Exam 20: Time-Series Analysis and Forecasting

The results of a quadratic model fit to time series data were $\tilde { y } _ { t }$ = 8.5 - 0.25t + 2.5t²,where t = 1 for 1998.The forecasted value for 2005 is 129.25.

The cyclical variation component of a time series measures the over-all general directional movement over a long period of time.

Coffee Imports The coffee imports (in millions of dollars)from a Latin American country for 10 years are shown below. Year t Exports 2011 1 96 2012 2 110 2013 3 125 2014 4 141 2015 5 132 2016 6 126 2017 7 118 2018 8 125 2019 9 133 2020 10 148 -{Coffee Imports Narrative} Use the regression technique to calculate the linear trend line.

Liquor Sales The number of cases of liquor sold by a liquor wholesaler in an 8-year period follows. 2011 270 2012 356 2013 398 2014 456 2015 358 2016 500 2017 410 2018 376 -{Liquor Sales Narrative} Exponential smoothing with a weight or smoothing constant of 0.2 will be used to forecast liquor sales.The forecast for 2019 is ____________________.

Liquor Sales The number of cases of liquor sold by a liquor wholesaler in an 8-year period follows. 2011 270 2012 356 2013 398 2014 456 2015 358 2016 500 2017 410 2018 376 -{Liquor Sales Narrative} A centered 3-year moving average is to be constructed for the liquor sales.The result of this process will lead to a total of ____________________ moving averages.

The mean absolute deviation (MAD)and the sum of squares for forecast error (SSE)are the most commonly used measures of forecast accuracy.The model that forecasts the data best will usually have the:

Given the following time series,compute the seasonal (quarterly)indexes,using the four-quarter centered moving averages. Quarter 2011 2012 2013 2014 2015 1 62 48 50 43 57 2 51 45 46 39 32 3 53 44 46 37 31 4 46 37 42 32 29

The cyclical component of a time series

The results of a quadratic model fit to time series data were $\tilde { y } _ { t }$ = 7.5 - 0.25t + 3.5t²,where t = 1 for 2011.The forecasted value for 2018 is:

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. Period t 1 40 2 45 3 44 4 47 5 48 6 50 7 52 8 51 9 48 10 47 -{Motor Oil Sales Narrative} Apply exponential smoothing with w = 0.1 and w = 0.8 to help detect the components of the time series.

Which of the following terms describes the up and down movements of a time series that vary both in length and intensity?

A trend is one of the four different components of a time series.It is a long-term,relatively smooth pattern or direction exhibited by a series,and its duration is more than one year.

The manager of a lingerie store believed that her store profits were following an exponential trend.She used statistical software to obtain the following prediction equation of profits: log₁₀(Profits)= 2 + 0.4X.The data she used were from 2011 through 2016,coded 0 to 5.Find the forecast of 2017 profits.

Carpet Outlet A carpet outlet has been keeping daily sales records over the past four weeks as shown below. Weat Day 1 2 3 4 Manday 22 27 24 25 Tuesday 25 29 25 27 Wednesday 27 28 28 25 Thursday 32 30 32 29 Friday 35 32 34 33 -{Carpet Outlet Narrative} Use the regression technique to calculate the linear trend line.

The time series component that reflects the irregular changes in a time series that are not caused by any other component,and tends to hide the existence of the other more predictable components,is called:

In determining weekly seasonal indexes for natural gas consumption,the sum of the 52 means for gas consumption as a percentage of the moving average is 5195.To get the seasonal indexes,each monthly mean is to be multiplied by (5200 / 5195).

The following are the values of a time series for the first four time periods: 1 2 3 4 23 25 28 24 Using exponential smoothing,with w = 0.30,the forecasted value for time period 5 is:

Mattress Sales Monthly mattress sales (in $1,000s)of a mattress store are shown below. Manth Jan. Feb. March April May June Sales 73 65 72 82 86 90 -{Monthly Mattress Sales Narrative} Compute the three-month and five-month moving averages.

Coffee Imports The coffee imports (in millions of dollars)from a Latin American country for 10 years are shown below. Year t Exports 2011 1 96 2012 2 110 2013 3 125 2014 4 141 2015 5 132 2016 6 126 2017 7 118 2018 8 125 2019 9 133 2020 10 148 -{The Pyramids of Giza Narrative} Use the seasonal indexes and the linear trend calculated in the previous questions to forecast the number of visitors in the next four quarters and describe the seasonal fluctuations in the number of visitors.

If data for a time series analysis are collected on a monthly basis only,which component of the time series may be ignored?