Time Series Analysis Fin

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TIME SERIES ANALYSIS

BINU PAUL (68)

BLAISE LOBO (69) JUDITH DSOUZA (82)

LIBI CHACKO (86)

NAMRATA BHOGLE (91)NIBY RAJU (92)


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Introduction to Time Series Analysis

Atime-series is a set of observations.

Examples

Measuring value of retail sales.

Historical data on sales, inventory, customercounts, interest rates, costs, etc

In time series analysis, we analyze the past

behavior of a variable in order to predict its futurebehavior.

Businesses are often very interested in forecastingtime series variables.


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Good forecasts can lead to

Reduced inventory costs.

Lower overall personnel costs.

Increased customer satisfaction.

The Forecasting process can be based on

Educated guess.

Expert opinions. Past history of data values.


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Forecasting is fundamental to decision-

making. There are three main methods:

Subjective forecasting

Extrapolation forecasting

Causal modeling (cause and effect)


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Time Series Terms

Stationary Data

Nonstationary Data

Seasonal Data


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Stationarity


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Non-stationarity (upward trend)

0

1

2

3

4

5

6

7


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Components of Time Series

Secular trend

A time series data may either show upward trend ordownward trend for a period of years

For example, population increases over a

period of time or sales of a commoditydecreases over time.

Seasonal variation

Seasonal variation are short-term fluctuation in atime series which occur periodically in a year andcontinues to repeat year after year

For example, weather conditions and customs ofpeople


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Components of Time Series

Cyclical Variation Recurrent upward or downward movements in a timeseries but the period of cycle is greater than a year

For example, the ups and downs in business activities are

the effects of cyclical variation.

Irregular Variation Fluctuations in time series that are short in duration, erraticin nature and follow no regularity in the occurrence pattern

Events like floods, earthquakes, wars, famines, etc.


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APPLICATIONS

Time Series Analysis is used for many applications

such as:

Economic Forecasting

Sales Forecasting

Budgetary Analysis

Stock Market Analysis


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Yield Projections

Process and Quality Control

Inventory Studies

Census Analysis


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MOVING AVERAGE METHOD

In statistics, a moving average, alsocalled rolling average, rollingmean or running average

A moving average (MA) is an average ofdata for a certain number of timeperiods.


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WHYUSE THEM?

Moving Averages, when graphed,allow us to see any trends in data thatare cyclical

By calculating the average of 2 ormore items in the data, any peaks andtroughs are smoothed out.


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265

265.25

270.75

269.25

4 Period Moving Average

Year 1996 1997 1998

Quarter 1 2 3 4 1 2 3 4 1 2 3 4

Sales 189 244 365 262 190 266 359 250 201 259 401 265


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Year 1996 1997 1998

Quarter 1 2 3 4 1 2 3 4 1 2 3 4

Sales 189 244 365 262 190 266 359 250 201 259 401 265

4 period Moving Average

Quarters 1-4 2-5 3-6 4-7 5-8 6-9 7-10 8-11 9-12

Moving

Average 265 265.25 270.75 269.25 266.25 269 267.25 277.75 281.5


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Year 1996 1997 1998

Quarter 1 2 3 4 1 2 3 4 1 2 3 4

Sales189 244 365 262 190 266 359 250 201 259 401 265

1 2 3 4 1 2 3 4 1 2 3 4

100

200

300

400

500

x

1996 1997

1998

x

x

x

x

x

x

x

x

x

x

x

Quarters 1-4 2-5 3-6 4-7 5-8 6-9 7-10 8-11 9-12

Moving

Average 265 265.25 270.75 269.25 266.25 269 267.25 277.75 281.5

x x x x x x x xx


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TYPES OF MOVINGAVERAGES

Simple moving average

Weighted moving average

Exponential moving average


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1. Simple moving average

Simple moving average (SMA) is the

unweighted mean of the previous ndata

points.

Example : a 5-day moving average would be

calculated by adding the closing prices for

the last 5 days and dividing the total by 5.


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2.Weighted moving average

A weighted average is any average thathas multiplying factors to give differentweights to data at different positions in

the sample window.

The more recent observations are

typically given more weight than olderobservations


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WeightedMoving Average

Use a 3 period weighted moving average to forecast thesales for week 11 giving a weight of 0.6 to the mostrecent period, 0.3 to the second most recent period, and0.1 to the third most recent period.

F11 = (0.6)*130 + (0.3)*110 + (0.1)* 115= 122.5

Thus we would forecast the sales for week 11 to be 122.5.

Sales for the

most recentperiod

Sales for 2nd

most recentperiod

Sales for 3rd

most recentperiod


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3.Exponential moving average

An exponential moving average (EMA), isa type of infinite impulse response filterthat applies weighting factors whichdecrease exponentially.

