Presentation On Time Series
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PRESENTATION ON TIME SERIES
PRESENTED BY:KHUSHBU SINHA & ROHIT KUMAR
INTRODUCTION
Time series analysis is used to detect patterns of change in statistical information over regular intervals of time.
We project these patter to arrive at an estimate for the future. thus, time series analysis helps us scope with certainty about the future.
EXAMPLE: BLOOD PRESSURE OF RAT
AIMS OF TIME SERIES ANALYSIS 1. Description
Describe a generating process using its time series.
2. Explanation If time series is bi-variate or multi-variate , then it may be possible to use variations in one variable to explain the variations in another variable.
3. Prediction
Use the knowledge of the past of the time series to predict its future.
IMPORTANCE SEARCHING FOR THE CAUSES OF THE ECONOMIC CHANGE IS ONE OF MOST DIFFICULT ANLYTICAL PROBLEMS IN BUSINESS AND ECONOMICS. THE SEARCH REQUIRE, ANALYSIS OF TIME SERIES DATA.
THUS, ANALYSIS OF TIME SERIES IS A GREAT IMPORTANCE TO STATICIAN TOWARDS PRACTICAL APPLICATION OF STATISTICAL DATA PERTAINING TO THE FIELD OF BUSINESS AND ECONOMICS. APART FROM THIS,
1. 2. 3. 4.
1.
IT HELPS IN UNDERSTANDING PAST BEHAVIOUR. IT HELPS IN FORECASTING AND PLAN. IT HELPS IN EVALUATING THE PRESENT ACCOMPLISHMENT. A COMPARISON CAN BE MADE BETWEEN THE BEHAVIOUR OF DIFFERENT TIME.
COMPONENTS OF TIME SERIES
WE USE TERM TIME SERIES TO REFER TO ANY GROUP OF STATISTICAL INFORMATION ACCUMULATED TO REGULAR INTERVALS. THESE ARE FOUR KINDS OF CHANGE , OR VARIATION INVOLVED IN TIME SERIES ANLYSIS:-
1. SECULAR TREND 2. CYCLIC FLUCTUATION 3. SEASONAL VARIATION 4. IRREGULAR VARIATION 2.
1. SECULAR TREND
WITH THE FIRST TYPE OF CHANGE, SECULAR TREND, THE VALUE OF THE VARIABLE TRENDS TO INCREASE OR DECREASE OVER A LONG TIME OF PERIOD. IT REPRESENTS THE LONG-TERM DIRECTION OF THE SERIES. SO, ONE WAY TO DESCRIBE THE TREND COMPONENT IS TI FIT A LINE VISUALLY TO A SET OF POINTS ON A GRAPH. TRENDS CAN BE LINEAR OR CURVILINEAR.
REASON S FOR STUDYING TRENDS 1. THE STUDY OF SECULAR TREND ALLOWS US TO DESCRIBE A HISTORICAL PATTERN. FOR EX- A UNIVERSITY MAY EVALUATE THE EFFECTIVENESS OF A RECRUITING PROGRAM BY EXAMINING ITS PAST ENROLLMENT TREND. 2. IT PERMITS US TO PROJECT PAST PATTERNS, OR TRENDS INTO THE FUTURE. FOR EX- CAN HELP US ESTIMATE THE POPULATION FOR SOME FUTURE TIME. 3. AND IT ALSO ALLOWS US TO ELMINATE THE TRENS COMPONENT FROM THE SERIES.WHICH MAKE US EASY TO STUDY THE OTHER THREE COMPONENTS OF THE TIME SERIES.IT GIVES US MORE ACCURATE IDEA OF THE SEASONAL COMPONENT. 3.
MEASUREMENT OF SECULAR TREND
Following are the principal method of estimating the secular movements:-
A. FREEHAND CURVE METHOD
B. METHOD OF AVERAGES a. semi averages b. Moving averages C. METHOD OF LEAST SQUARES
A. FREEHAND CURVE METHOD This term is used to any non-mathematical curve in statistical analysis, even when it is drawn with the aid of drafting. The curve should be drawn through the graph of the data in such a way that the areas above or below the trend are equal.
MERITS:1. Time and labour is saved. 2. More flexible than rigid mathematical function. 3. It makes possible rapid approximations of trend i.e. reliable.
