Exam 18: Time Series and Forecasting

Exhibit 18.2.The following table includes the information about a monthly time series. Refer to Exhibit 18.2.When the exponential smoothing method with α = 0.1 and α = 0.5 is applied,what is the speed of decline for which the mean absolute deviation (MAD)is better? What is this mean?

Exhibit 18.4.The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for the last four years: Refer to Exhibit 18.4.What is the seasonal index for the fourth quarter?

The exponential trend model is attractive when the increase in the series gets larger over time.

Exhibit 18.8.Quarterly sales of a department store for the last 7 years are given in the following table. The Excel scatterplot shown above indicates that the quarterly sales have an increasing trend and seasonality.Therefore,the linear regression model,Sales = β₀ + β₁Qtr1 + β₂Qtr2 + β₃Qtr3 + β₄t + ε with three seasonal dummy variables Qtr1,Qtr2 and Qtr3,and the decomposition method are proposed to make sales forecasts.For the regression model,the following Excel partial output is available. Refer to Exhibit 18.8.Using the regression equation for the linear trend model with seasonal dummy variables,what is the sales forecast for the fourth quarter of Year 8?

When the forecasting method of seasonal dummy variables is applied on a quarterly time series,four dummy variables are needed.

Exhibit 18.8.Quarterly sales of a department store for the last 7 years are given in the following table. The Excel scatterplot shown above indicates that the quarterly sales have an increasing trend and seasonality.Therefore,the linear regression model,Sales = β₀ + β₁Qtr1 + β₂Qtr2 + β₃Qtr3 + β₄t + ε with three seasonal dummy variables Qtr1,Qtr2 and Qtr3,and the decomposition method are proposed to make sales forecasts.For the regression model,the following Excel partial output is available. Refer to Exhibit 18.8.(Use Excel or statistical software. )Using the decomposition method, A)compute the adjusted seasonal indices for the four quarters. B)find the linear trend equation for the seasonally adjusted quarterly sales. C)make the sales forecasts for the first and fourth quarter of Year 8.

Which model is considered for a quarterly time series that seems to change on average by a fixed amount and seems to have seasonality?

Which model is assumed for a quarterly time series that seems to grow on average by an increasing amount (or decline by a decreasing amount)and seems to have seasonality?

When the decomposition model, ,is applied,forecasts are made as ,where represents the estimated trend for seasonally adjusted time series for period t,and is the seasonal index for period t.

Exhibit 18.8.Quarterly sales of a department store for the last 7 years are given in the following table. The Excel scatterplot shown above indicates that the quarterly sales have an increasing trend and seasonality.Therefore,the linear regression model,Sales = β₀ + β₁Qtr1 + β₂Qtr2 + β₃Qtr3 + β₄t + ε with three seasonal dummy variables Qtr1,Qtr2 and Qtr3,and the decomposition method are proposed to make sales forecasts.For the regression model,the following Excel partial output is available. Refer to Exhibit 18.8.Using the regression equation for the linear trend model with seasonal dummy variables,what is the sales forecast for the first quarter of Year 8?

Which of the following is not true of a time series with a cyclical component?

Exhibit 18.2.The following table includes the information about a monthly time series. Refer to Exhibit 18.2.When the exponential smoothing method with α = 0.1 and α = 0.5 is applied,what is the speed of decline for which the mean square error (MSE)is better? What is this mean?

Exhibit 18.8.Quarterly sales of a department store for the last 7 years are given in the following table. The Excel scatterplot shown above indicates that the quarterly sales have an increasing trend and seasonality.Therefore,the linear regression model,Sales = β₀ + β₁Qtr1 + β₂Qtr2 + β₃Qtr3 + β₄t + ε with three seasonal dummy variables Qtr1,Qtr2 and Qtr3,and the decomposition method are proposed to make sales forecasts.For the regression model,the following Excel partial output is available. Refer to Exhibit 18.8.What is the regression equation for the linear trend model with seasonal dummy variables?

Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.Using the linear trend equation,one can say that the predicted revenue increases by

Quantitative forecasting procedures are based on the judgment of the forecaster,who uses prior experience and expertise to make forecasts.

Which of the following types of trend models will best suit a series where the increase in value of the series gets larger over time?

Exhibit 18.8.Quarterly sales of a department store for the last 7 years are given in the following table. The Excel scatterplot shown above indicates that the quarterly sales have an increasing trend and seasonality.Therefore,the linear regression model,Sales = β₀ + β₁Qtr1 + β₂Qtr2 + β₃Qtr3 + β₄t + ε with three seasonal dummy variables Qtr1,Qtr2 and Qtr3,and the decomposition method are proposed to make sales forecasts.For the regression model,the following Excel partial output is available. Refer to Exhibit 18.8.(Use Excel. )Using MSE and MAD,compare the linear trend equation with seasonal dummy variables, , and the decomposition method equation, with and the quarterly seasonal indices: 0.9322,1.0066,0.9441,and 1.1171.Which of the two corresponding forecasting models is recommended?

In the time series decomposition method,to obtain the _______,we divide the original observations by their corresponding adjusted seasonal indices.

Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is an exponential trend equation?

Which of the following is a criticism made of qualitative forecasts?