Exam 20: Time-Series Analysis and Forecasting

One measure of the accuracy of a forecasting model is the:

In exponentially smoothed time series,the smoothing constant w is chosen on the basis of how much smoothing is required.In general,a small value of w such as 0.1 results in very little smoothing,while a large value of w such as 0.8 results in too much smoothing.

ebay Storefront Sales The sales figures (in $1000s)have been recorded in an ebay storefront as shown in the following table. Time Periad y Time Periad y 1 35 9 46 2 32 10 43 3 29 11 48 4 26 12 41 5 28 13 34 6 32 14 29 7 38 15 25 8 43 16 23 -{ebay Storefront Sales Narrative} Plot the percentage of trend.

Photo Equipment Store Earnings The quarterly earnings of a chain of Photo Equipment stores have been recorded for the years 2011-2014.These data (in millions of dollars)are shown in the accompanying table. Year Quarter 2011 2012 2013 2014 1 65 70 73 79 2 80 88 90 95 3 98 103 107 111 4 67 74 76 80 -A local newspaper that appears six days per week wanted to forecast two-day revenues from its business services classified ads section.The revenues (in $1,000s)were recorded for the past 52 weeks.From these data,the following regression equation was computed: $\tilde { y } _ { t }$ = 2000 + 0.6t- 150D₁ -40D₂ (t = 1,2,3,... ,156) where $D _ { 2 } = \left\{ \begin{array} { l } 1 \text { if Monday or Tuesday } \\0 \text { otherwise }\end{array} \right.$ and $D _ { 2 } = \left\{ \begin{array} { l } 1 \text { if Wednesday or Thursday } \\0 \text { otherwise }\end{array} \right.$ Forecast the two-day revenues for the next week.

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 random variation.

MAD averages the absolute differences between the actual and ____________________ values.

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: Year Quarter 2000 2001 2002 2003 Winter 210 215 218 220 Spring 260 275 282 290 Summer 480 490 505 525 Fall 250 255 265 270 -{The Pyramids of Giza Narrative} Discuss why exponential smoothing is not recommended as a forecasting method in this case.

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: Year Quarter 2000 2001 2002 2003 Winter 210 215 218 220 Spring 260 275 282 290 Summer 480 490 505 525 Fall 250 255 265 270 -{The Pyramids of Giza Narrative} Calculate the four-quarter centered moving averages.

Photo Equipment Store Earnings The quarterly earnings of a chain of Photo Equipment stores have been recorded for the years 2011-2014.These data (in millions of dollars)are shown in the accompanying table. Year Quarter 2011 2012 2013 2014 1 65 70 73 79 2 80 88 90 95 3 98 103 107 111 4 67 74 76 80 -{Photo Equipment Store Earnings Narrative} Forecast the quarterly earnings for the years 2015 and 2016.

If a time series displays a gradual or no trend and no evidence of seasonal variation,____________________ can be effective as a forecasting method.

Photo Equipment Store Earnings The quarterly earnings of a chain of Photo Equipment stores have been recorded for the years 2011-2014.These data (in millions of dollars)are shown in the accompanying table. Year Quarter 2011 2012 2013 2014 1 65 70 73 79 2 80 88 90 95 3 98 103 107 111 4 67 74 76 80 -{Photo Equipment Store Earnings Narrative} Develop a regression model,using indicator variables to represent quarters.

Hotel Occupancy A small hotel has recorded the number of rooms occupied during weekdays over a period of four weeks as is shown in the table below: Weat Day 1 2 3 4 Manday 16 15 18 21 Tue5day 22 21 20 25 Wednesday 20 23 20 24 Thursday 29 28 32 28 Friday 35 31 29 36 -{Hotel Occupancy Narrative} Calculate the seasonal (daily)indexes.

One application of seasonal indexes is to remove the seasonal variation in a time series.The process is called ____________________,and the result is called a seasonally adjusted time series.

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 smooth the liquor sales.The smoothed value for 2012 is_________________.

The autoregressive model $\tilde { y } _ { t }$ = 200 + 15y_{t - 1} was developed from a time series.Forecast the next value of the time series if the last observation was 8.

Microprocessors Annual production (in millions)of computer microprocessors in a large electronics company was recorded as shown below Year t Production 2011 1 26 2012 2 23 2013 3 21 2014 4 25 2015 5 32 2016 6 38 2017 7 43 2018 8 36 2019 9 29 2020 10 25 -{Microprocessors Narrative} Plot the percentage of trend.

ebay Storefront Sales The sales figures (in $1000s)have been recorded in an ebay storefront as shown in the following table. Time Periad y Time Periad y 1 35 9 46 2 32 10 43 3 29 11 48 4 26 12 41 5 28 13 34 6 32 14 29 7 38 15 25 8 43 16 23 -{ebay Storefront Sales Narrative} Describe the cyclical effect (if there is one).

Which of the following models might be appropriate to describe a new product that has experienced a rapid early growth rate followed by the inevitable leveling off?

A least squares linear trend line is just a simple regression line with the years recoded.

A time series can consist of four different components: long-term trend,cyclical variation,seasonal variation,and random variation.