DEMERITS:1. It is highly subjective. 2. It has little value as a bias of projection for future.
3. 4.
B. METHOD OF AVERAGES a. SEMI AVERAGE METHOD:- this methods employed when a straight line appears to be an adequate expression of trend. In this, data are divided into two equal halves, and simple arithmetic mean of each half is computed. b. MOVING AVERAGES METHOD:- like semi averages, this method also employs arithmetic means of items. But in this, there are so many averages as there are items in the series, except as averages may be calculated for 3,4,5,7,8,9 yearly periods. Averages are taken from overlapping periods. a. b.
FITTING THE LINEAR TREND BY THE LEAST SQUARE METHOD
THE WAY TO DESCRIBE SECULAR TREND BY LENEAR METHOD OR STRAIGHT LINE METHOD IS FOLLOWS:-
EQUATION TO ESTIMATING A STRAIGHT LINE:-
Ye =a +bX
Where, = Estimated value of the dependent variable. Ye X= independent variable.(time in tend analysis) a= y-intercept(where the value of y=0). b= slop of the trend line.
2. CYCLIC VARIATION It tends to move above and below the secular trend line for periods longer than 1 year. The most common example of this, is cyclic fluctuation in business cycle. The procedure used to identify cyclical variations is the residual method. Percent of trend= y / ye 100
*
Where Y= actual time series And y=eestimated trend value from the same point in he time series.
CALCULATION OF RELATIVE CYCLIC RESIDUALS X YEAR 1988
Y ACTUAL Ye=ESTIMA PERSCENT OF Y / Ye *1 0 0 BUSHELS T-ED TREND= BUSHELS 7.5 7.6 98.7
CYCLIC RESIDUA L=P.T*100 -1.3
1989
7.8
7.8
100.0
0.0
1990
8.2
8.0
102.5
2.5
1991
8.2
8.2
100.0
0.0
1992
8.4
8.4
100.0
-1.2
1993
8.5
8.6
98.8
-1.2
1994
8.7
8.8
98.9
-1.1
1995
9.1
9.0
101.1
1.1
3. SEASONAL VARIATION
SEASONAL VARIATION IS DEFINED THAT REPETITIVE AND PREDICTABLE MOVEMENT AROUND THE TREND LINE IN ONE YEAR OR LESS.IN ORDER TO DETECT SEASONAL VARIATIN, TIME INTERVALS MUST BE MEASURED IN SMALL UNITS, SUCH AS DAYS, WEEKS, MONTHS, OR QUARTERS. IT GENERALLY REFER TO THE ANNUAL PATTERNS OF ECONOMIC ACTIVITY.
FOLLOWING ARE THE MAIN REASONS TO STUDYING SEASONAL VARIATION:1. we can establish the pattern of past change. 2. To aid in short term forecasting and planning. 3. To compare changes in seasonal patterns, year after year. 1.
USES OF THE SEASONAL INDEX 1.It allows us to identify seasonal variation in a time series. 2.It is used to remove the effect of seasonality from a time series. 3.Once we have removed the seasonal variation, we can compute a deseasonalized trend line, which we can then project into the future. 4.
4. IRREGULAR VARIATION It is the final component of a time series. It represents the residual variation after trend. It occurs over short intervals and follows a random pattern. Because of the unpredictability of irregular variation, we do not attempt to explain it mathematically.
WE STUDY IRREGULAR VARIATION UNDER FOLLOWING HEADS 1. planning for the future is facilitated. 2. For time analysis and determination of the statistical position of an enterprise. 3. For time series analysis and control. 4. Reduction of undesirable variation. 5. For analysis of time series and economic.
TIME SERIES ANALYSIS IN FORECASTING
We must realize that the mechanical approach of time series is subject to considerable error ad change. It’s necessary for management to combine these simple procedures with knowledge of other factors in order to develop workable forecast. Analyst are constantly revising, updating, and discarding their forecasts. If we wish to cope successfully with the future, we must do the same.
When using the procedures, we should pay particular attention to two problems:1. In forecasting, we project past trend and seasonal variation into the future. We must ask, ” how regular and lasting were the past trends? What are the chances that these patterns are changing? 2. How accurate are the historical data we use in time series analysis?
