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Q:
NARRBEGIN: SA_116_118
The table below contains 5 years of monthly data on sales (number of units sold) for a particular company, in addition to extra columns containing information needed to answer some of the questions. The company suspects that except for random noise, its sales are growing by a constant percentage each month and that they will continue to do so for at least the near future. NARREND
Explain briefly whether the plot of the series visually supports the company's suspicion.
Q:
NARRBEGIN: SA_112_115
The table below contains the monthly number of airline tickets sold by a travel agency in Grand Rapids, Michigan NARREND
(A) Is this time series random? Perform a runs test and compute a few autocorrelations to support your answer.
(B) Does a linear trend appear to fit these data well? If so, estimate the linear-trend model for this time series, and interpret the value.
(C) Is there evidence of some seasonal pattern in these sales data? If so, characterize the seasonal pattern, and explain how to forecast future values.
Q:
The number of reported accidents at a manufacturing plant located in Flint, Michigan, was recorded at the start of each month. These data are provided in the table below: Is this time series random? Perform a runs test and compute a few autocorrelations to support your answer.
Q:
NARRBEGIN: SA_108_110
Suppose that simple exponential smoothing with is used to forecast monthly wine sales at a liquor store. After April's demand is observed, the forecasted demand for May is 4500 bottles of wine.
NARREND
(A) At the beginning of May, what is the forecast of July's wine sales?
(B) Suppose that actual demands during May and June are as follows: May, 5000 bottle of wine; June 4000 bottle of wine. After observing June's demand, what is the forecast for July's demand?
(C) Based on the data from (B), the demands during May and June average (5000+4000)/2 = 4500 bottle per month. This is the same as the forecast for monthly sales before we observed the May and June data. Yet after we observe the May and June demands for wine, our forecast for July demand has decreased from what it was at the end of April. Why?
Q:
NARRBEGIN: SA_103_107The Consumer Confidence Index (CCI) attempts to measure people's feelings about general business conditions, employment opportunities, and their own income prospects. The data shown below contains the annual average values of the CCI for the period 1977-2006.NARREND(A) Obtain an autocorrelation table for this series.(B) Use the results of (A) to specify one or more "promising" autoregression models. Estimate each model with the available data. Which model provides the best fit to the given data?(C) Use the best autoregression model from (B) to produce a forecast of the CCI in 2007. Also, provide a measure of the likely forecast error.(D) Use the moving average method with a carefully chosen span to forecast this time series in 2007 and 2008. Explain your choice of the span.(E) Between the best autoregression model and the best moving average model, which is best? Explain your answer.
Q:
NARRBEGIN: SA_99_102The data shown below contains the monthly sales (in thousands of dollars) at a local department store for each of the past 24 months.MonthSalesMonthSales19871310802108014100239751596841060169845103017104568951894579081910258105920950994021100410103822107511105023969121030241029NARREND(A) Develop a time series plot of the data.(B) Perform a runs test and compute a few autocorrelations to determine whether this time series is random.(C) Given your answers to (A) and (B), what type of forecast do you recommend? Explain your answer.(D) Use your answer to (C), to obtain a forecast for the next quarter (4 months). How reliable do you think this forecast is?
Q:
NARRBEGIN: SA_95_98Consider a random walk model with the following equation: , where is a normally distributed random series with mean of 0 and standard deviation of 12.NARREND(A) Use Excel to generate a time series of 25 values using this random walk model with a starting value of 200.(B) Conduct a runs test on the series you generated for (A). Is it random? Explain.(C) Conduct a runs test on the differences between successive values for the series you generated for (A). Is it random? Explain.(D) Use the time series you constructed in (A) to forecast the next observation.
Q:
NARRBEGIN: SA_92_94
Suppose that simple exponential smoothing with is used to forecast monthly Pepsi sales at a small grocery store. After March's demand is observed, the forecasted demand for April is 5000 cans of Pepsi.
