Test bank for forecasting and predictive analytics with forecast x tm 7th edition barry keating j ho

Test Bank for Forecasting and Predictive Analytics with Forecast X (TM), 7th Edition, Barry

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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.

Answer: A Difficulty: 1 Easy Topic: The Philosophy of Box-Jenkins Learning Objective: 7-02 Explain the philosophy of ARIMA modelling.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 1 Easy Topic: Introduction Learning Objective: 7-01 Define ARIMA: (Autoregressive Integrated Moving Average).

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: D Difficulty: 1 Easy Topic: Introduction Learning Objective: 7-01 Define ARIMA: (Autoregressive Integrated Moving Average).

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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.

Answer: D Difficulty: 1 Easy Topic: The Philosophy of Box-Jenkins Learning Objective: 7-02 Explain the philosophy of ARIMA modelling.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: C Difficulty: 1 Easy Topic: The Philosophy of Box-Jenkins Learning Objective: 7-02 Explain the philosophy of ARIMA modelling.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: A Difficulty: 1 Easy Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

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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.

Answer: C Difficulty: 1 Easy Topic: The Philosophy of Box-Jenkins Learning Objective: 7-02 Explain the philosophy of ARIMA modelling.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: C Difficulty: 1 Easy Topic: The Philosophy of Box-Jenkins Learning Objective: 7-02 Explain the philosophy of ARIMA modelling.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 1 Easy Topic: Introduction Learning Objective: 7-02 Explain the philosophy of ARIMA modelling.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: C Difficulty: 1 Easy Topic: The Philosophy of Box-Jenkins Learning Objective: 7-02 Explain the philosophy of ARIMA modelling.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: C Difficulty: 1 Easy Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: D Difficulty: 1 Easy Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: D Difficulty: 1 Easy Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 1 Easy Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: E Difficulty: 1 Easy Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: D Difficulty: 2 Medium Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: E Difficulty: 2 Medium Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: C Difficulty: 1 Easy Topic: Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: B Difficulty: 1 Easy Topic: Autoregressive Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

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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.

Answer: D Difficulty: 1 Easy Topic: Autoregressive Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: A Difficulty: 2 Medium Topic: Autoregressive Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: E Difficulty: 1 Easy Topic: Autoregressive Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 2 Medium Topic: Autoregressive Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: A Difficulty: 1 Easy Topic: Autoregressive Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 1 Easy Topic: Autoregressive Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: D Difficulty: 1 Easy Topic: Autoregressive Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

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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.

Answer: C Difficulty: 1 Easy Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 1 Easy Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: B Difficulty: 1 Easy Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

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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.

Answer: C Difficulty: 1 Easy Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: B Difficulty: 1 Easy Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: E Difficulty: 2 Medium Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: A Difficulty: 1 Easy Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic

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34) A time series that can be best represented as an ARMA(2, 0) model has a partialautocorrelation 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.

Answer: E Difficulty: 1 Easy Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: A Difficulty: 1 Easy Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 2 Medium Topic: Mixed Autoregressive and Moving-Average Models Learning Objective: 7-04 Explain in detail the two contributing models: the autoregressive model and the moving average model.

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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.

Answer: E Difficulty: 1 Easy Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 1 Easy Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: C Difficulty: 2 Medium Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

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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.

Answer: C Difficulty: 1 Easy Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: B Difficulty: 1 Easy Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: C Difficulty: 1 Easy Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

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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.

Answer: C Difficulty: 2 Medium Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: D Difficulty: 1 Easy Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 2 Medium Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

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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.

Answer: C Difficulty: 2 Medium Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: D Difficulty: 1 Easy Topic: The Box-Jenkins Identification Process Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: D Difficulty: 1 Easy Topic: Stationarity Learning Objective: 7-05 Discuss the importance of stationarity and demonstrate how to handle nonstationarity.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: C Difficulty: 1 Easy Topic: The Box-Jenkins Identification Process Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

Accessibility: Keyboard Navigation Gradable: automatic

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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.

Answer: E Difficulty: 1 Easy Topic: The Box-Jenkins Identification Process Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: D Difficulty: 2 Medium Topic: The Box-Jenkins Identification Process Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: E Difficulty: 1 Easy Topic: The Box-Jenkins Identification Process Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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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.

Answer: E Difficulty: 1 Easy Topic: The Box-Jenkins Identification Process Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: A Difficulty: 1 Easy Topic: The Box-Jenkins Identification Process Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: C Difficulty: 1 Easy Topic: Forecasting Seasonal Time Series Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

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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.

Answer: C Difficulty: 1 Easy Topic: Forecasting Seasonal Time Series Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

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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) Answer: B Difficulty: 1 Easy Topic: ARIMA: A Set of Numerical Examples Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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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) Answer: D Difficulty: 1 Easy Topic: ARIMA: A Set of Numerical Examples Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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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) Answer: B Difficulty: 1 Easy Topic: ARIMA: A Set of Numerical Examples Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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60) Electricity Usage Data (144 monthly observations):

Correlogram of the original electricity usage data:

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ARIMA Model: Audit Trail - Statistics Accuracy Measures

Value

AIC

2,234.86

BIC Mean Absolute Percentage Error (MAPE) R-Square Adjusted R-Square Root Mean Square Error Theil

2,240.80

Method Statistics Method Selected Model Selected T-Test For Non Seasonal AR T-Test For Seasonal MA

Forecast Statistics Durbin Watson(12) Mean

Value 1.96 17,474.95

2.18% Median

17,260.45

83.94% Variance 83.82% Ljung-Box 559.54 0.42

1,962,764.37 36.38

Value Box Jenkins ARIMA(1,0,0) × (0,1,1) 6.15 6.69

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.

