Business Statistics Tutorial Mahmudul Hasan Nakib Founder President (Inventive Point) BBA , MBA (Finance), AUB, SEU CMA, ICMAB(Studying) wwm

2. Time Series
• We often use / deal with statistical data which are
collected, observed or recorded at successive
intervals of time to determine the consistency of
gathering information from the past data. Such
data are considered as time series.
• When we observe data (numerical) at different
points of time.The set of observation is known as
time series.

3. Mathematically
• Mathematically , a time series is defined by the
values
Y₁ ,Y₂ --------- of a variableY at time t₁ , t₂ --------
Thus
Y is a function of t . SymbolizedY = F (t).
Example : Production, Sales, Profits of a company at
different points of time say over the last 5 years.

4. Role of Time Series Analysis
• 1) It helps in the understanding of the past behavior
of observed data.
• 2) It helps in planning future operations.
• 3) It helps in evaluating current accomplishments.
• 4) It helps to facilitate comparison.

5. Component of Time Series
• There are four basic types of variations which associates
the changes in the series over a period of time.
1) SecularTrend.
2) SeasonalVariations.
3) CyclicalVariations.
4) IrregularVariations.

6. • Any particular variableY in a series can be expressed as a
product of these components
Y =T x S x C x I
Where,T = Secular trend.
S = SeasonalVariations.
C= CyclicalVariations.
I = IrregularVariations.

7. Secular Trend
• We often talk that the population, prices, production
normally increases day to day.We observe such variables
over a long period of time. Some times we find variables
showing downward or constant tendency such death rate
of babies by diarrhea. All these variable we observe for a
long time which is known as a secular trend.

8. Types of Secular trends.
There are two types of Secular trends.
1) Linear or Straight line trends.
2) Non Linear trends.
The straight line trends is represented by the equation.
Yc = a+bx
Where,Yc denotes the trend values to distinguished from the actual
valueY.
∑ Y
a is theY intercept & a =
N

9. Types of Secular trends.
• b is the amount of change inY which associate with the change of
unit in X variable.
∑XY
b =
∑X²

10. Example :
• Nakib’s factory produces sugar in different years as follows.
1) Fit a straight line trend to these figure.
2) Estimate the likely sales of the company during 2005.
Year 201
0
2011 2012 2013 2014 2015 2016
Production
(in m.tonnes)
80 90 92 83 94 99 92

11. Math Solution