The standard components are trend, seasonal variation, cyclical variation, and irregular variation.
Incorrect! Try again.
13In the additive time-series model, an observation is represented by:
Components of time series
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The additive model expresses the observation as the sum of trend, seasonal, cyclical, and irregular components.
Incorrect! Try again.
14In the multiplicative time-series model, the components are:
Components of time series
Easy
A.Multiplied together
B.Added together
C.Converted into frequencies and then arranged into class intervals
D.Subtracted in order
Correct Answer: Multiplied together
Explanation:
The multiplicative model is written as .
Incorrect! Try again.
15Which method estimates trend by drawing a smooth line through plotted observations?
Measurement of variations of time series
Easy
A.Freehand curve method
B.Semi-average method
C.Ratio-to-trend method using seasonal percentages for each period
D.Moving average method
Correct Answer: Freehand curve method
Explanation:
The freehand curve method estimates the trend visually by drawing a smooth line through the data.
Incorrect! Try again.
16Which trend-measurement method divides a time series into two equal parts?
Measurement of variations of time series
Easy
A.Moving average method
B.Semi-average method
C.Link-relative method
D.Least-squares method
Correct Answer: Semi-average method
Explanation:
The semi-average method divides the data into two equal parts and calculates the average of each part.
Incorrect! Try again.
17What is the main purpose of a moving average?
Measurement of variations of time series
Easy
A.To increase seasonal variation
B.To create random fluctuations
C.To replace every observation with the largest value in the entire series
D.To smooth short-term fluctuations
Correct Answer: To smooth short-term fluctuations
Explanation:
A moving average smooths short-term changes so that the underlying trend is easier to observe.
Incorrect! Try again.
18What is the three-period moving average of , , and ?
Measurement of variations of time series
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The moving average is .
Incorrect! Try again.
19Which method fits a trend line by minimizing the sum of squared errors?
Measurement of variations of time series
Easy
A.Least-squares method
B.Semi-average method
C.A seasonal method based only on comparing the highest annual values
D.Freehand curve method
Correct Answer: Least-squares method
Explanation:
The least-squares method chooses the trend line that minimizes the sum of squared deviations.
Incorrect! Try again.
20A seasonal index of indicates that the value is typically:
Measurement of variations of time series
Easy
A. above the average
B. below the average
C. below the average
D.Exactly equal to the average
Correct Answer: above the average
Explanation:
An index of represents the average, so indicates a level above the average.
Incorrect! Try again.
21A company records its monthly sales for five consecutive years. Why is this data considered a time series?
Introduction to time series
Medium
A.The observations are arranged in chronological order
B.The observations are collected from several companies
C.The observations have equal arithmetic means
D.The observations contain only numerical variables
Correct Answer: The observations are arranged in chronological order
Explanation:
A time series consists of observations recorded and arranged according to time.
Incorrect! Try again.
22Which data set is most suitable for time-series analysis?
Introduction to time series
Medium
A.Annual incomes of 100 households in one city
B.Test scores of four classes in one semester
C.Daily closing prices of one stock for a year
D.Heights of 200 students measured on one day
Correct Answer: Daily closing prices of one stock for a year
Explanation:
Daily stock prices are repeated observations of the same variable indexed over time.
Incorrect! Try again.
23Quarterly revenue was recorded as , , , and million. What does the time-series value million represent?
Introduction to time series
Medium
A.Difference between two consecutive quarters
B.Revenue recorded during the third quarter
C.Average revenue across all four quarters
D.Revenue forecast for the fourth quarter
Correct Answer: Revenue recorded during the third quarter
Explanation:
Each value in a time series corresponds to a particular time period; million is the third-quarter observation.
Incorrect! Try again.
24A retailer wants to forecast demand that changes noticeably from month to month. Which recording frequency is most appropriate?
Introduction to time series
Medium
A.Five-year observations
B.One cross-sectional observation
C.Decennial observations
D.Monthly observations
Correct Answer: Monthly observations
Explanation:
Monthly observations preserve the month-to-month movements needed for analysis and forecasting.
Incorrect! Try again.
25Which statement best distinguishes time-series data from cross-sectional data?
Introduction to time series
Medium
A.Time-series data compare many units at one fixed time
B.Time-series data must always be recorded every day
C.Time-series data track a variable across successive times
D.Time-series data cannot contain nonperiodic fluctuations
Correct Answer: Time-series data track a variable across successive times
Explanation:
Time-series data follow one or more variables through time, whereas cross-sectional data compare units at a given time.
Incorrect! Try again.
26Ice-cream sales rise each summer and fall each winter in a broadly repeated pattern. Which component primarily explains this movement?
Components of time series
Medium
A.Cyclical variation
B.Seasonal variation
C.Secular trend
D.Irregular variation
Correct Answer: Seasonal variation
Explanation:
A pattern recurring within each year at fixed seasons is a seasonal variation.
