Question Tag: Time series

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QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

Question

The sales of PQR Nigeria Plc. in thousands of Naira are listed in the table below for each quarter for years 2005 – 2008.

Sales of PQR in N’000s

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2005	22	35	82	37
2006	24	46	81	44
2007	25	40	87	49
2008	29	42	100	55

Required:

a. Calculate the trend in the above data using the Least Squares Method. (12 Marks)
b. Estimate the sales for each quarter using the trend line. (4 Marks)
c. Calculate the percentage variation for each quarter’s actual sales from the estimate obtained in (b) above. (4 Marks)

(Total: 20 Marks)

Answer

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Tags: Least Squares, Sales Forecasting, Time series, Trend Estimation
Level: Level 1

Topic: Forecasting
Series: NOV 2014

QTB – May 2017 – L1 – SA – Q18 – Statistics

This question calculates the centered moving average for a specific year in a time series of cocoa production.

Question

A ten-year record of cocoa production in a certain farm is tabulated as follows:

Year	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012
Production (tonnes)	42	52	41	48	64	67	77	66	73	89

Based on a 4-year moving total, the centered moving average for the year 2007 is:
A. 79.5
B. 69.5
C. 59.5
D. 49.5
E. 39.5

Answer

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Tags: Business Statistics, Moving Average, Time series
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q14 – Statistics

This question involves identifying the estimable components of a time series.

Question

The TWO components of a Time Series which are usually estimable are:
A. Trend and Cyclic variation
B. Seasonal variation and Trend
C. Random movements and Trend
D. Seasonal variation and Random movements
E. Cyclic variation and Seasonal variation

Answer

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Tags: Forecasting, Seasonal Variation, Time series, Trend
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2016 – L1 – SB – Q6a – Data Collection Analysis

This question involves calculating moving averages and centered moving averages for quarterly sales data.

Question

The quarterly sales figures of company ABC Plc. for 3 years are as recorded below:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
Year 1	30	34	37	41
Year 2	45	49	54	57
Year 3	59	66	70	74

Required:
i. Calculate:

The moving averages.
(9 marks)

ii. The centered moving average for Quarter 3, Year 1.
(1 mark)

Answer

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Tags: Moving Averages, Seasonal Adjustment, Time series
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2016

QTB – May 2016 – L1 – SA – Q17 – Statistics

Calculating the trend stock for a future month based on historical stock figures.

Question

A company takes stock for 5 months in each year. The stock figures of materials for the most recent three years are as tabulated below:

Determine the trend stock for month 6.

A. 84

B. 85

C. 86

D. 87

E. 88

Answer

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Tags: Forecasting, Time series, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2015 – L1 – SA – Q19 – Statistics

Identifying the components separated during the deseasonalisation of business data.

Question

Deseasonalisation of business data is a process of separating two components of a time series which are:

A. Trend and cyclical variation
B. Irregular and cyclical variation
C. Trend and seasonal variation
D. Cyclical and seasonal variation
E. Seasonal and irregular variations

Answer

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Tags: Deseasonalisation, Statistical Analysis, Time series
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q14 – Statistics

Identifying types of variations present in time series data.

Question

Which of the following represents the types of variations in time series analysis?

A. Trend and cyclical variation
B. Irregular and cyclical variation
C. Trend and seasonal variation
D. Cyclical and seasonal variation
E. Seasonal and irregular variations

Answer

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Tags: Time series, Trend Analysis, Variations
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q12 – Statistics

Identifying the correct term for the amount of time activities can be delayed in project management.

Question

The amount of time during which a path of activities could be delayed without affecting the overall project duration is called:

A. Independent float
B. Total float
C. Free float
D. Excess time float
E. Average time float

Answer

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Tags: Analysis, Statistical Methods, Time series
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q11 – Statistics

Identifying methods used to measure trends in time series data.

Question

The following methods are used to measure the trend of a time series EXCEPT:

A. Semi-average
B. Moving average
C. Free-hand
D. Deseasonalisation
E. Least squares

Answer

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Tags: Statistical Methods, Time series, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2015

BMF – May 2018 – L1 – SA – Q19 – Basics of Business Finance and Financial Markets

Identifies methods for measuring trends in time series.

Question

Which of the following methods CANNOT be utilized for trend measurement in time series data?
A. Free hand method
B. Semi-average method
C. Moving average method
D. Least squares method
E. Spearman’s ranking method

Answer

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Tags: Statistical Methods, Time series, Trend Measurement
Level: Level 1

Topic: Basics of Business Finance and Financial Markets
Series: MAY 2018

MI – May 2024 – L1 – SB – Q1 – Forecasting Techniques-Analysis, Moving Averages

Analyze a time series and describe two models for estimating seasonal variation.