NARREND
(A) Suppose that actual demands during April and May are as follows: May, 5500 cans; June 4500 cans. After observing May's demand, what is the forecast for June's demand?
(B) Based on the data from (A), the demands during April and May average (5500+4500)/2 = 5000 cans per month. This is the same as the forecast for monthly sales before we observed the April and May data. Yet after we observed the April and May demands for Pepsi, our forecast for June demand has decreased from what it was at the end of March. Why?
Q:
NARRBEGIN: SA_92_94
Suppose that simple exponential smoothing with is used to forecast monthly Pepsi sales at a small grocery store. After March's demand is observed, the forecasted demand for April is 5000 cans of Pepsi.
NARREND
At the beginning of April, what is the forecast of June's Pepsi sales?
Q:
NARRBEGIN: SA_89_91The number of employees on the payroll at a computer software company is recorded at the start of each month from January 2007 to December 2009. These data are shown below.YearJanFebMarchAprilMayJuneJulyAug.Sept.Oct.Nov.Dec2007348352 330 3473393703803924004104053672008350341 345 3553423503703954104014053652009348349 350 350342377369400410406400370NARRENDUse the method of moving averages with an appropriate span to forecast retail sales for 2010. Do you obtain a good fit? Do you have confidence in your forecast? Explain your answers.
Q:
NARRBEGIN: SA_89_91The number of employees on the payroll at a computer software company is recorded at the start of each month from January 2007 to December 2009. These data are shown below.YearJanFebMarchAprilMayJuneJulyAug.Sept.Oct.Nov.Dec2007348352 330 3473393703803924004104053672008350341 345 3553423503703954104014053652009348349 350 350342377369400410406400370NARRENDPerform a runs test and compute a few autocorrelations to determine whether this time series is random.
Q:
NARRBEGIN: SA_89_91The number of employees on the payroll at a computer software company is recorded at the start of each month from January 2007 to December 2009. These data are shown below.YearJanFebMarchAprilMayJuneJulyAug.Sept.Oct.Nov.Dec2007348352 330 3473393703803924004104053672008350341 345 3553423503703954104014053652009348349 350 350342377369400410406400370NARRENDDevelop a time series plot of the data. Does the data appear random on the plot?
Q:
A car dealer in Big Rapids, Michigan is using Holt's method to forecast weekly car sales. Currently the level is estimated to be 45 cars per week, and the trend is estimated to be 5 cars per week. During the current week, 25 cars are sold. After observing the current week's sales, forecast the number of cars three weeks from now. Use .
Q:
What changes, if any, would you suggest to improve the forecast?
Q:
Run the moving average fit again, this time holding out the last 6 observations to validate the fit. What do you find?
Q:
NARRBEGIN: SA_84_87The data shown below contains total monthly retail sales (in dollars) a small sporting goods store for the years 2006-2008.NARRENDUse the method of moving averages with an appropriate span to forecast retail sales for the first half of 2009. Do you obtain a good fit? Do you have confidence in your forecast? Explain your answers.
Q:
NARRBEGIN: SA_84_87
The data shown below contains total monthly retail sales (in dollars) a small sporting goods store for the years 2006-2008. NARREND
Obtain a time series graph of the data. If you will be using a moving average model of the data, what information does this graph provide to help specify such a model?
Q:
Rite Aid pharmacy in Big Rapids, Michigan is using simple exponential smoothing to predict monthly birthday card sales. At the end of October 2004, the pharmacy's forecast for December 2004 sales was 400. In November, 420 cards were sold, and during December, 425 cards were sold. At the end of December 2004, what is the pharmacy's forecast for the total number of cards that will be sold during March and April of 2005? Use .
Q:
We compare the percent of variation explained R2 for a regression model with seasonal dummy variables to the MAPE for the smoothing model with seasonality to see which model is more accurate.
Q:
Regression models with seasonal dummy variables produce coefficients for each quarter, which represent the additive or multiplicative factors relative to the annual average.
