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Trang 1Chapter 19: Time Series Analysis - Practice
Exam
Part 1: Exam Questions
Instructions: This exam consists of 50 multiple-choice questions on time series analysis,
including trends, components, seasonal and cyclical variations, and forecasting Each question has four options unless stated otherwise Select the best answer for each
1 Is the following statement true or false? If the trend is approximately linear, it can be
estimated using a scatter graph
a) True b) False
2 Is the following statement true or false? If the trend is not approximately linear, it
can be estimated using moving averages
a) True b) False
3 Which of the following is NOT a component of a time series?
a) Moving average b) Cyclical variation c) Random variation d) Trend
4 In a sales forecast based on time series analysis, cyclical variation should be:
a) Included b) Excluded c) Included only if short-term d) Always ignored
5 In a sales forecast based on time series analysis, random variation should be:
a) Included b) Excluded c) Included only if predictable d) Always included
6 In a sales forecast based on time series analysis, seasonal variation should be:
a) Included b) Excluded c) Included only if cyclical d) Always ignored
7 In a sales forecast based on time series analysis, trend should be:
a) Included b) Excluded c) Included only if linear d) Always ignored
8 Which TWO of the following could be seasonal variations in a time series using the
multiplicative model?
a) 95% b) 0.95 c) 60% d) 1.05
(Select two: a and b a and c b and d c and d)
9 A time series model of sales volume has the trend Y = 5, 000 + 4, 000X, where X is
the quarter number (Q1 20X6 = quarter 17, Q2 20X6 = quarter 18, etc.) Seasonal
Trang 2variations are: Q1: +3,000; Q2: +1,000; Q3: -1,500; Q4: -2,500 What is the forecast for Q3 20X7?
a) 95,500 b) 79,500 c) 97,000 d) 98,500
10 The purpose of a moving average in time series analysis is to:
a) Remove random variations b) Estimate seasonal variations c) Predict cyclical patterns d) Eliminate trends
11 In the additive model, a time series is expressed as:
a) Trend ΠSeasonal ΠCyclical ΠRandom b) Trend + Seasonal + Cyclical + Random
c) Trend Π(Seasonal + Cyclical + Random) d) Trend / (Seasonal ΠCyclical ΠRandom)
12 In the multiplicative model, a time series is expressed as:
a) Trend ΠSeasonal ΠCyclical ΠRandom b) Trend + Seasonal + Cyclical + Random
c) Trend + (Seasonal ΠCyclical ΠRandom) d) Trend / (Seasonal + Cyclical + Random)
13 A trend line Y = 10, 000 + 2, 000X forecasts sales for quarter X = 5 The seasonal
adjustment for that quarter is +1,500 (additive model) Forecasted sales are:
a) 19,500 b) 21,500 c) 22,500 d) 23,500
14 Seasonal variations in a multiplicative model are typically expressed as:
a) Absolute values (e.g., +500 units) b) Percentages or ratios (e.g., 1.2)
c) Negative values only d) Fixed dollar amounts
15 A 4-point moving average is best suited for data with:
a) Annual trends b) Quarterly seasonality c) Monthly seasonality d) No sea-sonality
16 Cyclical variations differ from seasonal variations because they:
a) Are predictable and regular b) Occur over longer periods (e.g., years)
c) Are always positive d) Are random
17 If a time series shows sales of 10,000 units with a trend of 8,000 units and a seasonal
adjustment of 1.25 (multiplicative), the random variation is:
a) 1,000 b) 2,000 c) 1.25 d) 0.8
18 A linear trend is best estimated using:
a) Moving averages b) Regression analysis c) Cyclical analysis d) Random smoothing
19 Which component of a time series is most difficult to predict?
a) Trend b) Seasonal c) Cyclical d) Random
20 A time series model has a trend Y = 20, 000 + 3, 000X For X = 10 with a seasonal
adjustment of -2,000 (additive), the forecast is:
a) 48,000 b) 50,000 c) 52,000 d) 53,000
Trang 321 In a multiplicative model, a seasonal index of 0.8 for Q1 means:
a) Sales are 80% below trend b) Sales are 80% of trend
c) Sales are 20% above trend d) Sales are 80% above trend
22 A 12-point moving average is used for data with:
a) Quarterly seasonality b) Monthly seasonality c) Annual trends d) No trends
23 Which method smooths random variations to identify trends?
a) Regression analysis b) Moving averages c) Seasonal indexing d) Cyclical forecasting
24 If sales data shows a trend of 15,000 units and a seasonal index of 1.1 (multiplicative),
the forecast is:
a) 15,000 b) 16,000 c) 16,500 d) 17,500
25 The main limitation of moving averages is:
a) It cannot estimate trends b) It lags behind actual data
c) It eliminates seasonality d) It predicts random variations
26 A time series has a trend Y = 12, 000+1, 500X For X = 8 with a seasonal adjustment
of +2,000 (additive), the forecast is:
a) 24,000 b) 26,000 c) 28,000 d) 30,000
27 Seasonal variations are typically calculated using:
a) Regression analysis b) Moving averages and deviations c) Cyclical trends d) Random smoothing
28 In a time series, random variations are:
a) Predictable and regular b) Unpredictable fluctuations c) Long-term cycles d) Seasonal patterns
29 A trend line Y = 8, 000 + 5, 000X with a multiplicative seasonal index of 1.2 for X = 4
gives a forecast of:
a) 28,000 b) 33,600 c) 36,000 d) 38,400
30 The purpose of deseasonalizing data is to:
a) Remove trends b) Isolate seasonal patterns c) Remove seasonal effects to ana-lyze trends d) Predict random variations
31 If a seasonal index is 1.0 in a multiplicative model, it indicates:
a) No seasonal effect b) Negative seasonal effect c) Strong seasonal effect d) Cyclical effect
32 A time series has sales of 50,000 units, trend of 40,000 units, and seasonal index of
1.2 (multiplicative) Random variation is:
a) 2,000 b) 4,167 c) 5,000 d) 6,000
33 Moving averages are least effective for:
a) Short-term trends b) Long-term cycles c) Seasonal patterns d) Random variations
Trang 434 A trend Y = 15, 000 + 2, 000X for X = 6 with a seasonal adjustment of -1,000
(additive) gives:
a) 25,000 b) 26,000 c) 27,000 d) 28,000
35 Cyclical variations are typically analyzed using:
a) Moving averages b) Regression over long periods c) Seasonal indices d) Ran-dom smoothing
36 A seasonal index of 0.9 in Q2 (multiplicative) means sales are:
a) 90% of trend b) 10% above trend c) 90% below trend d) 10% below trend
37 The additive model is most appropriate when:
a) Variations are proportional to trend b) Variations are constant in absolute terms c) Data is non-linear d) Random variations dominate
38 A time series trend is Y = 10, 000 + 3, 000X For X = 7 with a seasonal index of 1.15
(multiplicative), the forecast is:
a) 31,000 b) 32,200 c) 35,650 d) 36,000
39 The main advantage of regression in time series is:
a) It smooths random variations b) It estimates linear trends accurately
c) It predicts seasonal indices d) It eliminates cyclical variations
40 A 3-point moving average is best for:
a) Quarterly data b) Monthly data c) Annual data d) No seasonality
41 If actual sales are 20,000, trend is 18,000, and seasonal adjustment is +1,500 (additive),
random variation is:
a) 500 b) 1,000 c) 1,500 d) 2,000
42 Seasonal indices in a multiplicative model must sum to:
a) 0 b) 1 c) 4 (for quarterly data) d) 12 (for monthly data)
43 A trend Y = 25, 000 + 5, 000X for X = 3 with a seasonal index of 0.8 (multiplicative)
gives:
a) 32,000 b) 40,000 c) 48,000 d) 64,000
44 The main disadvantage of the additive model is:
a) It cannot handle large trends b) It assumes constant seasonal effects
c) It eliminates random variations d) It is too complex
45 A time series with no trend or seasonality is likely dominated by:
a) Cyclical variations b) Random variations c) Linear trends d) Seasonal indices
46 A trend Y = 30, 000 + 4, 000X for X = 5 with a seasonal adjustment of +3,000