Question

a. Describe how a time series can be analyzed. (10 Marks)

b. “There are TWO models used to estimate seasonal variation.” List and briefly describe the TWO models. (10 Marks)

Answer

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Tags: Additive model, Moving Averages, Proportional Model, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting Techniques-Analysis, Moving Averages
Series: MAY 2024

QT – May 2019 – L1 – Q5b – Forecasting

Compute 5-period moving averages, weighted moving averages, and comment on their suitability for forecasting

Question

The number of enquiries being made to a mail order business during a Monday to Friday working week is given as:

Week	Monday	Tuesday	Wednesday	Thursday	Friday
1	34	36	24	25	41
2	33	34	24	23	43
3	35	37	25	25	47

Required: i) Plot the data on a graph.
ii) Compute a 5-period moving average for the data.
iii) Compute a ‘weighted’ moving average for the data if the smoothing constant is $α = 0.5$ .
iv) Superimpose the graphs of (ii) and (iii) on your graph in (i) above.
v) Comment on the suitability of the two smoothing methods above. (16 marks)

Answer

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Tags: Data Plotting, Forecasting, Moving Averages, Time series, Weighted Moving Averages
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2019 – L1 – Q5a – Forecasting

Explain the concepts of moving averages and exponential smoothing in time series forecasting.

Question

The objective of smoothing methods is to smooth out the random variations due to irregular components of the time series and provide an overall impression of the pattern of movement in the data over time.

Required:
Explain the following smoothing methods:

i) Moving averages (2 marks)
ii) Exponential smoothing (2 marks)

Answer

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Tags: Exponential Smoothing, Forecasting, Moving Averages, Smoothing Methods, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

Question

The number of clients who consulted Tsoo Consult within a period of three years were recorded as follows:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
1	75	70	75	80
2	95	85	80	65
3	100	105	115	90

Required:
a) Assuming a 4 quarterly cycle, calculate the centred trend values for the data by moving average method. (4 marks)

b) Using (a) above and the multiplicative model, calculate the average seasonal variations. (5 marks)

c) Using (b) above, calculate the adjusted average seasonal variations for the data. (5 marks)

d) Using the trend and the adjusted average seasonal variation, forecast the number of clients for Year 4 based on the multiplicative model. (6 marks)

Answer

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Tags: Forecasting, Moving Averages, Multiplicative Model, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2016 – L1 – Q2 – Forecasting

This question asks for the creation of a linear regression trend equation, seasonal components, and forecasts for chocolate sales.

Question

Countess Company trades in bars of Golden Tree Chocolate from Tema Cocoa Processing Company Limited. The number of bars of chocolate sold per quarter over a four-year period by Countess Company is:

YEAR	QUARTER 1	QUARTER 2	QUARTER 3	QUARTER 4
1	20	10	4	11
2	33	17	9	18
3	45	23	11	25
4	60	30	13	29

Required:

i) Plot the data on a graph (3 marks)

ii) Calculate a linear regression trend equation for the data (5 marks)

iii) Calculate the four seasonal components using a multiplicative model (5 marks)

iv) Forecast the number of bars of chocolate for the next two years (5 marks)

v) Comment on the reliability of the forecasts in iv) above (2 marks)

Answer

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Tags: Forecasting, Linear Regression, Multiplicative Model, Seasonal Components, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2016

QT – Nov 2016 – L1 – Q7 – Forecasting

Analyze absenteeism trends using time series and forecasting techniques for Dropper Ltd.

Question

The personnel department of Dropper Ltd, a large cocoa processing company in DropperLand, is concerned about absenteeism among its shop floor workforce. The mean number of absentees per day for each quarter of the years 1999 to 2001 and Quarter 1 in 2002 is given in the table below:

	Q1	Q2	Q3	Q4
1999	25.10	14.40	9.50	23.70
2000	27.90	16.90	12.40	26.10
2001	31.40	19.70	15.90	29.90
2002	34.50	–	–	–

Required:
a) Plot the data on a graph, leaving space for the remaining 2002 figures. (3 marks)

b) Using the method of 2-quarterly centered moving averages,
i) Determine the trend in the series and superimpose this on your graph in (a). (4 marks)
ii) Determine the equation of the trend line above by considering only the first and last centered moving average value on your graph in (i). (3 marks)

c) Using an appropriate decomposition model, determine the seasonal variations in the data. Give reasons for your choice of model. (5 marks)

d) Use your analysis above to roughly forecast the mean number of absentees for the remaining quarters of 2002. Comment on your forecast. (5 marks)

Answer

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Tags: Absenteeism, Forecasting, Seasonal Variations, Time series, Trend
Level: Level 1

Topic: Forecasting
Series: NOV 2016

QT – May 2018 – L1 – Q4 – Forecasting

Calculate centered moving averages, seasonal variations, and forecast sales using the multiplicative model.

