THỐNG KÊ KINH DOANH_Ch10

7/30/2019 THNG K KINH DOANH_Ch10

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BUSINESS STATISTIC

NGUYEN TRUONG SON


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CONTENTS

Chapter 1 Collecting data

Chapter 2 Presenting data Chapter 3 Summarizing data

Chapter 4 Correlation & Regression

Chapter 5 Probability & Expected value


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CONTENTS (Cont.)

Chapter 6 The normal distribution and

confidence interval Chapter 7 Financial model

Chapter 8 Linear programming

Chapter 9 Index numbers

Chapter 10 Time based forecasting model


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CHAPTER 10

Time based

forecastingmodel


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LEARNING OBJECTIVE

To introduce the idea of time based models and their

uses in forecasting.

To discuss meaning of trend in data and the use of

linear regression to estimate them.

To develop the ideas of forecasting time series,

discussing component involve.


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Introduction


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10.1 Linear time based models

Data collected over a period of time is

usually called a time series. As discussed previously, this type of data is

normally display on a line graph with time

periods forming the x-axis and data values

shown on the y-axis


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10.1 Linear time based models

0

10

20

30

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999No.oflicences

Year

No. of colour TV liences (millions)

Trends in time seriesTrend is usually used to describe the underlying direction

of a time series. In example 10.1 above, the data has an

upward trend as it clearly increases over time.


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10.2 Forecasting using simple linear models

Once the linear model has been estimated,

the production of forecasts is relativelystraightforward.

However, it should be remembered that in

forecasting into the future extrapolation is

used. Assumption that the pattern seen in the past

will continue into the future.


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10.3 Components of a time series

Trend (T)

As already discussed for the simple linearmodels, the trend is the underlying movement in

the data it may upward, downward or staionary.

Seasonal factors (S)

These are regular fluctuations within a completetime period (a day, a week, a month v.v.)

The important thing about seasonal factors is that

they represent some sort of repeating pattern


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Cyclical factors

These are long term fluctuations in the data andare similar to seasonal factors.

Its difficult to identify unless a long series of data

is available.

They may be related to economic factors exampleholiday sales may reduce during periods of

recession.


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Random or residual factors (S)

As in statistical analysis, there will be someunpredictable element to the data.

Example: Something like unusual weather

conditions effecting holiday sales.

The effects can not be forecasted.


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Since the cyclical elements will not consider

in detail here and random elements areimpossible to predict.

The model consists of isolating the two

predictable components:

Trend

Seasonal effects.


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10.4 Forecasting the trend

The aim here is smooth out the effects due

to the other factors, leaving only theunderlying direction of the series to be

forecast.

This could be done simply be eye taking

some sort of straight line through the dataand attempting to the trend it.


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Moving average

Taking the average of each successive nobservations in turn formed by dropping the first

point in the sequence and picking up the next

one each time.

Average are generally take over the natural

periodof the data (the amount of time over which

the seasonal pattern reapeats)

For quarterly data is 4

For daily data is 5 or 7


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Moving average

Odd-point movingaverages

Day

No. of

enquires 5 point moving average

M 33

Tu 41W 77 66.2

Th 81 67.4

F 99 69

M 39 70.4

Tu 49 72.2

W 84 73.8Th 90 75.4

F 107 76.6

M 47 78

Tu 55 80.4

W 91 81.6

Th 102

F 113


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Moving average

Odd-point moving averages

0

20

40

60

80

100

120

M Tu W Th F M Tu W Th F M Tu W Th F

No. of enquires

5 point moving average


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Moving average

Even-point moving averagesYear Quarter Holiday sales 4-point moving average Centered moving average1996Q1 3576

Q2 2927 2,894.25

Q3 2710 2,865.75 2,880.00

Q4 2364 2,790.75 2,828.25

1997Q1 3462 2,692.00 2,741.38

Q2 2627 2,587.00 2,639.50Q3 2315 2,527.00 2,557.00

Q4 1944 2,550.00 2,538.50

1998Q1 3222 2,624.75 2,587.38

Q2 2719 2,649.00 2,636.88

Q3 2614

Q4 2041


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Moving average

Even-point moving averages

0

500

1000

1500

2000

2500

3000

3500

4000

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

1996 1997 1998

Holiday

Sales

Holiday sales data with centred moving average

Holiday sales

Centered moving average


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Forecasting the trend from moving average

T = a + bx Where:

T : centered moving average trend

X : the time period

b =nxy - xynx- (x)2 2

ya = -

bxn n


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10.5 Forecasting the seasonal effects

The additive model

y = T + S +C + E Since the forecast of C = the cyclical effects will

not be considered here, so the model is:

y = T + S + E

S+ E = y - T


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10.5 Forecasting the seasonal effects

The multiplicative model

y = T * S * C * E Since the forecast of C = the cyclical effects will

not be considered here, so the model is:

y = T * S * E

S * E = y / T


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THE END

MANY THANKSFOR

YOUR ATTENTION

THỐNG KÊ KINH DOANH_Ch10

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