Time series

​ ​ ​ ​​The quarterly sales of Meshek Traders during the years 2022, 2023 and 2024 were as tabulated below:

​​Explain THREE uses of time series analysis in business decision making.

​ ​ ​ ​ ​​A company tracked its quarterly sales (in millions) over the past 3 years as shown in the table below:

​ ​​Explain THREE methods of estimating the trend line in time series analysis.

​ ​ ​ ​ ​ ​​The data below represents the sales made by Yatta Traders for a period of three years:

​ ​​Differentiate between the “multiplicative model” and “additive model” as used in time series

​ ​ ​ ​​A car hire company has provided the data below showing the number of cars hired out for the last 10 months ending 31 March 2024:

​ ​ ​ ​​The following data shows the quarterly sales of cars for Excellent Auto Enterprises for a period of three years:

​ ​ ​ ​ ​​The data below shows the sales made by Kuza Limited over a period of 6 years:

​ ​​In the context of time series analysis, distinguish between the following terms:

(i) “Mean absolute deviation” and “mean squared error”.

(ii) “Additive model” and “multiplicative model”

​ ​ ​ ​ ​ ​ ​ ​​The quarterly profits of Nyota Limited during the years 2019, 2020, and 2021 were as tabulated below:

​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​​The data below relate to the profits of Soko Yetu Groceries (in thousands of shillings) over a period of four years.

​​ The data below relates to the sales of Madi and Sons Electrical Company for the six months ending 30 June 2022:

​ ​ ​ ​ ​​The table below shows the quarterly profits of Kahawa Limited (in millions of shillings) for the years 2019, 2020 and 2021:

​​Explain the following terms as used in time series analysis:

(i) Cyclical variations.

(ii) Random variations.

(iii) Seasonal variations.

(iv) Trend. 

​ ​ ​ ​ ​ ​ ​ ​​The following data relates to the profits reported by XYZ Ltd. in each of the months in the year 2020:

​ ​ ​​The following data presents the quarterly imports of electrical products by a certain electronics company for the given four-year period:

​​Enumerate two advantages and two disadvantages of the ordinary least squares method of forecasting.

​ ​ ​​The data given below shows the profits in shillings million made by an economic sector in your country during the various quarters of the given years.

​​ In the context of time series analysis, describe three differences between "additive" and "multiplicative" models.

​ ​ ​ ​​The data below represent the number of students enrolled in a certain college over a four year period:

​Estimate the enrollment of students in each of the four quarters of year 2019 using the simple least squares method. 

​​Highlight the four components of a time series.

​ ​ ​ ​ ​ ​​The following data show quarterly production of oranges by a certain large scale farmer in thousands of kilogrammes:

The following data were obtained from the records of Kiwandani Limited for the year 2015:


Required:
(i) The least squares regression function relating direct labour hours and total overhead cost.
(ii) The coefficient of determination. Comment on your result.

The data below show the number of cars imported by a certain car dealer over a four-year period:


Required:
(i) The trend equation, using the least squares method.

(ii) Average seasonal index for each quarter using the multiplicative model.

(iii) Year 2015 seasonally adjusted import forecasts for each quarter.

​​The data below represent the sales made by Pengo Traders for a period of three years:


Required:
(i) The centred moving average trend values.
(ii) The seasonal additive indices.
(iii) The deseasonalised time series.

​​Highlight the four components of a time series.