are correct.

17) A time series that can be best represented as a MA(2) model has a partial autocorrelation function that

A) exponentially declines to zero as lag length increases.

B) cyclically declines to zero as lag length increases.

C) has one large negative spike and then goes to zero.

D) has one large positive spike and then goes to zero.

E) All of the options are correct.

18) The order of a moving-average (MA) process can best be determined by the

A) Durbin-Watson statistic.

B) Box-Pierce chi-square statistic.

C) autocorrelation function.

D) partial autocorrelation function.

E) All of the options are correct.

19) Autoregressive models are best described as

A) simple averages of lagged values of the series.

B) weighted averages of lagged series values plus white noise.

C) weighted average of white noise series.

D) weighted averages of normal random variates.

E) None of the options are correct.

20) An autocorrelation and partial autocorrelation function for an AR-type process differs from that of a MA-type process in

A) what series is being analyzed.

B) their length.

C) diagnostic ability to access a moving-average model.

D) that they are opposites.

E) All of the options are correct.

21) For an autoregressive model solution to a forecasting problem, the autocorrelation plot should _______ and the partial autocorrelation plot should _______.

A) gradually approach zero; dramatically cut off to zero.

B) dramatically approach zero; exponentially approach one.

C) slowly approach one; and cyclically approach zero.

D) dramatically cut off to zero; decline to zero either monotonically or in a wavelike manner.

E) None of the options are correct.

22) The autocorrelation function correlogram should show significant correlation (spikes) at lags of _______ if an autoregressive-type model generates the true data.

A) one

B) two

C) three

D) four

E) None of the options are correct.

23) Which of the following patterns of the partial autocorrelation function correlogram is inconsistent with an underlying autoregressive data process?

A) Exponentially declining to zero

B) Cyclically declining to zero

C) Positive at first, then negative and increasing to zero

D) Negative at first, then positive and declining to zero

E) All of the options are correct.

24) The partial autocorrelation function shows one spike at lag length one. Such a series can be modeled as an _______ model.

A) AR(1)

B) AR(2)

C) AR(3)

D) AR(4)

E) None of the options are correct.

25) A time series that can be best represented as an AR(2) model has a partial autocorrelation function that

A) exponentially declines to zero as lag length increases.

B) cyclically declines to zero as lag length increases.

C) has one large negative spike and then goes to zero.

D) has one large positive spike and then goes to zero.

E) None of the options are correct.

26) The order "p" of an autoregressive (AR) process can best be determined by the

A) Durbin-Watson statistic.

B) Box-Pierce chi-square statistic.

C) autocorrelation function.

D) partial autocorrelation function.

E) All of the options are correct.

27) Mixed moving-average models of order (1, 1) have spikes exhibited in

A) the autocorrelation function.

B) the partial autocorrelation function.

C) both autocorrelation and partial-autocorrelation functions.

D) neither the autocorrelation and partial-autocorrelation functions.

E) None of the options are correct.

28) ARMA(p, q) models have autocorrelation and partial-autocorrelation functions that

A) may both show spikes.

B) may both show monotonically declining estimates.

C) may look amazingly similar.

D) may look quite dissimilar in the nature of adjustment.

E) All of the options are correct.

29) For an ARMA(1, 2) solution to a forecasting problem, the autocorrelation plot should have _______ spike(s) and the partial autocorrelation plot should have _______ spike(s)?

A) 1; 2

B) 2; 1

C) 1; 1

D) 2; 2

E) None of the options are correct.

30) The autocorrelation function correlogram should show spikes close to _______ lags if an ARMA (2, 3)-type model generates the true data.

A) one

B) two

C) three

D) four

E) None of the options are correct.

31) The partial-autocorrelation function correlogram should show spikes close to _______ lags if an ARMA (2, 3)-type model generates the true data.

A) one

B) two

C) three

D) four

E) None of the options are correct.

32) Which of the following patterns of the partial-autocorrelation function correlogram is inconsistent with an underlying ARMA data process?

A) Exponentially declining to zero

B) Cyclically declining to zero

C) Positive at first, then negative and increasing to zero

D) Negative at first, then positive and declining to zero

E) None of the options are correct.

33) The autocorrelation function of a time series shows coefficients significantly different from zero at lags 1 through 4. The partial-autocorrelation function shows one spike and monotonically increases to zero as lags length increases. Such a series can be modeled as a(n) _______ model.

A) ARMA(1, 4)

B) ARMA(2, 4)

C) MA(3)

D) ARMA(4, 1)

E) None of the options are correct.

34) A time series that can be best represented as an ARMA(2, 0) model has a partial-autocorrelation function that

A) has no significant lags.

B) slowly declines to zero as lag length increases.

C) has one large negative spike and then goes to zero.

D) has one large positive spike and then goes to zero.

E) None of the options are correct.

35) The order of an ARMA(p, q) process can best be determined by the

A) number of AR and MA terms that are significant.

B) Box-Pierce chi-square statistic.

C) autocorrelation function alone.

