Question 1

In the Durbin-Watson test,if the calculated d-statistic is greater than the upper value of the d-statistic,then:

Accepted Answer

If the calculated d-statistic is greater than the upper value, it indicates no evidence of positive autocorrelation, so we do not reject the null hypothesis that the error terms are not autocorrelated.

Question 2

Box-Jenkins methodology begins by determining if the time series under consideration is stationary.

Accepted Answer

This statement is true, as Box-Jenkins methodology requires the time series to be stationary before proceeding with model identification, estimation, and diagnostics.

Question 3

All of the following are forecasting methods except:

Accepted Answer

MAD autocorrelation is not a forecasting method, but rather a measure of forecast accuracy. The other choices (Holt-Winters double exponential smoothing, Box-Jenkins, and time series regression) are all commonly used forecasting methods.

Question 4

Which of the following is not a component of time series?

Accepted Answer

Smoothing constant is not a component of time series. It is a parameter used in exponential smoothing models to control the weight given to the most recent observations in the forecast.

Question 5

Box-Jenkins models describe the future time series value by using past time series values,which are called autoregressive terms.

Accepted Answer

Box-Jenkins models are based on autoregressive (AR), moving average (MA), and differencing (D) terms, which use past time series values to predict future values.

Question 6

Box-Jenkins methodology transforms nonstationary time series values into stationary time series values.

Accepted Answer

The Box-Jenkins methodology involves a series of steps, one of which is data transformation to achieve stationarity. This is necessary because many time series models rely on the assumption of stationarity, which means that the statistical properties of the series remain constant over time. Nonstationary series, by contrast, show trends, seasonality, or other patterns that change over time, making it difficult to identify underlying patterns or forecast future values. The Box-Jenkins approach includes various techniques such as differencing, logarithmic or power transformations, seasonal adjustments, and others to achieve stationarity.

Question 7

Box-Jenkins models describe the future time series value by using a seasonal moving-average term when the SPAC dies down fairly quickly (at lags 12 and 24)and the SPC has a spike at lag 12 and cuts off after lag 12.

Accepted Answer

The description provided in the statement is consistent with the characteristics of a Box-Jenkins model with a seasonal moving-average term. The seasonal term captures the periodic fluctuations in the data, such as the spike at lag 12 and the cut-off after lag 12 for the SPC. Additionally, the SPAC dying down fairly quickly at lags 12 and 24 suggests that an autoregressive term may not be required in the model.

Question 8

Increasing seasonal variation implies that the time series is nonstationary with respect to its variance.

Accepted Answer

Seasonal variation is a type of nonstationarity that affects the variance of a time series. By definition, if the seasonal variation is increasing, then the variability of the time series is changing over time, which means that the time series is not stationary in terms of its variance. Therefore, the statement is true.

Question 9

If the errors produced by a forecasting method for 3 observations are +3,+3,and -3,then what is the mean absolute deviation?

Accepted Answer

The mean absolute deviation (MAD) is calculated by finding the absolute value of each error, adding them together, and dividing by the number of observations. 
Here, the absolute values of the errors are 3, 3, and 3. 
Adding them together, we get 9. 
Dividing by the number of observations (which is 3), we get 3. 
Therefore, the MAD is 3.

Question 10

When a forecaster uses the ______________ method,she or he assumes that the time series components are changing slowly over time.

Accepted Answer

Exponential smoothing is a method where the forecast for the next period is based on the weighted average of past observations, with more weight given to more recent observations. This method assumes that the time series components are changing slowly over time, which makes it a good choice for forecasting data that is not subject to sudden or drastic changes.

Question 11

When a forecaster uses the _________________ method,she or he assumes that the time series components are changing quickly over time.

Accepted Answer

The Box-Jenkins method is used when time series components are changing quickly over time, as it involves identifying and estimating models that can capture complex patterns and dynamics in the data.

Question 12

Box-Jenkins models describe the future time series value by using past error terms,which are called moving-average terms.

Accepted Answer

Box-Jenkins models do utilize past error terms, called moving-average terms, to predict future values of a time series.

Question 13

If the errors produced by a forecasting method for 3 observations are -1,-2,and -6,then what is the mean squared error (deviation)?

Accepted Answer

The answer of If the errors produced by a forecasting...

Question 14

To carry out combined regular and seasonal differencing,you take the seasonal differences of the regular differences.

Accepted Answer

The answer of To carry out combined regular and seasonal...

Question 15

Box-Jenkins models describe the future time series value by using a nonseasonal autoregressive term when the SAC dies down fairly quickly (at lags 12 and 24)and the SPAC has a spike at lag 12 and cuts off after lag 12.

Accepted Answer

Box-Jenkins models use seasonal autoregressive terms when the SPAC has a spike at a seasonal lag (e.g., lag 12) and cuts off, indicating a seasonal pattern rather than a nonseasonal one.

Question 16

Cyclical differencing is one of the types of differencing used by the Box-Jenkins methodology.

Accepted Answer

The answer of Cyclical differencing is one of the types...

Question 17

For monthly seasonal data,we define the nonseasonal level of the Sample Autocorrelation Function (SAC)to be lags 12 and 24.

Accepted Answer

The nonseasonal level of the SAC for monthly seasonal data is defined at lag 1 and 2, not 12 and 24.

Question 18

The no-trend time series model is given by:

Accepted Answer

The no-trend time series model only includes a constant term, so it is given by TR_t = B₀.

Question 19

A time series is considered stationary if the statistical properties follow a trend of cyclical variation.

Accepted Answer

A time series is considered stationary if its statistical properties do not vary with time. This means that the mean, variance, and autocovariance of the series remain constant over time. A trend or cyclical variation violates this definition of stationarity.

Question 20

If the errors produced by a forecasting method for 3 observations are +3,+3,and -3,then what is the mean squared error?

Accepted Answer

MSE = [(3)² + (3)² + (−3)²]/3 = (9 + 9 + 9)/3 = 9

Quiz 16: Time Series Forecasting and Index Numbers