Numerical Case Study

On

“Business Statistics”By

Aditya Purohit(BBA 2nd Year)

106/10 civil lines,

Ajmer 305001

Website: www.dezyneecole.com

NUMERICAL CASE STUDY ON TIME SERIES ANALYSIS:

(i) A Company produced Tea every economic year, the tea production of a company are as follows:

Year Production[‘000 lbs.]

Year Production[‘000 lbs.]

1986 165 1998 2801987 178 1999 3511988 236 2000 3201989 213 2001 3701990 180 2002 3661991 163 2003 3251992 150 2004 2561993 187 2005 3041994 210 2006 2911995 237 2007 2711996 203 2008 2741997 215 2009 272

Draw a time series graph on a graph paper relating to the following data and show the trend by free hand curve and comment on the trend by giving emphasis in the component of time series and business cycle and comment on the company’s position and elaborate the stage or year of production according to the business cycle.

(ii) Also find the trend of production by the method of a 3 yearly cycle and also suggest the minimum and maximum level of production according to the time series analysis and trend value for the company for the following data:

Year Production[in tonnes]

2000 112001 122002 102003 82004 92005 102006 122007 112008 132009 14

SUMMARY

TOOLS and TECHNIQUES used in solving the case study:

Meaning of Analysis of Time Series:

“ A Time Series may be defined as a collection of magnitudes belonging to different time periods, of some variable or composite of variables, such as production of steel, per capita income, gross national product, production of tobacco, or index of industrial production ”.

Utility of Time Series:

1. It helps in Understanding Past behavior.

2. It helps in forecasting.

3. It helps in evaluating Current Accomplishments.

4. It helps in Comparison.

Use of Long term or secular trend:

Ina time series secular trend means long term changes. In any time if we see the changes between two periods, we will find increasing or decreasing or even a constant trend.

Methods used in measuring long term or secular trend in case study:

(i) Free hand curve method.

(ii) Moving average method.

(i)

Comment on trend with emphasis on component of time series

By observing the trend line and trend analysis from the graph, we can clearly depict that it is a secular or long term trend component of time series and by observation, we can analyze that an increasing trend has been seen in production of the company from the starting year i.e. 1986 to 2009 (ignoring the short term fluctuations) and high’s have been recorded in the year 1988, 1995, 1999(drastic), 2001, 2002, 2005 and 2007.

Comment according to the business cycle

According to the business cycle components, the years for different stages of production are as follows:

YEARS IN

PROSPERITY STAGE: 1986, 1987, 1988, 1999, 2001 & 2002.

YEARS IN

DECLINE STAGE: 1989, 1990, 1991, 2000 & 2003.

YEARS IN

DEPRESSION STAGE: 1992, 1993 & 2004.

YEARS IN

IMPROVEMENT STAGE: 1994, 1995, 1996, 1997, 1998, 2005, 2006, 2007, 2008 & 2009.

By looking at the trend according to the business cycle, we observe that although for five years company’s production declined, even it felt in depression stage for three years but overall, company’s production have shown rapid improvement and even prosperity.

Company has altogether managed to maintain its prosperity in production and has shown remarkable improvement as compared to past years.

Year Production 3 Yearly Totals 3 Yearly Moving

[in tonnes] Average2000 11 - -

2001 12 33 112002 10 30 102003 8 27 92004 9 27 92005 10 31 102006 12 33 112007 11 36 122008 13 38 13

2009 14 - -

(ii)

Comment according to the trend observed

By watching the trend analysis from the graph, we can clearly depict that for the original data, minimum level of production has been recorded in the year 2003 which was 8 tonnes and the maximum level of production has been recorded in the year 2009 which was 14 tonnes.

In the same way, by watching the trend analysis for 3 yearly moving average, we can depict that the minimum level of production has been recorded consistently for two years i.e. 2003 and 2004 which was 9 tonnes for both the years and the maximum level of production has been recorded in the year 2008 which was 13 tonnes.

Comparison of the two Graphs

(I: Graph from 1986 to 2009)

(II: 3 Yearly m.a. graph from 2000 to 2009)

If we compare the trend lines and trend analysis for both the graphs, we can clearly remark that if the company would have produced as per the 3 yearly m.a. graph, then it would have produced more in tones as compared to the production done by the company from years 1986 to 2009.

REASON: As per the 3 yearly m.a. graph is concerned, it clearly shows that the trend line has shown rapid growth significantly both for 3 yearly m.a. as well as for original data.

Bibliography

On completing this case study successfully, I would like to thank my subject teacher Ma’am Neha who cleared all my doubts regarding the case study and for supporting me in every step of this case study and I would also like to thank my parents who were always there with me in every phase of the case study.