D) partial-autocorrelation function alone.

E) None of the options are correct.

36) Which of the following are incorrect?

A) Spikes in the partial-autocorrelation function indicate moving-average terms.

B) Spikes in the autocorrelation function indicate autoregressive terms.

C) Most economic data can be modeled as a higher-order ARMA(p, q) model.

D) For an ARMA(p, q) model, both the autocorrelation and partial-autocorrelation functions show abrupt stops.

E) All of the options are correct.

37) Which of the following is a stationary time series?

A) A series in which consecutive values depend only on the interval of time between them

B) A series whose mean is constant over time

C) A series with no trend

D) A series whose autocorrelation function shows no significant spikes

E) All of the options are correct.

38) Which of the following is not a way to induce stationarity out of non-stationary data?

A) First-difference the original series.

B) Second-difference the original series.

C) Transform the original series using logarithms.

D) Examine the data in percentage terms.

E) None of the options are correct.

39) ARMA models applied to non-stationary data are called

A) ARIMA(p, q) models.

B) ARMA(p, d, q) models.

C) ARIMA(p, d, q) models.

D) MA(p, q) models.

E) MA(d, q) models.

40) Integration refers to the

A) moving-average order of a time series.

B) autoregressive order of a time series.

C) number of differences required to induce data stationarity.

D) fit of an ARIMA model.

E) None of the options are correct.

41) Most economic time series are integrated of what order?

A) Zero

B) One

C) Two

D) Four

E) None of the options are correct.

42) What transformation will transform any trend in variance to a trend in the mean of a time series?

A) First-differencing the data.

B) Squaring the data.

C) Taking natural logarithms of the data.

D) Second-differencing the data.

E) All of the options are correct.

43) Which of the following models utilizes a transformed series to induce a stationary series?

A) ARIMA(1, 0, 1)

B) ARIMA(1, 0, 0)

C) ARIMA(1, 1, 1)

D) ARIMA(0, 0, 1)

E) None of the options are correct.

44) Which of the following is not a way to generate stationarity data out of non-stationary data?

A) First-difference the original series.

B) Second-difference the original series.

C) Transform the original series using logarithms.

D) Examine a non-linear form of the model.

E) All of the options are correct.

45) Which of the following best describes the autocorrelation function (ACF) of a non-stationary time series?

A) The ACF has several significant spikes.

B) The ACF has coefficients that very gradually go to zero.

C) The ACF has a spurious pattern of spikes as lags increase.

D) The null of zero autocorrelation is rejected for a significant amount of lags.

E) All of the options are correct.

46) Which of the following is not a characteristic of a time series best represented as an ARIMA(3, 0, 1) model?

A) The original series is stationary.

B) The autocorrelation function has one dominant spike.

C) The partial-autocorrelation function has one dominant spike.

D) The partial-autocorrelation function has three spikes.

E) None of the options are correct.

47) Which of the following is not a first step in the ARIMA model selection process?

A) Examine the autocorrelation function of the raw series.

B) Examine the partial-autocorrelation function of the raw series.

C) Test the data for stationarity.

D) Estimate an ARIMA(1, 1, 1) model for reference purposes.

E) All of the options are correct.

48) Which of the following rules is not a useful first step in the ARIMA model selection process?

A) If the autocorrelation function stops after q spikes, the appropriate model is a MA(q) type.

B) If the partial-autocorrelation function stops after p spikes, then the appropriate model is an AR(p) type.

C) If the autocorrelation function does not rapidly approach zero, then first-difference the data.

D) If the partial-autocorrelation function quickly approaches zero, then data first differencing may be recommended.

E) All of the options are correct.

49) The third step of the ARIMA model selection process is to diagnose whether the correct model has been chosen. Which of the following is not used in this diagnostic process?

A) The autocorrelation function of the forecast errors

B) The partial autocorrelation function of the forecast errors

C) The Ljung-Box Z statistic

D) The chi-square distribution

E) All of the options are correct.

50) The Q-statistic

A) is based on the estimated autocorrelation function.

B) is used to test whether a series is white noise or not.

C) follows the chi-square distribution.

D) tests whether the residual autocorrelations as a set are significantly different from zero.

E) All of the options are correct.

51) Using the Ljung-Box statistic applied to a sample with 30 degrees of freedom, we cannot reject the null of a white noise process if the sample Q-value is less than _______ at the 10% level of significance.

A) 10

B) 20

C) 30

D) 40

E) None of the options are correct.

52) The Q-statistic follows which probability distribution?

A) Normal

B) Standard Normal

C) t distribution

D) F distribution

E) None of the options are correct.

53) The diagnostic step in the Box-Jenkins model selection process essentially examines the forecast errors for

A) trend.

B) serial correlation.

C) independence.

D) white noise.

E) All of the options are correct.

54) What is the null hypothesis being tested using the Ljung-Box statistic?

A) The set of autocorrelations is jointly equal to zero.

B) The set of autocorrelations is jointly not equal to zero.

C) The set of autocorrelations is jointly equal to one.

