Quiz 7

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

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

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

gradually approach zero; dramatically cut off to zero.

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

two

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

Negative at first, then positive and declining to zero Cyclically declining to zero Positive at first, then negative and increasing to zero Exponentially declining to zero All of the options are correct.

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)?

2; 1

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

AR(1)

ARMA models applied to non-stationary data are called

ARIMA(p, d, q) models.

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. MA(3)

ARMA(1, 4)

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

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

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.

MA(4)

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

None of the options are correct.

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

None of the options are correct.

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

The partial-autocorrelation function has one dominant spike.

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

The set of autocorrelations is jointly equal to zero.

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 Value Method Selected Box Jenkins Model Selected ARIMA(0,0,1) × (0,0,0) T-Test For Constant 39.07 T-Test For Non Seasonal MA − 11.13 Consider the ARIMA model specified above.

This is an MA1 model.

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

Use of explanatory variables

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

autocorrelation function.

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

both autocorrelation and partial-autocorrelation functions.

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

cyclically declines to zero as lag length increases. has one large negative spike and then goes to zero. exponentially declines to zero as lag length increases. has one large positive spike and then goes to zero. All of the options are correct.

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

he null of zero autocorrelation is rejected for a significant amount of lags. The ACF has several significant spikes. The ACF has coefficients that very gradually go to zero. The ACF has a spurious pattern of spikes as lags increase. All of the options are correct.

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

is not an adequate forecasting model.

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

may look quite dissimilar in the nature of adjustment. may both show spikes. may both show monotonically declining estimates. may look amazingly similar. All of the options are correct.

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

number of AR and MA terms that are significant.

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

number of differences required to induce data stationarity.

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

one two three four All of the options are correct.

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

one two three four None of the options are correct.

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

partial autocorrelation function.

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

produces white noise forecast errors.

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

serially independent.

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

that they are opposites.

Electricity Usage Data (144 monthly observations): 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.

the chosen ARIMA model took into account seasonality.

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

three

Autoregressive models are best described as

weighted averages of lagged series values plus white noise