Question 1

If a forecasting model produces forecast errors (residuals) that are negatively correlated, then we expect a negative residual to be followed by another negative residual to be followed by another negative residual and so forth.

Accepted Answer

Negatively correlated residuals indicate that a negative residual is likely to be followed by a positive residual, and vice versa, suggesting a pattern of alternation rather than continuation.

Question 2

Large values of the Durbin-Watson d statistic indicate that positive autocorrelation among the forecast errors exists.

Accepted Answer

The Durbin-Watson d statistic is used to detect the presence of autocorrelation in the residuals from a regression analysis. A value close to 2 suggests no autocorrelation, while values deviating significantly from 2 indicate positive or negative autocorrelation, with values less than 2 suggesting positive autocorrelation and values greater than 2 suggesting negative autocorrelation.

Question 3

To deseasonalize a time series, assuming a multiplicative model, the observed values are divided by the appropriate seasonal index.

Accepted Answer

In a multiplicative model, the observed values are indeed divided by the seasonal index to deseasonalize the time series, as this process helps in removing the seasonal component to analyze the underlying trend and cyclical components more clearly.

Question 4

The reason for testing for the presence of autocorrelation in a regression-based trend forecasting model is that one assumption of the regression analysis is that the residuals are not correlated.

Accepted Answer

Autocorrelation refers to the correlation of a signal with a delayed copy of itself. In the context of regression analysis, the assumption is that the residuals (errors) from the model are independent of each other. If residuals are correlated (autocorrelation), it violates the assumption of independence, potentially leading to inefficient estimates and invalid statistical inferences. Testing for autocorrelation helps ensure the validity of the regression model's assumptions.

Question 5

If the observed value in a time series for period 3 is yt = 128, and the seasonal index that applies to period 3 is 1.20, then the deseasonalized value for period 3 is 153.6

Accepted Answer

The deseasonalized value is calculated by dividing the observed value by the seasonal index, so for period 3, it would be $128 / 1.20 = 106.67$, not 153.6.

Question 6

If the forecast errors are autocorrelated, this is a good indication that the model has been specified correctly.

Accepted Answer

Autocorrelated forecast errors suggest that the model has missed some information that is present in the error terms, indicating a model misspecification or that some of the time series structure has not been captured.

Question 7

An advantage of exponential smoothing techniques over a regression-based trend model is that the exponential smoothing model allows us to weigh each observation equally, thereby giving a fairer method of developing a forecast.

Accepted Answer

Exponential smoothing techniques give more weight to recent observations, unlike regression-based models which can weigh observations equally or based on other criteria.

Question 8

If the Durbin-Watson d statistic has a value close to 2, there is reason to believe that there is no autocorrelation between the forecast errors.

Accepted Answer

The Durbin-Watson d statistic tests for autocorrelation in the residuals from a statistical regression analysis. A value close to 2 suggests there is no autocorrelation.

Question 9

Recently, a manager for a major retailer computed the following seasonal indexes:  The manager then developed the following least squares trend model based on the past five years of quarterly data: = 200 + 11.5t. Based on this, the seasonally adjusted forecast for quarter 25, which is the winter quarter, is 489.11

Accepted Answer

The answer of Recently, a manager for a major retailer...

Question 10

If a time series involves monthly data there will be a total of 12 seasonal indexes.

Accepted Answer

In a time series with monthly data, there are 12 months in a year, so there will be 12 seasonal indexes, one for each month, to account for seasonal variations.

Question 11

Herb Criner, an analyst for the Folgerty Company, recently gave a report in which he stated that the annual sales forecast based on 20 years of annual sales data was done using a seasonally adjusted, trend- based forecasting technique. Given the information presented here, this statement has the potential to be credible.

Accepted Answer

The answer of Herb Criner, an analyst for the Folgerty...

Question 12

The Durbin-Watson test for autocorrelation can be reliably applied to any sample sizes.

Accepted Answer

The Durbin-Watson test's reliability can be affected by the sample size, as small sample sizes may not provide accurate estimates of autocorrelation.

Question 13

In a single exponential smoothing model, finding the forecast value for each period requires having the actual and forecasted values from the proceeding period. The first period should use an estimated average value based on previous estimates.

Accepted Answer

The answer of In a single exponential smoothing model, finding...

Question 14

If the Durbin-Watson test leads you to reject the null hypothesis, then you are concluding that the forecast errors are positively autocorrelated.

Accepted Answer

Rejecting the null hypothesis in a Durbin-Watson test indicates evidence against the null hypothesis of no autocorrelation, suggesting that there is autocorrelation in the residuals, which can often be positive.

Question 15

It is possible to conduct a statistical test for autocorrelation using the Durbin-Watson test and not be able to make a definitive conclusion about whether there is autocorrelation or not based on the data.

Accepted Answer

The Durbin-Watson test statistic can fall into an inconclusive range, where it neither strongly supports the presence nor the absence of autocorrelation, requiring further analysis or different tests to make a definitive conclusion.

Question 16

A seasonally unadjusted forecast is one that is made from seasonal data without any adjustment for the seasonal component in the time series.

Accepted Answer

A seasonally unadjusted forecast is indeed made from seasonal data without adjusting for the seasonal variations, meaning it does not account for regular patterns that occur within specific time periods.

Question 17

When using the multiplicative time-series model to determine the seasonal indexes, the first step is to isolate the seasonal and random components from the cyclical and trend components.

Accepted Answer

The multiplicative time-series model involves decomposing the time series into its components, and the first step is to separate the seasonal and random components from the trend and cyclical components to analyze them individually.

Question 18

If you suspect that a nonlinear trend exists in your data, one way to deal with it in a trend-based forecasting application is to transform the independent variable, for example by squaring the time measure or maybe taking the square-root of the time measure.

Accepted Answer

Transforming the independent variable, such as by squaring or taking the square root of the time measure, can help linearize a nonlinear trend, making it easier to apply linear trend-based forecasting methods.

Question 19

The purpose of deseasonalizing a time series is that a strong seasonal pattern may make it difficult to see a trend in the time series.

Accepted Answer

Deseasonalizing a time series removes the seasonal component of the data, making it easier to identify and analyze underlying trends, cycles, and other patterns without the noise of seasonal effects.

Question 20

Recently, a manager for a major retailer computed the following seasonal indexes:  Note that the index for Summer Qtr is missing. However, it can be determined that the index for that period is approximately 1.03

Accepted Answer