Moving AveragesJehanzaib Ali

MBA [Finance], MS [Finance]

Definition

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.

Simple Moving Average-A practical view 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.

Example

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.

Calculating Moving Averages

Moving Averages      Data   Moving Average =TrendDay 1 Morning 170

Afternoon 140 180 -40Evening 230 182 48

Day 2 Morning 176 186 -10Afternoon 152 187 -35Evening 233 189 44

Day 3 Morning 182 192 -10Afternoon 161 195 -34Evening 242

Extracting Data (Actual-Trend Figure)

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

Random Variation-Calculations

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

Forecasting for Day 4

Calculate the total intervals in the data.

Take the average of the intervals. 180 to 195 (6 intervals) (195-180)/6=2.5

Forecasting for Day 4 (cont.) 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

Day 4 Forecasting-Calculation

Forecasting for Day 4Moving 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

Probability

Sample Space

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}

Event

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}

Probability

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.

Probability-A simple example 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

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