Brief Explanation of moving averages and probability

1. JehanzaibAli
MBA [Finance], MS [Finance]

2.  The moving average is simply an average.An
observer can choose various periods
(measured in minutes, hours, days, weeks,
etc.) the moving average should consider.
 It takes past data to forecast future changes.

3.  It is used in trend analysis. In stock market, for an example, moving average is
used in generating signals for investors whether to buy a particular security or
not.

4.  A simple example of daily sales figures taken 3 times a
days i.e. at morning, afternoon and evening time has
been explained in the following slides.
 Based upon the data of 3 days sales, a forecasted figures
of day 4 (Morning, Afternoon & Evening) has been
calculated.

5. Moving Averages
Data Moving Average =Trend
Day 1 Morning 170
Afternoon 140 180 -40
Evening 230 182 48
Day 2 Morning 176 186 -10
Afternoon 152 187 -35
Evening 233 189 44
Day 3 Morning 182 192 -10
Afternoon 161 195 -34
Evening 242

6. ACTUAL-TREND FIGURES TOGETHER
M A E
Day 1 0 -40 48
Day 2 -10 -35 44
Day 3 -10 -34 0
Total -20 -109 92
Average -10 46-36
(-40-35-34)/3

7. ACTUAL; EXPECTED AND RANDOM
Day 1 Day 2 Day 3
A E M A E M A
ACTUAL 140 230 176 152 233 182 161
Exptected
(trend+seasonal) 228 176 151 235 182 159
Random (actual-
expected) -4 2 0 1 -2 0 2
144
Afternoon Moving Average + Seasonal Variation
180+(-36)=144

8.  Calculate the total intervals in the data.
 Take the average of the intervals.
 180 to 195 (6 intervals)
 (195-180)/6=2.5

9.  Although you have actual figure of Day 3
evening. However, take the figure on the
basis of Day 3 Afternoon moving average in
order to calculate the trend for Day 4 as:
 Forecasted figure for Day 3 evening =
195+2.5=197.5

10. Forecasting for Day 4
Moving
Average trend
Seasonal
Variation Forecasted
Morning 197.5 2.5 -10 190
Afternoon 200 2.5 -36 166.2
Evening 202.5 2.5 46 251.0

12. The set of collection of all possible outcomes
of an experiment is called sample space. e.g.
if a die is rolled once, all possible outcomes
are:
S={1,2,3,4,5,6}

13.  Each possible outcome of an experiment is
called an event.An event is a subset of
sample space. Suppose, die is rolled and we
are expecting an event that a number
appears on the top of the dice is an even
number.
 Let this event is represented by A.
 Thus, A={2,4,6}

14.  Probability is defined as a chance of occuring
an event. It is denoted by P(E), where P is
probability and E is any event.An event can
be denoted by any alphabet A, B, C, D ……..Z.

15.  If a die is rolled, find the probability than number
appears on the top of the die is an even number.
Let A is defined as event of occurring an even
number.
S={1,2,3,4,5,6}, A={2,4,6}
n(S)=6 n(A)=3
P(A)=n(A)/n(S)
=3/6
=1/2 or 0.5