Exam 20: Time-Series Analytics and Forecasting

Carpet Outlet A carpet outlet has been keeping daily sales records over the past four weeks as shown below. ​ ​ -{Carpet Outlet Narrative} Use the regression technique to calculate the linear trend line.

Suppose that we calculate the four-period moving average of the following time series The centered moving average for period 3 is:

The time-series model y_t = T_t×C_t×S_t×R_t is used for forecasting,where T_t,C_t,S_t,and R_t are respectively the trend,cyclical,seasonal,and random variation components of the time series,and y_t is the value of the time series at time t.The following estimates are obtained: = 120, = 1.02, = 0.95,and = 0.90.The model will produce a forecast of:

The trend equation for annual sales data (in millions of dollars)is = 65 + 2.5t,where t = 1 for 2011.The monthly seasonal index for December is 0.97.The forecasted sales' value for December of 2020 is:

The level of construction employment in West Virginia is lowest during the winter.A model designed to forecast construction employment in Charleston should use:

The purpose of using the moving average is to take away the short-term seasonal and random variation,leaving behind a combined trend and cyclical movement.

The Pyramids of Giza The Pyramids of Giza is one of the most visited monuments in Egypt.The number of visitors per quarter has been recorded (in thousands)as shown in the accompanying table: ​ ​ -{The Pyramids of Giza Narrative} Calculate the four-quarter centered moving averages.

The mean absolute deviation is the summation of the residuals divided by the sample size.

Carpet Outlet A carpet outlet has been keeping daily sales records over the past four weeks as shown below. ​ ​ -{Carpet Outlet Narrative} What do the daily indexes tell us?

Motor Oil Sales As part of an effort to forecast future sales,the monthly motor oil sales (in thousands of gallons)for the past 10 months are recorded.These data are shown below. ​ ​ -{Motor Oil Sales Narrative} Draw the time series and the two sets of exponentially smoothed values.Does there appear to be a trend component in the time series?

Biodiesel Sales Biodiesel (a vegetable oil or animal fat based diesel fuel)sales in Nebraska have been recorded over the past 10 months as shown below. ​ ​ -{Biodiesel Sales Narrative} Draw the time series and the two sets of exponentially smoothed values.Does there appear to be a trend component in the time series?

Liquor Sales The number of cases of liquor sold by a liquor wholesaler in an 8-year period follows. ​ ​ -{Liquor Sales Narrative} A centered 3-year moving average is to be constructed for the liquor sales.The moving average for 2012 is ____________________.

Quarterly enrollments in business statistics class for three years are shown in the table below.Compute the four-quarter centered moving averages.

The formula S_t = wy_t + (1 −w)St−₁ is used in time-series forecasting with exponential smoothing,where S_t is the exponentially smoothed time series at time t,y_t is the value of the time series at time t,and w is the smoothing constant.The forecasted value at time t + 1 where w = .4 is given by:

In forecasting,we use data from the past in predicting the future value of the variable of interest.

The Pyramids of Giza The Pyramids of Giza is one of the most visited monuments in Egypt.The number of visitors per quarter has been recorded (in thousands)as shown in the accompanying table: ​ ​ -{The Pyramids of Giza Narrative} Use the seasonal indexes computed in the previous question to deseasonalize the original time series data,and plot the deseasonalized time series.

Seasonal variations will not be present in a deseasonalized time series.

Which of the following methods is appropriate for forecasting a time series when the trend,cyclical,and seasonal components of the series are not significant?

The following is the list of mean absolute deviation (MAD)statistics for each of the models you have estimated from time-series data: Based on the MAD criterion,the most appropriate model is

Liquor Sales The number of cases of liquor sold by a liquor wholesaler in an 8-year period follows. ​ ​ -{Liquor Sales Narrative} Exponential smoothing with a weight or smoothing constant of 0.2 will be used to smooth the liquor sales.The smoothed value for 2014 is_________________.