Q:
In a regression model with seasonal dummy variables, the coefficients on the dummy variables represent the additive factor relative to the reference quarter value, not the multiplicative factor.
Q:
In a multiplicative seasonal model, we multiply a "base" forecast by an appropriate seasonal index. These indexes, one for each season, typically average to 1.
Q:
In an additive seasonal model, we add an appropriate seasonal index to a "base" forecast. These indexes, one for each season, typically average to 0.
Q:
Winter's method is an exponential smoothing method, which is appropriate for a series with trend but no seasonality.
Q:
Seasonal variations will not be present in a deseasonalized time series.
Q:
To deseasonalize an observation (assuming a multiplicative model of seasonality), multiply it by the appropriate seasonal index.
Q:
The seasonal component of a time series is more likely to exhibit the relatively steady growth of a variable, such as the population of Egypt from 35 million in 1960 to 75 million in 2005.
Q:
If we use a value close to 1 for the level smoothing constant and a value close to 0 for the trend smoothing constant in Holt's exponential smoothing model, then we expect the model to respond very quickly to changes in the level, but very slowly to changes in the trend.
Q:
Holt's method is an exponential smoothing method, which is appropriate for a series with seasonality and possibly a trend.
Q:
If we use a value close to 1 for the smoothing constant in a simple exponential smoothing model, then we expect the model to respond very slowly to changes in the level.
Q:
In exponential smoothing models, the forecast is based on the level at time t, Lt, which is not observable and can only be estimated.
Q:
Simple exponential smoothing is appropriate for a series without a pronounced trend or seasonality.
Q:
The smoothing constants in exponential smoothing models are effectively a way to assign different weights to past levels, trends and cycles in the data.
Q:
Every form of exponential smoothing model has at least one smoothing constant, which is always between 0 and 1.
Q:
The smoothing constant used in simple exponential smoothing is analogous to the span in moving averages.
Q:
If the span of a moving average is large " say, 12 months " then few observations go into each average, and extreme values have relatively large effect on the forecasts.
Q:
To calculate the five-period moving average for a time series, we average the values in the two preceding periods, and the values in the three following time periods.
Q:
We compute the five-period moving averages for all time periods except the first two.
Q:
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.
Q:
A moving average is the average of the observations in the past few periods, where the number of terms in the average is the span.
Q:
The moving average method is perhaps the simplest and one of the most frequently-used extrapolation methods.
Q:
Correlogram is a bar chart of autocorrelation at different lags.
Q:
In a random walk model, there are significantly more runs than expected, and the autocorrelations are not significant.
Q:
An equation for the random walk model is given by the equation: , where is the change in the time series from time t to time t " 1, is a constant, and is a random variable (noise) with mean 0 and some standard deviation .
Q:
If a time series exhibits an exponential trend, then a plot of its logarithm should be approximately linear.
Q:
An exponential trend is appropriate when the time series changes by a constant percentage each period.
Q:
The trend line was calculated from quarterly data for 2000 " 2004, where t = 1 for the first quarter of 2000. The trend value for the second quarter of the year 2005 is 0.75.
Q:
The most common form of autocorrelation is positive autocorrelation, where large observations tend to follow large observations and small observations tend to follow small observations.
Q:
An autocorrelation is a type of correlation used to measure whether the values of a time series are related to their own past values.
Q:
The null hypothesis in a runs test is the data series is random
Q:
If a random series has too few runs, then it is zigzagging too often.
Q:
The runs test is a formal test of the null hypothesis of randomness. If there are too many or too few runs in the series, then we conclude that the series is not random.
Q:
A meandering pattern is an example of a random time series.
Q:
As is the case with residuals from regression, the forecast errors for nonregression methods will always average to zero
Q:
A shortcoming of the RMSE (root mean square error) is that it is not in the same units as the forecast variable.
Q:
Forecasting software packages typically report several summary measures of the forecasting error. The most important of these are MAE (mean absolute error), RMSE (root mean square error), and MAPE (mean absolute percentage error).