Answer: A Difficulty: 2 Medium Topic: Forecasting Seasonal Time Series Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

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61) Electricity Usage Data (144 monthly observations):

Correlogram of the original electricity usage data:

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ARIMA Model: Audit Trail - Statistics Accuracy Measures

Value

AIC

2,234.86

BIC Mean Absolute Percentage Error (MAPE) R-Square Adjusted R-Square Root Mean Square Error Theil

2,240.80

Forecast Statistics Durbin Watson(12) Mean

Value 1.96 17,474.95

2.18% Median

17,260.45

83.94% Variance 83.82% Ljung-Box 559.54 0.42

1,962,764.37 36.38

Method Statistics Method Selected Model Selected T-Test For Non Seasonal AR T-Test For Seasonal MA

Value Box Jenkins ARIMA(1,0,0) × (0,1,1) 6.15 6.69

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.

Answer: C Explanation: This result is obtained by setting the "seasonality" to "12" in the first 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. The model is acceptable.

Difficulty: 2 Medium Topic: Total Houses Sold Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

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62) Audit Trail - Statistics Accuracy Measures Value Forecast Statistics Value AIC 75.20 Durbin-Watson(1) 2.08 BIC 81.80 Mean 0.80 Mean Absolute Percentage Error (MAPE) 43.45% Max 1.64 R-Square 35.63% Min 0.14 Adjusted R-Square 35.30% Sum Squared Deviation 25.97 Root Mean Square Error 0.29 Range 1.50 Theil 0.63 Ljung-Box 7.33

Method Statistics Method Selected Model Selected T-Test For Constant T-Test For Non Seasonal MA

Value Box Jenkins ARIMA(0,0,1) × (0,0,0) 39.07 − 11.13

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.

Answer: A Difficulty: 2 Medium Topic: Total Houses Sold Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

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63) Audit Trail - Statistics Accuracy Measures Value Forecast Statistics Value AIC 81.29 Durbin-Watson(1) 1.92 BIC 87.88 Mean 0.94 Mean Absolute Percentage Error (MAPE) 33.12% Max 1.71 R-Square 23.75% Min 0.24 Adjusted R-Square 23.37% Sum Squared Deviation 22.60 Root Mean Square Error 0.29 Range 1.47 Theil 0.77 Ljung-Box 23.28

Method Statistics Method Selected Model Selected T-Test For Non Seasonal AR T-Test For Constant

Value Box Jenkins ARIMA(1,0,0) × (0,0,0) 8.00 15.18

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.

Answer: C Difficulty: 2 Medium Topic: ARIMA: A Set of Numerical Examples Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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64) Audit Trail - Statistics Accuracy Measures AIC BIC Mean Absolute Percentage Error (MAPE) R-Square Adjusted R-Square Root Mean Square Error Theil

Method Statistics Method Selected Model Selected T-Test For Non Seasonal AR T-Test For Non Seasonal AR

Value 95.61 102.21

Forecast Statistics Durbin-Watson(1) Mean

Value 1.99 4.40

8.06% Max

6.36

91.56% Min Sum Squared 91.51% Deviation 0.30 Range 0.96 Ljung-Box

0.04 219.27 6.32 4.41

Value Box Jenkins ARIMA(2,1,0) × (0,0,0) −2.51 −1.66

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 Answer: C Difficulty: 2 Medium Topic: ARIMA: A Set of Numerical Examples Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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65) Audit Trail - Statistics Accuracy Measures AIC BIC Mean Absolute Percentage Error (MAPE) R-Square Adjusted R-Square Root Mean Square Error Theil

Method Statistics Method Selected Model Selected T-Test For Non Seasonal AR T-Test For Non Seasonal AR T-Test For Constant T-Test For Non Seasonal MA T-Test For Seasonal MA T-Test For Seasonal MA

Value 1,017.13 1,031.27

Forecast Statistics Durbin-Watson Mean

Value 1.96 1,748.21

7.04% Standard Deviation

223.30

53.03% Max 49.77% Min 152.05 Mode 0.69 Range Ljung-Box

2,272.60 1,281.30 1,878.20 991.30 13.48

Value Box Jenkins ARIMA(2,0,1) × (0,0,2) 0.05 0.02 0.01 0.00 −1.34 −1.02

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.

Answer: A Explanation: Because this is a seasonal model (as estimated by ForecastX) the number of lags used by the researcher should be 16 (i.e., four times the number of seasons). Thus the critical value is found in the chi-square with 16 – 5 degrees of freedom to be about 17.

Difficulty: 2 Medium Topic: ARIMA: A Set of Numerical Examples Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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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.

Answer: A Difficulty: 1 Easy Topic: ARIMA: A Set of Numerical Examples Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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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.

Answer: C Difficulty: 1 Easy Topic: Overfitting Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

Accessibility: Keyboard Navigation Gradable: automatic 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.

Answer: A Difficulty: 1 Easy Topic: Overfitting Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

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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 Answer: D Difficulty: 1 Easy Topic: ARIMA: A Set of Numerical Examples Learning Objective: 7-06 Estimate an ARIMA model with ForecastX and use the appropriate diagnostic statistics to judge its fit and/or accuracy.

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Test Bank for Forecasting and Predictive Analytics with Forecast X (TM), 7th Edition, Barry

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 Answer: A Difficulty: 1 Easy Topic: Forecasting Seasonal Time Series Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

Accessibility: Keyboard Navigation Gradable: automatic 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 Answer: C Difficulty: 1 Easy Topic: Overfitting Learning Objective: 7-07 Employ an ARIMA model for forecasting time-series data.

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