Incorrect! Try again.
27A country's real output alternates between expansion and recession over periods lasting several years. Which time-series component does this illustrate?
Components of time series
Medium
A.Cyclical variation
B.Irregular variation
C.Seasonal variation
D.Daily variation
Correct Answer: Cyclical variation
Explanation:
Multi-year fluctuations associated with business expansions and recessions are cyclical variations.
Incorrect! Try again.
28A factory's production drops suddenly because of an unexpected earthquake. Which component best represents this change?
Components of time series
Medium
A.Seasonal variation
B.Cyclical variation
C.Secular trend
D.Irregular variation
Correct Answer: Irregular variation
Explanation:
Unexpected events such as earthquakes create irregular or random movements in a time series.
Incorrect! Try again.
29A city's population increases steadily over three decades despite short-term fluctuations. Which component is represented by the sustained increase?
Components of time series
Medium
A.Cyclical variation
B.Irregular variation
C.Secular trend
D.Seasonal variation
Correct Answer: Secular trend
Explanation:
A persistent long-term direction of movement is called the secular trend.
Incorrect! Try again.
30Under the additive model of a time series, which equation represents an observation ?
Components of time series
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
In the additive model, trend, seasonal, cyclical, and irregular components combine by addition.
Incorrect! Try again.
31A multiplicative model is generally more appropriate when seasonal fluctuations:
Components of time series
Medium
A.Occur only once during the observed period
B.Remain constant in magnitude at every series level
C.Increase in magnitude as the series level rises
D.Disappear whenever the trend becomes positive
Correct Answer: Increase in magnitude as the series level rises
Explanation:
The multiplicative model is suitable when component effects are proportional to the level of the series.
Incorrect! Try again.
32In an additive model, , , , and . What is the irregular component ?
Components of time series
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Using , we obtain .
Incorrect! Try again.
33Annual sales for four consecutive years are , , , and units. Using the semi-average method, what are the two semi-averages?
Measurement of variations of time series
Medium
A. and
B. and
C. and
D. and
Correct Answer: and
Explanation:
The averages are and .
Incorrect! Try again.
34For observations , , and , what is the centered three-period moving average assigned to the middle period?
Measurement of variations of time series
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The moving average is , assigned to the middle period.
Incorrect! Try again.
35Why is a four-quarter moving average usually centered before it is aligned with quarterly observations?
C.Its average initially falls between two quarters
D.Its total must equal four before interpretation
Correct Answer: Its average initially falls between two quarters
Explanation:
An even-period moving average lies between time points, so centering aligns it with an actual quarter.
Incorrect! Try again.
36A fitted linear trend is , where corresponds to 2024. What is the trend estimate for 2027?
Measurement of variations of time series
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
For 2027, , so .
Incorrect! Try again.
37When time values are coded so that , which formula gives the least-squares estimate of the intercept in ?
Measurement of variations of time series
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
With , the normal equation gives .
Incorrect! Try again.
38In the ratio-to-moving-average method, an observed quarterly value is and its centered moving average is . What is the seasonal relative?
Measurement of variations of time series
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The seasonal relative is .
Incorrect! Try again.
39The unadjusted quarterly seasonal indices are , , , and . Is an adjustment required before using them?
Measurement of variations of time series
Medium
A.No, because their sum is
B.No, because their average is
C.Yes, because their sum must be
D.Yes, because each index must equal
Correct Answer: No, because their sum is
Explanation:
Quarterly seasonal indices should total , which these indices already do.
Incorrect! Try again.
40A multiplicative time series has an observed value of and a seasonal index of . What is the seasonally adjusted value?
Measurement of variations of time series
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The adjusted value is .
Incorrect! Try again.
41Two series contain exactly the same observed values but in different chronological orders. Which statistic can differ between them solely because of the reordering?
Introduction to time series
Hard
A.The sample variance
B.The sample mean
C.The sample median
D.The lag-1 autocorrelation
Correct Answer: The lag-1 autocorrelation
Explanation:
Autocorrelation depends on which observations are adjacent in time. Reordering does not change the mean, variance, or median.
Incorrect! Try again.
42A forecasting model is evaluated by randomly assigning observations from a strongly autocorrelated time series to training and test sets. What is the principal methodological problem?
Introduction to time series
Hard
A.Random assignment eliminates the seasonal component
B.Temporal dependence can leak future information into training
C.The fitted model becomes algebraically unidentified
D.The test set necessarily has a larger variance
Correct Answer: Temporal dependence can leak future information into training
Explanation:
Random splitting can place future observations in training while earlier observations are in testing. A chronological or rolling-origin evaluation better preserves the forecasting structure.
Incorrect! Try again.