Q:
You will always get more accurate forecasts by using more complex forecasting methods.
Q:
Extrapolation forecasting methods are quantitative methods that use past data of a time series variable " and nothing else, except possible time itself " to forecast values of the variable.
Q:
Econometric forecasting models, also called causal models, use regression to forecast a time series variable by using other explanatory time series variables.
Q:
The cyclic component of a time series is more likely to exhibit business cycles that record periods of economic recession and inflation.
Q:
The seasonal component of a time series is harder to predict than the cyclic component; the reason is that cyclic variation is much more regular.
Q:
The time series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called cyclical.
Q:
The time series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period, is called seasonal.
Q:
If the observations of a time series increase or decrease regularly through time, we say that the time series has a random (or noise) component.
Q:
A trend component of a time series is a long-term, relatively smooth pattern or direction exhibited by a series, and its duration is more than one year.
Q:
A time series can consist of four different components: trend, seasonal, cyclical, and random (or noise).
Q:
A time series is any variable that is measured over time in sequential order.
Q:
A regression approach can also be used to deal with seasonality by using_____variables for the seasons.
a. smoothing
b. response
c. residual
d. dummy
Q:
There are a variety of deseasonalizing methods, but they are typically variations of:
a. ratio-to-seasonality methods
b. ratio-to-exponential-smoothing methods
c. ratio-to-moving-average methods
d. linear trend
Q:
Winters' model differs from Holt's model and simple exponential smoothing in that it includes an index for:
a. seasonality
b. trend
c. residuals
d. cyclical fluctuations
Q:
Which of the following is not a method for dealing with seasonality in data
a. Winter's exponential smoothing model
b. deseasonalizing the data, using any forecasting model, then reseasonalizing the data
c. multiple regression with lags for the seasons
d. multiple regression with dummy variables for the seasons
Q:
When using Holt's model, choosing values of the smoothing constant that are near 1 will result in forecast models which
a. react very quickly to changes in the level
b. react very quickly to changes in the trend
c. react very quickly to changes in the level and the trend
d. react very slowly to changes in the level and the trend
Q:
Holt's model differs from simple exponential smoothing in that it includes a term for:
a. seasonality
b. trend
c. residuals
d. cyclical fluctuations
Q:
Suppose that a simple exponential smoothing model is used (with a = 0.30) to forecast monthly sandwich sales at a local sandwich shop. After June's demand is observed at 1520 sandwiches, the forecasted demand for July is 1600 sandwiches. At the beginning of July, what would be the forecasted demand for August?
a. 1520
b. 1544
c. 1550
d. 1600
Q:
Suppose that a simple exponential smoothing model is used (with = 0.40) to forecast monthly sandwich sales at a local sandwich shop. The forecasted demand for September was 1560 and the actual demand was 1480 sandwiches. Given this information, what would be the forecast number of sandwiches for October?
a. 1480
b. 1528
c. 1560
d. 1592
Q:
When using exponential smoothing, if you want the forecast to react quickly to movements in the series, you should choose:
a. values of near 1
b. values of near 0
c. values of midway between 0 and 1
d. it depends on the data set
Q:
When using exponential smoothing, a smoothing constant must be used. The value for :
a. ranges between 0 and 1
b. ranges between "1 and +1
c. equals the largest observed value in the series
d. represents the strength of the association between the forecasted and observed values
Q:
The data below represents sales for a particular product. If you were to use the moving average method with a span of 4 periods, what would be your forecast for period 5?PeriodSales (in units)190212031104100a. 90b. 100c. 105d. 110
Q:
The data below represents sales for a particular product. If you were to use the moving average method with a span of 3 periods, what would be your forecast for period 5?PeriodSales (in units)190212031104100a. 90b. 100c. 105d. 110
Q:
The following are the values of a time series for the first four time periods:t123424252627Using a four-period moving average, the forecasted value for time period 5 is:a. 24.5b. 25.5c. 26.5d. 27.5