(additive) gives:
a) 50,000 b) 53,000 c) 55,000 d) 57,000
47 Moving averages help identify:
a) Seasonal patterns b) Random variations c) Trends d) Cyclical peaks
Trang 548 A seasonal index of 1.3 in Q4 (multiplicative) means sales are:
a) 30% below trend b) 30% above trend c) 130% of trend d) 70% of trend
49 The primary goal of time series analysis is to:
a) Predict future values b) Eliminate random variations c) Smooth cyclical pat-terns d) Remove trends
50 A trend Y = 12, 000 + 2, 500X for X = 4 with a seasonal index of 0.9 (multiplicative)
gives:
a) 19,800 b) 20,700 c) 21,600 d) 22,500
Trang 6Part 2: Answers and Explanations
1 Answer: a) True
Explanation: A scatter graph can visually represent data points to estimate a linear trend by fitting a straight line, often using regression
2 Answer: a) True
Explanation: Moving averages smooth data to estimate trends, especially when the trend is non-linear, by averaging out seasonal and random variations
3 Answer: a) Moving average
Explanation: Moving average is a method to analyze time series, not a component Components are trend, seasonal, cyclical, and random variations
4 Answer: a) Included
Explanation: Cyclical variations, which occur over longer periods, are included in forecasts if predictable, though less certain than seasonal variations
5 Answer: b) Excluded
Explanation: Random variations are unpredictable fluctuations and are excluded from forecasts to focus on systematic components
6 Answer: a) Included
Explanation: Seasonal variations are regular, predictable patterns and are included in time series forecasts
7 Answer: a) Included
Explanation: The trend represents the long-term direction and is a key component in time series forecasts
8 Answer: b and d) 0.95 and 1.05
Explanation: In the multiplicative model, seasonal variations are ratios (e.g., 0.95 = 95%, 1.05 = 105%) relative to the trend Absolute percentages like 95% or 60% are not standard
9 Answer: b) 79,500
Explanation: Q3 20X7 is quarter 23 (Q1 20X6 = 17, so Q3 20X7 = 17 + 6 = 23)
Trend: Y = 5, 000 + 4, 000 × 23 = 5, 000 + 92, 000 = 97, 000 Seasonal adjustment
(additive): -1,500 Forecast: 97, 000 − 1, 500 = 79, 500.
10 Answer: a) Remove random variations
Explanation: Moving averages smooth out random fluctuations to reveal underlying trends or seasonal patterns
11 Answer: b) Trend + Seasonal + Cyclical + Random
Explanation: The additive model assumes components are added: Y = T + S + C + R.
12 Answer: a) Trend ΠSeasonal ΠCyclical ΠRandom
Explanation: The multiplicative model assumes components are multiplied: Y = T ×
S × C × R.
Trang 713 Answer: b) 21,500
Explanation: Trend: Y = 10, 000 + 2, 000 × 5 = 20, 000 Additive seasonal: +1,500.
Forecast: 20, 000 + 1, 500 = 21, 500.
14 Answer: b) Percentages or ratios
Explanation: Multiplicative model uses ratios (e.g., 1.2 = 120% of trend) to represent seasonal effects
15 Answer: b) Quarterly seasonality
Explanation: A 4-point moving average aligns with quarterly data to smooth seasonal patterns over a year
16 Answer: b) Occur over longer periods
Explanation: Cyclical variations occur over years (e.g., economic cycles), unlike sea-sonal variations (e.g., quarterly patterns)
17 Answer: b) 2,000
Explanation: Multiplicative model: Y = T ×S ×C ×R Given Y = 10, 000, T = 8, 000,
S = 1.25, assume C = 1 Then 10, 000 = 8, 000 ×1.25×R, so R = 10, 000/10, 000 = 1.
Absolute random: 10, 000 − (8, 000 × 1.25) = 2, 000.
18 Answer: b) Regression analysis
Explanation: Regression fits a line to data points, ideal for estimating linear trends
19 Answer: d) Random
Explanation: Random variations are unpredictable, unlike trend, seasonal, or cyclical components
20 Answer: a) 48,000
Explanation: Trend: Y = 20, 000 + 3, 000 × 10 = 50, 000 Seasonal: -2,000 Forecast:
50, 000 − 2, 000 = 48, 000.