43A monthly series is , where is a deterministic monthly effect and . If each year's value is formed by averaging its 12 months, what series results?
Introduction to time series
Hard
A.A seasonal annual series with period
B.A constant annual series equal to
C.A constant annual series equal to
D.An annual series with an increasing trend
Correct Answer: A constant annual series equal to
Explanation:
The annual average is . Aggregation removes the zero-mean monthly seasonal component.
Incorrect! Try again.
44Which pair of constraints most directly makes the seasonal component identifiable in standard additive and multiplicative decompositions, respectively?
Components of time series
Hard
A. and
B. and
C. and
D. and
Correct Answer: and
Explanation:
Additive seasonal effects are centered to sum to zero. Multiplicative seasonal indices are conventionally normalized to have arithmetic mean .
Incorrect! Try again.
45Under the additive model , suppose . At , , , and . What is ?
Components of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Here , so .
Incorrect! Try again.
46For the multiplicative model , an observation has , , , and . What is the irregular factor?
Components of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The irregular factor is .
Incorrect! Try again.
47The seasonal fluctuations of a sales series are approximately units when its level is and units when its level is . Which decomposition is most appropriate before further diagnostics?
Components of time series
Hard
A.An additive model, because the relative amplitude decreases
B.A multiplicative model, because the relative amplitude is stable
C.A trend-only model, because seasonality is level-dependent
D.An additive model, because the absolute amplitude increases
Correct Answer: A multiplicative model, because the relative amplitude is stable
Explanation:
The seasonal amplitude is about of the level in both cases. This proportional behavior supports a multiplicative decomposition.
Incorrect! Try again.
48Suppose a quarterly additive series is , where repeats every four quarters. Ignoring irregular variation, what is ?
Components of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Seasonal differencing cancels . The linear trend contributes .
Incorrect! Try again.
49A series displays recurrent expansions and contractions lasting between three and seven years, with no fixed duration or calendar timing. Which component best describes this behavior?
Components of time series
Hard
A.Secular trend
B.Cyclical variation
C.Seasonal variation
D.Irregular variation
Correct Answer: Cyclical variation
Explanation:
Cyclical movements persist for multiple years but need not have a fixed period. Seasonal movements repeat at stable calendar frequencies.
Incorrect! Try again.
50If with all factors positive, which transformation converts the decomposition into an additive form without approximation?
Components of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The logarithm converts a product into a sum exactly, making multiplicative components additive on the log scale.
Incorrect! Try again.
51For quarterly observations , what is the centered four-quarter moving average aligned with the third observation?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The adjacent four-quarter averages are and . Centering gives .
Incorrect! Try again.
52Let , where has period and its five values sum to zero. Away from the endpoints, what does a centered five-term moving average equal exactly?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
A symmetric moving average preserves a linear trend at its center, while averaging one complete seasonal cycle removes the zero-sum seasonal component.
Incorrect! Try again.
53Raw quarterly seasonal indices are . After normalizing them so that their sum is , what is the normalized index for the third quarter?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The raw indices sum to , so the correction factor is . Thus the third-quarter index is .
Incorrect! Try again.
54A least-squares trend is fitted to using . What is the forecast corresponding to the next coded value ?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Because , . Also, , giving .
Incorrect! Try again.
55Annual observations for years 1 through 6 are . Using the semi-average method, what is the trend forecast for year 7?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The semi-averages are at year 2 and at year 5. The annual increase is , so year 7 is .
Incorrect! Try again.
56An observed quarterly value is , and its multiplicative seasonal index is on a base- scale. What is the deseasonalized value?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
A base- index of is a factor of . Deseasonalizing gives .
Incorrect! Try again.
57In the link-relative method, February, March, and April have link relatives , , and , respectively. If January's chain relative is , what is April's chain relative before drift correction?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Successive chain relatives are , , and .
Incorrect! Try again.
58An exponential trend has the form . If and , with , what is the trend value at ?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Since and , . Therefore, .
Incorrect! Try again.
59Centering two adjacent four-term simple moving averages produces a five-observation weighted moving average. What are its weights from earliest to latest observation?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Averaging adjacent four-term averages halves the weights of the two endpoints, while each of the three shared observations retains weight .
Incorrect! Try again.
60Under , suppose , , , and . What is the estimated cyclical factor?
Measurement of variations of time series
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The cyclical factor is .
Incorrect! Try again.
Did this save you a night before the exam?
LPU Notes is free, and it stays free. Ads cover part of the server bill.
The rest comes out of a student's own pocket: the domain, the storage,
and keeping the site up through the weeks everyone needs it at once.
The payment button didn't load. An ad blocker or a filtered network is the usual reason.
to try again.
Nothing here is ever locked, and nothing unlocks. Chip in only if it was worth it.
What it pays for →