Exponential moving averages reduce thelag by applying more weight to recentprices relative to older prices


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MERITS

Easy to understand and easy to use.

It is an objective method.

It is a flexible method.

Meaningful comparison.


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DEMERITS Impossible to calculate trend values for all the

items of the series.

It depends on certain conditions.

Not follow any mathematical pattern.

Selection of period is a difficult task.

Affected by extreme values.


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CASE STUDY

Cedar Fair operates seven amusementparks and five separately gated waterparks. Its combined attendance (in

thousands) for the last 12 years is givenin the following table. A partner asks youto study the trend in attendance.Compute a three-year moving averageand a three-year weighted movingaverage with weights of 0.2, 0.3, and 0.5for successive years.


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Year Attendance

(000)

3 Year Moving Average Forecast for 4th year

1993 5761

1994 6148

1995 6783=(5761+ 6148+ 6783)/3 6230

1996 7445=(6148+6783 + 7445 )/3 6792

1997 7405

=(6783+ 7445 + 7450)/3 7226

1998 11450=(7445 + 7405+11450)/3 8766

1999 11224=(7450 +11450 +11224)/3 10041

2000 11703=(11450+11224+11703 )/3 11459

2001 11890=(11224+11703+11890 )/3 11605

2002 12380=(11703+11890+12380 )/3 11991

2003 12181=(11890+12380+12181 )/3 12150

2004 12557=(12380+12181+12557)/3 12372


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Year Attendance

(000)

Using Weighted Moving Average Weighted Moving

Average

1993 5761

1994 6148

1995 6783 =0.2(5761) + 0.3(6148) + 0.4(6783)5709.8

1996 7445 =0.2(6148) + 0.3(6783)+ 0.4(7445)6242.5

1997 7405 =0.2(6783) + 0.3(7445) + 0.4(7450) 6570.1

1998 11450

=0.2(7445)+ 0.3(7405) + 0.4(11450) 8290.5

1999 11224=0.2(7450) + 0.3(11450) + 0.4(11224) 9414.6

2000

11703 =0.2(11450) + 0.3(11224) + 0.4(11703) 10338.4

2001 11890=0.2(11224)+0.3(11703)+ 0.4(11890) 10511.7

2002 12380=0.2(11703) + 0.3(11890) + 0.4(12380) 10859.6

2003 12181=0.2(11890) + 0.3(12380) + 0.4(12181) 10964.4

=0.2 12380 + 0.3 12181 + 0.4 12557 11153.1


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0

5000

10000

15000

20000

25000

30000

35000

40000

Year 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Cedar Fair

Attendance 3yr moving average Weighted Moving Average


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Case study:2

The Vintage Restaurant, on Captiva Island near Fort

Myers, is owned and operated by Karen Payne. The

restaurant just completed its third year of operation.

During that time Karen sought to establish a reputation for

the restaurant as a high quality dining establishment that

specializes in fresh seafood. Through the efforts of Karenand her staff, her restaurant has become one of the best and

fastest growing restaurants on the island.

Karen believes that to plan for the growth of the restaurant

in the future, she needs to develop a system that willenable her to forecast food and beverages sales by month

for up to one year in advance. Karen compiled the

following data(in thousands of dollars). On total food and

Beverages sales for the three years of operation


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Managerial Report

Perform an Analysis of the Sales Data for theVintage Restaurant . Prepare a Report for Karen That

summarizes your findings, forecast and

Recommendations.

A Forecast of Sales for January to December for the

Fourth Year

Assume January Sales to be $295000 what is theForecast error of that Month


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Month First Year Second Year Third Year

January 242 263 282

February 235 238 255

March 232 247 265

April 178 193 205

May 184 193 210

June 140 149 160

July 145 157 166

August 152 161 174

September 110 122 126

October 130 130 148

November 152 167 173

December 206 230 235


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Month Using 3 Year Moving Average Forecast for 4th year

January =(242 + 263 + 282)/3 262

February =(235 + 238+ 255)/3 243

March =(232 + 247 + 265)/3 248

April =(178+193 + 205)/3 192

May =(184+193 + 210)/3 196

June =(140 +149 +160)/3 150

July =(145 +157 +166)/3 156

August =(152 +161 +174)/3 162

September =(110 +122 +126)/3 119

October =(130 +130 +148)/3 136

November =(152 +167 +173)/3 164

December =(206 + 203 + 235)/3 215


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0

200

400

600

800

1000

1200

Vinatge Restaurant

First Year Second Year Third Year 3year moving Average


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Assume January Sales to be $295000 what

is the Forecast error of that Month?

Forecast error= Actual - Budgeted forecast

= 295000 262000

= 33000

Forecast error of January Month = 33000


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References

http://www.forex-training.com/moving_average.htm

http://www.decisionpoint.com/tacourse/MovingAve.html

http://www.answers.com/topic/moving-average-inventory-method


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