Data Analysis: Chapter 14
Jonah's Autos has analyzed their annual revenue (in millions) for the past 6 years. The model is yt = 2.56e0.165t. The revenue expected revenue in two years is _____.
$3.56 million
Nancy is the manager of a gas station in Cleveland, Ohio. She is collecting various types of data about her business. Identify the time series variables.
- Nancy collected the price of a gallon of gas from every gas station in Cleveland on the first day of the month for the past year. - Nancy counted the number of customers each Saturday for the past six months.
A common choice of a smoothing constant is
.2
In a small neighborhood community, it has been documented that home sales vary quarterly throughout the year and that the sales have been consistently increasing over the past 5 years. The quarterly indexes were found to be 0.73 for quarter 1, 0.90 for quarter 2, and 1.4 for quarter 3. What is the value of the fourth quarter seasonal index? Round to two decimals.
0.97
The smoothing constant, α, can be any value between ____ and ____
0; 1
To compute a trailing moving average forecast with m = 4 for the 5th time period, you would need to use data from periods __________.
1-4
When using Excel's Data Analysis Tool to compute the exponential smoothing forecast, the damping factor is equal to ____________.
1-a
Order the steps used to fit a trend on Excel.
1. Plot a line chart of the time series data with the time variable on the horizontal axis 2. from the chart tools select the layout tab 3. click trend line 4. click trend line options 5. choose the type of trend line and check off Display Equation on chart
A regression model with monthly seasonal binary variables would have ___ binaries
12
Jonah's Autos has analyzed their annual revenue for the past 6 years. The model is yt = 2.56e0.165t. The revenue is increasing at a rate of ___ each year.
16.5%
Given an exponential model: yt = 4.6e-0.165t,, the prediction for y in year 3 is _____.
2.80
In a small neighborhood community, it has been documented that home sales have 3 distinct seasons per year. After deseasonalizing the data a seasonal index of 1.34 was calculated for the second season. This seasonal index implies that home sales are ____% ______ than the average annual sales.
34%; greater
To compute a centered moving average with m = 3 for the 5th time period, you would need to use data from periods __________.
4-6
Jonah's Autos wanted to analyze their number of weekly car sales. An employee in the accounting department fitted a linear trend to the data. The model is yt = 20+5t. The forecast for week 6 is ___ cars sold.
50
Jonah's Autos wanted to analyze their number of weekly car sales. An employee in the accounting department fitted a linear trend to the data. The model is is yt = 20+5t. The number of cars sold is increasing by an average of ___ cars per ___
5; week
Refer to the data below. Using the exponential smoothing technique with α=0.1, and F1 = y1, what is the forecast for period 3? Period Actual Data 1 560 2 1,300 3 750 4 1,465 5 725 6 675 7 575 8 815
634
In a small neighborhood community, it has been documented that home sales vary quarterly each year and that the sales have been consistently increasing over the past 5 years. A regression model with quarterly binary predictors was developed: Sales = 49.02 + 0.74time - 2.19Qtr1 + 1.39Qtr2 + 2.56Qtr3. Calculate the sales forecast for the fourth quarter of year 6.
66.78
In a small neighborhood community, it has been documented that home sales vary quarterly throughout the year and that the sales have been consistently increasing over the past 5 years. The quarterly indexes were found to be 0.73 for quarter 1, 0.90 for quarter 2, and 1.4 for quarter 3. Also, a trend analysis revealed the following model yt=10+3.04t would reflect how the number of sales have been gradually increasing each year. What would be the forecast for the number of home sales for the second quarter of year 6?
69.2
Choose the definition of the cycle component of a time series.
A repetitive up and down movement that covers several years.
Choose the definition of the seasonal component of a time series.
A repetitive up and down pattern within a year, week, or day.
Choose the definition of the trend component of a time series.
A sustained movement in one direction over time
What are the two broad ways that quantitative forecasting methods are classified?
Causal and Time-series
Believability
Does the extrapolated trend appear reasonable?
Overall fit
Does the model fit past data?
Fit to recent data
Does the model fit the most recent observations well?
yt = (ae)^bt
Exponential
The Dow Jones Industrial Average is strongly affected by changes in low-priced stocks.
False
True or false: A high R2 for a linear trend model guarantees future predictions will be good.
False
True or false: A linear trend model can be fitted using Excel's regression function and letting time be the response variable.
False
The exponential smoothing formula is
Ft+1 = αyt + (1-α)Ft
For time series data that exhibit a trend or have seasonal components one can use
Holt's method for adding a trend component. Winter's method for adding both a trend and a seasonal component.
yt = a + bt
Linear
Choose the definition of the irregular component of a time series.
Movement with no apparent pattern, also called noise
The criteria to break a tie in choosing a trend model would be
Occam's Razor
yt = a + bt + ct^2
Quadratic
To determine if a linear trend model is a good fit to past data one would look at the value of
R^2
In a small neighborhood community data collected over a 20 year period has revealed that home sales vary quarterly each year. If we construct a regression model with seasonal binary variables, the model would be:
Sales = b0+ b1time + b2Qtr1 + b3Qtr2 + b4Qtr3
Why are moving average smoothing techniques used in forecasting?
To reduce the impact of random fluctuations
True or False: An exponential trend model is commonly used for financial data because analysts often compare percentage growth rates for revenue, costs, or salaries.
True
True or false: An exponential trend model can be fitted by transforming the response variable y using ln(y) and then using regression analysis to find the slope and intercept. The exponential model parameters are a=eintercept and b = slope.