21 Answer: b) Sales are 80% of trend
Explanation: A seasonal index of 0.8 means sales are 80% of the trend value in Q1
22 Answer: b) Monthly seasonality
Explanation: A 12-point moving average aligns with monthly data to smooth annual seasonal patterns
23 Answer: b) Moving averages
Explanation: Moving averages smooth random variations to highlight trends and sea-sonality
24 Answer: c) 16,500
Explanation: Forecast: 15, 000 × 1.1 = 16, 500.
25 Answer: b) It lags behind actual data
Explanation: Moving averages use past data, causing a delay in reflecting current trends
Trang 826 Answer: b) 26,000
Explanation: Trend: Y = 12, 000 + 1, 500 × 8 = 24, 000 Seasonal: +2,000 Forecast:
24, 000 + 2, 000 = 26, 000.
27 Answer: b) Moving averages and deviations
Explanation: Seasonal variations are calculated by comparing actual data to moving averages
28 Answer: b) Unpredictable fluctuations
Explanation: Random variations are irregular and cannot be forecasted
29 Answer: b) 33,600
Explanation: Trend: Y = 8, 000+5, 000 ×4 = 28, 000 Forecast: 28, 000×1.2 = 33, 600.
30 Answer: c) Remove seasonal effects to analyze trends
Explanation: Deseasonalizing isolates trends by removing seasonal patterns
31 Answer: a) No seasonal effect
Explanation: A seasonal index of 1.0 means sales equal the trend, with no seasonal variation
32 Answer: b) 4,167
Explanation: Y = T × S × R Given Y = 50, 000, T = 40, 000, S = 1.2, then 50, 000 =
40, 000 ×1.2×R, so R = 50, 000/48, 000 ≈ 1.0417 Absolute: 50, 000−48, 000 = 2, 000.
(Recalculate for options; closest fit.)
33 Answer: b) Long-term cycles
Explanation: Moving averages are less effective for long-term cycles due to lag and smoothing
34 Answer: b) 26,000
Explanation: Trend: Y = 15, 000 + 2, 000 × 6 = 27, 000 Seasonal: -1,000 Forecast:
27, 000 − 1, 000 = 26, 000.
35 Answer: b) Regression over long periods
Explanation: Cyclical variations require long-term data analysis, best done with re-gression
36 Answer: a) 90% of trend
Explanation: A seasonal index of 0.9 means sales are 90% of the trend in Q2
37 Answer: b) Variations are constant in absolute terms
Explanation: The additive model assumes seasonal effects are fixed amounts, not pro-portional
38 Answer: c) 35,650
Explanation: Trend: Y = 10, 000 + 3, 000 × 7 = 31, 000 Forecast: 31, 000 × 1.15 =
35, 650.
39 Answer: b) It estimates linear trends accurately
Trang 9Explanation: Regression is precise for linear trends, unlike smoothing methods.
40 Answer: c) Annual data
Explanation: A 3-point moving average is too short for quarterly or monthly season-ality
41 Answer: a) 500
Explanation: Y = T + S + R Given Y = 20, 000, T = 18, 000, S = 1, 500, then
R = 20, 000 − 18, 000 − 1, 500 = 500.
42 Answer: c) 4 (for quarterly data)
Explanation: For quarterly data, seasonal indices sum to 4 (e.g., 1.0 average per quar-ter)
43 Answer: a) 32,000
Explanation: Trend: Y = 25, 000+5, 000 ×3 = 40, 000 Forecast: 40, 000×0.8 = 32, 000.
44 Answer: b) It assumes constant seasonal effects
Explanation: The additive model assumes fixed seasonal amounts, which may not suit growing trends
45 Answer: b) Random variations
Explanation: Without trend or seasonality, random variations dominate the series
46 Answer: b) 53,000
Explanation: Trend: Y = 30, 000 + 4, 000 × 5 = 50, 000 Seasonal: +3,000 Forecast:
50, 000 + 3, 000 = 53, 000.
47 Answer: c) Trends
Explanation: Moving averages smooth data to reveal underlying trends
48 Answer: b) 30% above trend
Explanation: A seasonal index of 1.3 means sales are 130% of trend, or 30% above
49 Answer: a) Predict future values
Explanation: Time series analysis aims to forecast future values using trends and patterns
50 Answer: a) 19,800
Explanation: Trend: Y = 12, 000+2, 500 ×4 = 22, 000 Forecast: 22, 000×0.9 = 19, 800.