D) The set of autocorrelations is between zero and four.

E) All of the options are correct.

55) What problem arises when applying ARIMA-type models to highly seasonal monthly data?

A) Autocorrelation

B) Heteroscedasticity

C) Extremely high-order AR and MA processes

D) Stationarity

E) All of the options are correct.

56) Besides using sophisticated ARIMA-type models capable of internally handling data seasonality, an alternative is to use

A) seasonal dummy variables.

B) trend dummy variables.

C) deseasonalized data, and then reseasonalize to generate forecasts.

D) Holt's smoothing.

E) All of the options are correct.

57)

What ARIMA model is suggested by the above correlogram?

A) ARIMA (2, 1, 2)

B) ARIMA (0, 0, 1)

C) ARIMA (2, 0, 4)

D) ARIMA (0, 1, 2)

58)

What ARIMA model is suggested by the correlogram above?

A) ARIMA (0, 1, 0)

B) ARIMA (0, 1, 1)

C) ARIMA (1, 1, 0)

D) ARIMA (1, 0, 0)

59)

The correlogram above suggests what type of ARIMA model?

A) ARIMA (1, 1, 1)

B) ARIMA (0, 0, 1)

C) ARIMA (1, 1, 2)

D) ARIMA (0, 2, 1)

60) Electricity Usage Data (144 monthly observations):

Correlogram of the original electricity usage data:

ARIMA Model:

This electricity usage result was obtained by setting the "seasonality" to "12" in the first ForecastX dialog box and using 30 lags for the Ljung-Box. The model was chosen automatically by ForecastX. The critical value of the Ljung-Box with 30 − 2 = 28 degrees of freedom is about 38.

In the electricity usage data above

A) the chosen ARIMA model took into account seasonality.

B) the chosen ARIMA model does not include any adjustment for seasonality.

C) the chosen ARIMA model appears to suffer from autocorrelation.

D) the chosen ARIMA model appears to suffer from multicollinearity.

61) Electricity Usage Data (144 monthly observations):

Correlogram of the original electricity usage data:

ARIMA Model:

This electricity usage result was obtained by setting the "seasonality" to "12" in the first ForecastX dialog box and using 30 lags for the Ljung-Box. The model was chosen automatically by ForecastX. The critical value of the Ljung-Box with 30 − 2 = 28 degrees of freedom is about 38.

In the electricity usage model above

A) the residuals do not appear to be white noise.

B) the "Q" statistic is not statistically significant.

C) there is one autoregressive term.

D) there are no seasonal terms.

62)

Consider the ARIMA model specified above.

A) This is an MA1 model.

B) This is an AR1 model.

C) There is one degree of normal differencing used.

D) The model adjusts for seasonality.

63)

The ARIMA model above represents an analysis of data with 200 observations and the default values for the diagnostic statistics. Is the "Q" statistic acceptable?

A) Yes, because the critical value is about 26.

B) Yes, because the critical value is about 32.

C) No, because the critical value is about 17.

D) No, because the critical value is about 6.

64)

The ARIMA model above was estimated from 200 observations of data. Twelve lags were used to calculate the "Q" statistic.

The ARIMA model above would require how many degrees of freedom in the test statistic to determine if the model is appropriate?

A) 3

B) 6

C) 10

D) 14

65)

The ARIMA model above was estimated using 78 quarterly observations. Using the recommended diagnostic statistic (with the recommended lag structure), examine whether this is an appropriate model.

A) The model is appropriate because the critical value is about 17.

B) The model is appropriate because the critical value is about 33.

C) The model is inappropriate because the critical value is about 8.

D) The model is inappropriate because the critical value is about 12.

66)

The correlogram above was calculated from the residuals to an ARIMA model that analyzed quarterly data.

A) The model appears to have produced white noise.

B) The model does not seem to be an appropriate model.

C) The model appears to be seasonal.

D) The model could be an AR16.

67) A possible problem (or at least a consideration) that should be taken into account when using ARIMA would be

A) multicollinearity.

B) autocorrelation.

C) overfitting.

D) the Slutsky-Yule effect.

68) In order to detect overfitting the researcher

A) should examine different samples of the data to see if that produces unstable results.

B) should note that an overfit model will have a low forecast error.

C) will usually consult the Durbin-Watson statistic.

D) could use the t-statistics of the individual coefficients.

69)

Examine the autocorrelation plot shown. What would likely be the dominant cause of this pattern?

A) Random variation

B) Cyclicality

C) Seasonality

D) Trend

70)

Examine the autocorrelation plot shown. What might cause this pattern?

A) Trend mixed with seasonality

B) Trend mixed with cyclicality

C) Seasonality mixed with cyclicality

D) Seasonality alone

71) ARIMA (Box-Jenkins) models are able to replicate almost any pattern found in data. While this is an attractive characteristic of the estimation process, it may also cause a problem not encountered with many other estimating models. What is that problem?

A) Hildreth-Lu Complex

B) Heteroscedasticity

C) Overfitting

D) Underfitting