Trend and residual variation discussion



SECTION A 10 marks

Instruction: Highlight the correct answer



2. The components that makes up a typical time series are:

A. Trend and residual variation

B. Seasonal and residual variations

C. Trend and long-term cyclic variations

D. Trend, seasonal and residual variations



3. Short term but regular variations are:

A. sudden

B. determined by formula

C. seasonal

D. determined by some table values



4. The main purpose of a time series moving averages is to:

A. determine the coefficient of correlation

B. smooth out the time series

C. show the correlation between the time series and the regression line

D. determine the linear coefficient



5. The best fitting trend line is the one for which squares or errors are the:

A. most

B. least

C. positive

D. negative



6. Given a projected trend value of 66 and a seasonal value of 2.5. Based on the additive model, the estimated forecast data value for a particular period would be:

A. 64.5

B. 67.25

C. 68.5

D. 71


7. Which of the following is aDISADVANTAGEof using a moving average technique to determine time series trend?

A. The trend values obtained do not reflect the general trend.

B. Only one trend value can be obtained for either of the end points of the series.

C. No trend values are obtained for the beginning and end time points of the series.

D. Each moving average trend value obtained does not correspond with a time point



8. The original data value of a time series is 3.2 and the corresponding seasonal variation value is – 2.16. What is the seasonal adjusted value base on the additive model?

A. -5.23

B. 1.04

C. 5.23

D. 5.36



Use the following information to answer Questions 8 and 9

With reference to the following Time Series data:

Time Point 1 2 3 4 5 6 7 8
Data Values 9 14 17 12 10 14 19 15


9. What is thethree (3)period moving total for time point 3?

A. 36

B. 39

C. 40

D. 43



10. What is thefour (4)period centered moving average for time point 3?

A. 13

B. 13.125

C. 13.25

D. 15.75




Given that the actual value using the additive time series model is: 

A. -1.12

B. 2.6

C. 4.39

D. 5.41



Use the following information to answer Questions 11 – 13

The following is a time series for the first 5 months of 2006:

2006 45 50 52 48 55


12. The three point (3) moving totals are:

A. -110, -118, -130

B. 63, 59, 65

C. 120, 145, 112

D. 147, 150, 155



13. The three point moving averages are:

A. 20.3, 24, 25.3

B. 36.7, 39.3, 43.3

C. 40, 48.3, 37.3

D.49, 50, 51.67



Suppose the equation of the trend line for the time series is given by wheretis thenthposition of the time series, estimate the value ofyat the end of the year. 

A. 30

B. 34

C. 51

D. 63

15. Month by month changes in sales related to holiday and other special events would be an example of:

A. trend values

B. total sales

C. seasonal variations

D. residual variations



Use the following information to answer Questions 15and 16

The table shows the number of units (1000) of an item sold by a company from 1991 2000.

X=4-year centred moving averages


Year Data X Year Data X
1991 9.47   1996 7.55  
1992 9.26   1997 7.24  
1993 8.86   1998 7.01  
1994 7.81   1999 6.88  
1995 8.01   2000 7.03  



16. The first value for the 4-year centred moving average is:

A. 8.39

B. 8.76

C. 8.85

D. 8.96



17. Using values for the 4-year moving averages from question 15, the two values of the deviation y-for 1996 is:

A. 0.23

B. 0.10

C. 0.10

D. 0.23



18. Centred moving averages represents the:

A. seasonal variations

B. trend values

C. original values

D. residual variations


In a time series analysis, if the value for the and , then the seasonal variation would be: 

A. 5

B. 10

C. 15

D. 20



20. Which of the following isNOTa characteristic of exponential smoothing?

A. Smooths random variations in a data

B. Easily altered weighting scheme

C. Weights each historical value equally

D. Has minimal data storage requirements



21. A six months moving average forecast is better than a three months moving average forecast if demand:

A. is rather stable

B. has been changing due to recent promotional efforts

C. follows an upward trend

D. follows a downward trend



22. When there is no significant upward or downward movement (or trend) in a time series data overtime, then the data is said to be:

A. Critical

B. Invalid

C. Non-stationary

D. Stationary







Use the following information to answer Questions 22 -24

The table below contains the number of complaints received from the students in 2013:

Month Complaints Weight
January 44 0.0
February 49 0.1
March 57 0.2
April 80 0.3
May 121 0.4
June 150 0.5


23. If a three term moving average is used to smooth this series, what would be the second calculated term?

A. 43

B. 62

C. 86

D. 117


24. What would be the last term of a 4-month moving average?

A. 85

B. 98

C. 102

D. 117



25. If the weights listed on the column 3 of the table are applied, what is the moving average at the month of May?

A. 10.0

B. 18.6

C. 34.4

D. 58.5



26. ___________ use(s) management judgement, expertise and opinion to make forecasts.

A. Qualitative methods

B. Quantitative methods

C. Regression

D. Time series

27. In exponential smoothing, the closer alpha is to _____, the greater the reaction to the most recent demand.

A. 1

B. 0

C. 1

D. 1 or 1



28. _______ is the difference between the forecast and actual demand.

A. Forecast mistake

B. Forecast error

C. Forecast accuracy

D. Mean Absolute Deviation, MAD



29. Which of the following isNOTpresent in a time series?

A. Operational variations

B. Seasonality

C. Trend

D. Random variations




In a time series analysis, Calculate the actual valueyusing the time series model. 

A. 30

B. 80

C. 150

D. 160



31. All the following are forecasting techniquesEXCEPT:

A. Causal models

B. Qualitative models

C. Optimistic Predictor models

D. Time-series models



32. Time-Series analysis is described best as the forecasting techniques that:

Attempt to incorporate judgemental or subjective factors in decision making.

Relies on quantitative data and incorporates variables or factors that might influence quantity being forecasted.

Develops the best statistical relationship between dependent and independent variables.

Make assumption about what will happen in the future as a function of what happened in the past.



33. Bob forecasted the total hospital impatient days for three months.

Months January February March
Forecast 250 300 275
Actual 243 315 286





With the actual data received, the mean absolute deviation (MAD) of his forecasted model is:







34. Which of the following isNOTa quantitative forecasting model?

A. Exponential Smoothing

B. Trend Analysis

C. Consumer Market Survey

D. Causal Regression Analysis


35. The time series demand pattern that is shown in the diagram is:














In exponential smoothing, the smoothing constant has a value: 

A. less than 0

B. between -1 and 1 inclusive

C. between 0 and 1 inclusive

D. greater than 1










SECTION B30 marks

Instruction: AnswerALLquestions.ALLworking must beCLEARLYshown.


Building Materials Ltd. wants to predict their sales for the fiscal year 2020, and the financial team was provided with the following table with actual sales value in thousands of dollars:


Month Sales ($000)
January 153
February 147
March 204
April 198
May 216
June 139
July 162



Writing all answers to the nearest whole number:

(i) Compute a four month simple moving average forecast for the sales from May to August 2020.

(4 marks)


(ii) If the actual sales for August is $183,000, what is the percentage error in the forecast?(2 marks)



Compute a four month weighted moving average forecast for the sales from May to August 2020, using the weights: .(4 marks) 



Compute the exponential smoothing forecast from February to August using and an initial forecast for January as $150,000.(6 marks) 


(v) Calculate the Mean Absolute Deviation (MAD) for each forecasting method.(4 marks)


(vi) Calculate the Mean Square Error (MSE)for the weighted moving average(3 marks)


(vii) Calculate the Mean Absolute Percentage Error (MAPE) for the exponential smooth forecast.( 7 marks)



































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