Question

a) The quarterly unit sales of electronic items of a retail company for the last three years are as follows:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2013	100	115	70	210
2014	120	165	100	220
2015	150	195	120	270

Required:
i) Calculate a centered three-moving average of the unit sales. (3 marks)
ii) Calculate the trend using a centered four-quarterly moving average. (4 marks)
iii) Calculate the four seasonal variations using (ii) and the multiplicative model. (7 marks)
iv) Forecast the number of unit sales for the year 2016 using the multiplicative model. (4 marks)
v) Comment on your answer in (iv). (2 marks)

Answer

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Tags: Forecasting, Moving Averages, Seasonal Variations, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2018

QT – Nov 2018 – L1 – Q6b – Forecasting

Calculate the moving average, trend values, seasonal variation, and forecast membership.

Question

Membership of Pro Amalion, a network of professional volunteers, has grown over the years but in the months of the second quarter, there was always a decline. The table below shows membership records for a period of four years:

Year	1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
Year 1	713	694	735	755
Year 2	767	733	766	780
Year 3	787	755	798	814
Year 4	816	790	826	843

Required:
i) Calculate the centered four-quarterly moving average of membership. (4 marks)
ii) Using a least squares trend equation based on (i) above, calculate the trend values. (5 marks)
iii) Using (ii) above, calculate the percentage seasonal variation and the average seasonal variation of membership. (5 marks)
iv) Determine the seasonally adjusted forecast of membership for each of the four quarters of Year 5. (4 marks)

Answer

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Tags: Forecasting, Least Squares, Membership Forecast, Moving Averages, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting
Series: NOV 2018

QT – Nov 2018 – L1 – Q6a – Forecasting

State the two main models of time series analysis.

Question

State the TWO (2) main models of time series analysis. (2 marks)

Answer

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Tags: Additive model, Forecasting, Models, Multiplicative Model, Time series
Level: Level 1

Topic: Forecasting
Series: NOV 2018

QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

Question

Quarterly sales of a Golden Tree Chocolate Bar at a popular mall in KoKoLand City are given as follows:

YEAR	QUARTER 1	QUARTER 2	QUARTER 3	QUARTER 4
1	1260	756	588	1596
2	1352	966	579	2028
3	1786	920	865	2273

Required:
(i) Calculate the trend in the series using a 4-point centered moving average method. (4 Marks)

(ii) Using (i), calculate the Average Seasonal Variation based on the Additive Model of Time Series analysis. (4 Marks)

(iii) Using the values in (ii), determine the Adjusted Average Seasonal Variation for the Time Series Data. (4 Marks)

(iv) Prepare Seasonal Adjusted Forecast for Year 4 using the Additive Model. (4 Marks)

Answer

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Tags: Additive model, Forecasting, Seasonal Variation, Time series, Trend Analysis
Level: Level 1

Topic: Forecasting
Series: NOV 2015

Question Tag: Time series

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QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

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QTB – May 2017 – L1 – SA – Q18 – Statistics

This question calculates the centered moving average for a specific year in a time series of cocoa production.

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QTB – May 2017 – L1 – SA – Q14 – Statistics

This question involves identifying the estimable components of a time series.

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QTB – May 2016 – L1 – SB – Q6a – Data Collection Analysis

This question involves calculating moving averages and centered moving averages for quarterly sales data.

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QTB – May 2016 – L1 – SA – Q17 – Statistics

Calculating the trend stock for a future month based on historical stock figures.

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QTB – May 2015 – L1 – SA – Q19 – Statistics

Identifying the components separated during the deseasonalisation of business data.

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QTB – May 2015 – L1 – SA – Q14 – Statistics

Identifying types of variations present in time series data.

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QTB – May 2015 – L1 – SA – Q12 – Statistics

Identifying the correct term for the amount of time activities can be delayed in project management.

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QTB – May 2015 – L1 – SA – Q11 – Statistics

Identifying methods used to measure trends in time series data.

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BMF – May 2018 – L1 – SA – Q19 – Basics of Business Finance and Financial Markets

Identifies methods for measuring trends in time series.

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MI – May 2024 – L1 – SB – Q1 – Forecasting Techniques-Analysis, Moving Averages

Analyze a time series and describe two models for estimating seasonal variation.

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QT – May 2019 – L1 – Q5b – Forecasting

Compute 5-period moving averages, weighted moving averages, and comment on their suitability for forecasting

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QT – May 2019 – L1 – Q5a – Forecasting

Explain the concepts of moving averages and exponential smoothing in time series forecasting.

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QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

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QT – May 2016 – L1 – Q2 – Forecasting

This question asks for the creation of a linear regression trend equation, seasonal components, and forecasts for chocolate sales.

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QT – Nov 2016 – L1 – Q7 – Forecasting

Analyze absenteeism trends using time series and forecasting techniques for Dropper Ltd.

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QT – May 2018 – L1 – Q4 – Forecasting

Calculate centered moving averages, seasonal variations, and forecast sales using the multiplicative model.

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QT – Nov 2018 – L1 – Q6b – Forecasting

Calculate the moving average, trend values, seasonal variation, and forecast membership.

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QT – Nov 2018 – L1 – Q6a – Forecasting

State the two main models of time series analysis.

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QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

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