True
True or false: Excel will calculate TMA values for a time series from the Add Trendline option.
True
True or false: Relative indexes allows one to compare changes over time regardless of variable units.
True
Which method should be used when your time series has both trend and seasonality?
Winter's method for adding both a trend and a seasonal component.
Occam's Razor
Would a simpler model suffice?
The Consumer Price Index is an example of
a weighted index number
The components of a times series can be modeled in two ways. The _____ model is used for short-run series with values that have similar magnitude. The ____ model is used for long-run series with increasing or decreasing magnitude.
additive; multiplicative
To measure relative change over time in a variable,
an index is calculated by choosing a base period and taking a ratio of the current period to the base period.
Quantitative forecasts make _____ explicit by forcing the analyst to clearly state and explain their ____
assumptions; assumptions
A way to initialize the exponential smoothing model is to ____ the first several observed values.
average
To calculate a seasonal index one would first need to calculate a ____ moving average
centered
Excel's TMA trendline is a _____ choice compared to the other choices.
conservative
A linear trend model is used when the time series values increase by a _____ amount each period whereas an exponential trend model is used when the values are increasing by a ___ amount each time period.
constant; increasing
A repetitive up-and-down movement across several years is called a
cycle
The four components of a time series are
cyclical trend seasonal irregular
The process of deseasonalizing a time series is called
decomposition
Time series models can be classified as
decomposition models trend models smoothing models
An advantage of the exponential smoothing method over the moving average is that over time the earlier observations have _____ influence on the forecast than the most recent observations.
decreasing
Observations in a time series data set are divided by a seasonal index in order to ________ the data set.
deseasonalize
The coefficient of ____ can be used as a measure of fit for an exponential model.
determination
One of the potential issues with a trailing moving average is that _________ weight is given to the recent m observations.
equal
If the adjusted seasonal index is 1.00 for season A, this implies that values for season A are _____ the average of all the seasonal values.
equal to
Tracking forecast ___ is a way to determine if a forecast model fits the time series.
error
Random disturbance in a time series is called _____ component or random _____
error; noise
Because financial time series data often grow faster than a linear trend, a preferred model is the ____ model
exponential
When forecasting using a linear trend model one should be wary of ____ too far into the future.
extrapolating
When using Excel's Data Analysis Tool to compute the exponential smoothing forecast, the ____ observation is used to initialize the forecasts.
first
Index numbers are frequently used
for financial data comparisons.
A positive exponent in an exponential model indicates a(n) ____ in the time series.
increase
When time series data appears to be increasing or decreasing over time by the same amount a __________ trend model would be most appropriate.
linear
Exponential smoothing works well when
many SKUs are forecast each time period. data is trendless.
A seasonal time series shows a cyclical pattern
monthly quarterly
When the average of a time series is changing over time we can use calculate a _____ average
moving
The TMA method is best considered a ____ - ____ ahead forecast
one-period
The time interval over which time series data are collected is called the _____. Common time intervals are monthly, yearly, or quarterly.
period
Forecasting is part of a company's ___ process and helps ____ makers analyze trends and patterns so they can deal with contingencies.
planning; decision
When fitting a trend model on Excel one would choose ______ model for a quadratic trend.
polynomial
Forecasts help a dialogue be more ____
productive
A ___________ trend model is often used when the time series has a turning point at some time period.
quadratic
A repetitive up-and-down pattern within a year is typically called
seasonal
A linear trend is typically used for
short-run modeling. baseline forecasting. simple modeling.
The coefficient in the exponent of an exponential model, y = aebt, is the ____ in a linear regression where ln(y) is the response variable.
slope
The direction and amount of a linear trend is indicated by the ____ of the trend line
slope
When calculating an exponential smoothing forecast, you must multiply the previous period's actual, yt, by a ___ constant
smoothing
One of the terms in the exponential smoothing model multiplies the current demand, yt, by the
smoothing constant
If today's consumer price index were equal to 212 this means
that on average prices are now slightly more than double those in 1982-1984.
A measure of fit for an exponential trend model is
the coefficient of determination.
In a small neighborhood community, it has been documented that home sales vary quarterly each year and that the sales have been consistently increasing over the past 5 years. A regression model with quarterly binary predictors was developed: Sales = 49.02 + 0.74time - 2.19Qtr1 + 1.39Qtr2 + 2.56Qtr3. If the coefficient estimates obtained in the regression are statistically different from zero, an interpretation of the coefficient of Qtr1 reveals that __________.
the home sales are approximately 2.19 lower in quarter 1 than in quarter 4 on average.
Jonah's Autos has analyzed they number of used cars on their lots over the past 10 years. The model is yt = 987 - 35.4t + 3.78t2. This model indicates that
the number of cars decreased and then increased over time.
A linear trend can be fitted using simple regression where ____ is the explanatory variable.
time
An index number allows comparisons between two or more ___-series variables
time
A variable whose observations are recorded in a consistent sequential order is considered a ____ ____ variable
time series
A sustained, general movement in one direction over time is called a ___
trend
A quadratic trend model is often used when the time series has a ____ point at some time period.
turning
Linear and exponential trend models are widely used because they have only ____ parameters whereas the ____ model is used for time series that show a turning point.
two; quadratic
The CPI is an example of a Laspeyres index which applies _____ to reflect the importance of various items that make up a "basket" of goods and services.
weights
Forecasting helps a company analyze a ___ ___ future that might impact the organization.
what-if
One should recognize that forecasts are always
wrong
In the exponential smoothing method, the simple approach for initializing the process is to let F1 = ______
y1
