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Exam 6: Times Series Analysis and Forecasting

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Question 31

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Monthly sales at a coffee shop have been analyzed.The seasonal index values are $\begin{array} { c r } \text { Month } & \text { Index } \\\hline \text { Jan } & 1.38 \\\text { Feb } & 1.42 \\\text { Mar } & 1.35 \\\text { Apr } & 1.03 \\\text { May } & .99 \\\text { June } & .62 \\\text { July } & .51 \\\text { Aug } & .58 \\\text { Sept } & .82 \\\text { Oct } & .82 \\\text { Nov } & .92 \\\text { Dec } & 1.56\end{array}$ and the trend line is 74123 + 26.9(t).Assume there is no cyclical component and forecast sales for year 8 (months 97 - 108).

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Question 32

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Quantitative forecasting methods can be used when past information about the variable being forecast is unavailable.

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What is a stable time series,and what forecasting methods are appropriate for one?

To select a value for  for exponential smoothing

All quarterly time series contain seasonality.

In situations where you need to compare forecasting methods for different time periods,the most appropriate accuracy measure is

The number of plumbing repair jobs performed by Auger's Plumbing Service in each of the last nine months are listed below. $\begin{array} { c c | c c | c c } \text { Month } & \text { Jobs } & \text { Month } & \text { Jobs } & \text { Month } & \text { Jobs } \\\hline \text { March } & 353 & \text { June } & 374 & \text { September } & 399 \\\text { April } & 387 & \text { July } & 396 & \text { October } & 412 \\\text { May } & 342 & \text { August } & 409 & \text { November } & 408\end{array}$ a.Assuming a linear trend function, forecast the number of repair jobs Auger's will perform in December using the least squares method. b.What is your forecast for December using a three-period weighted moving average with weights of .6, .3, and .1? How does it compare with your forecast from part (a)?

If a time series has a significant trend pattern,then one should not use a moving average to forecast.

Discuss the effects of using a small smoothing constant value and when it is most appropriate to use.Then,do the same for a large smoothing constant value.

Trend in a time series must be linear.

A time series model with a seasonal pattern will always involve quarterly data.

Business at Terry's Tie Shop can be viewed as falling into three distinct seasons: (1)Christmas (November-December); (2)Father's Day (late May - mid-June); and (3)all other times.Average weekly sales (in $'s)during each of these three seasons during the past four years has been as follows: $\begin{array} { c c c c c } \text { Season } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } & \text { Year 4 } \\\hline 1 & 1856 & 1995 & 2241 & 2280 \\2 & 2012 & 2168 & 2306 & 2408 \\3 & 985 & 1072 & 1105 & 1120\end{array}$ Determine a forecast for the average weekly sales in years 5 and 6 for each of the three seasons.

The trend pattern is easy to identify by using

A four-period moving average forecast for period 10 would be found by averaging the values from periods 10,9,8,and 7.

An alpha ()value of .2 will cause an exponential smoothing forecast to react more quickly to a sudden drop in demand than will an  equal to .4.

Coyote Cable has been experiencing an increase in cable service subscribers over the last few years due to increased advertising and an influx of new residents to the region.The number of subscribers (in 1000's)for the last 16 months are as follows: $\begin{array} { c c | c c | c c } \hline \hline \text { Month } & \text { Sales } & \text { Month } & \text { Sales } & \text { Month } & \text { Sales } \\\hline 1 & 12.8 & 7 & 20.6 & 12 & 23.8 \\2 & 14.6 & 8 & 18.5 & 13 & 25.1 \\3 & 15.2 & 9 & 19.9 & 14 & 24.7 \\4 & 16.1 & 10 & 23.6 & 15 & 26.5 \\5 & 15.8 & 11 & 24.2 & 16 & 28.9 \\6 & 17.2 & & & & \\\hline \hline\end{array}$ Forecast the number of subscribers for months 17,18,19,and 20.

The number of girls who attend a summer basketball camp has been recorded for the seven years the camp has been offered.Use exponential smoothing with a smoothing constant of .8 to forecast attendance for the eighth year. 47,68,65,92,98,121,146

The number of new contributors to a public radio station's annual fund drive over the last ten years is 63,58,61,72,98,103,121,147,163,198 Develop a trend equation for this information,and use it to predict next year's number of new contributors.

Gradual shifting of a time series to relatively higher or lower values over a long period of time is called

With fewer periods in a moving average,it will take longer to adjust to a new level of data values.