REFERENCE
BY THE BOOK OF STATICS FOR MANAGEMENT.
WRITTEN BY:- 1.RICHARD I. LEVIN 2. DAVID S. RUBIN
THANK
YOU
Success is the ability to go from one failure to another with no loss of enthusiasm.
PRESENTED BY:KHUSHBU SINHA & ROHIT KUMAR
INTRODUCTION
Time series analysis is used to detect patterns of change in statistical information over regular intervals of time.
We project these patter to arrive at an estimate for the future. thus, time series analysis helps us scope with certainty about the future.
EXAMPLE: BLOOD PRESSURE OF RAT
AIMS OF TIME SERIES ANALYSIS 1. Description
Describe a generating process using its time series.
2. Explanation If time series is bi-variate or multi-variate , then it may be possible to use variations in one variable to explain the variations in another variable.
3. Prediction
Use the knowledge of the past of the time series to predict its future.
IMPORTANCE SEARCHING FOR THE CAUSES OF THE ECONOMIC CHANGE IS ONE OF MOST DIFFICULT ANLYTICAL PROBLEMS IN BUSINESS AND ECONOMICS. THE SEARCH REQUIRE, ANALYSIS OF TIME SERIES DATA.
THUS, ANALYSIS OF TIME SERIES IS A GREAT IMPORTANCE TO STATICIAN TOWARDS PRACTICAL APPLICATION OF STATISTICAL DATA PERTAINING TO THE FIELD OF BUSINESS AND ECONOMICS. APART FROM THIS,
1. 2. 3. 4.
1.
IT HELPS IN UNDERSTANDING PAST BEHAVIOUR. IT HELPS IN FORECASTING AND PLAN. IT HELPS IN EVALUATING THE PRESENT ACCOMPLISHMENT. A COMPARISON CAN BE MADE BETWEEN THE BEHAVIOUR OF DIFFERENT TIME.
COMPONENTS OF TIME SERIES
WE USE TERM TIME SERIES TO REFER TO ANY GROUP OF STATISTICAL INFORMATION ACCUMULATED TO REGULAR INTERVALS. THESE ARE FOUR KINDS OF CHANGE , OR VARIATION INVOLVED IN TIME SERIES ANLYSIS:-
1. SECULAR TREND 2. CYCLIC FLUCTUATION 3. SEASONAL VARIATION 4. IRREGULAR VARIATION 2.
1. SECULAR TREND
WITH THE FIRST TYPE OF CHANGE, SECULAR TREND, THE VALUE OF THE VARIABLE TRENDS TO INCREASE OR DECREASE OVER A LONG TIME OF PERIOD. IT REPRESENTS THE LONG-TERM DIRECTION OF THE SERIES. SO, ONE WAY TO DESCRIBE THE TREND COMPONENT IS TI FIT A LINE VISUALLY TO A SET OF POINTS ON A GRAPH. TRENDS CAN BE LINEAR OR CURVILINEAR.
REASON S FOR STUDYING TRENDS 1. THE STUDY OF SECULAR TREND ALLOWS US TO DESCRIBE A HISTORICAL PATTERN. FOR EX- A UNIVERSITY MAY EVALUATE THE EFFECTIVENESS OF A RECRUITING PROGRAM BY EXAMINING ITS PAST ENROLLMENT TREND. 2. IT PERMITS US TO PROJECT PAST PATTERNS, OR TRENDS INTO THE FUTURE. FOR EX- CAN HELP US ESTIMATE THE POPULATION FOR SOME FUTURE TIME. 3. AND IT ALSO ALLOWS US TO ELMINATE THE TRENS COMPONENT FROM THE SERIES.WHICH MAKE US EASY TO STUDY THE OTHER THREE COMPONENTS OF THE TIME SERIES.IT GIVES US MORE ACCURATE IDEA OF THE SEASONAL COMPONENT. 3.
MEASUREMENT OF SECULAR TREND
Following are the principal method of estimating the secular movements:-
A. FREEHAND CURVE METHOD
B. METHOD OF AVERAGES a. semi averages b. Moving averages C. METHOD OF LEAST SQUARES
A. FREEHAND CURVE METHOD This term is used to any non-mathematical curve in statistical analysis, even when it is drawn with the aid of drafting. The curve should be drawn through the graph of the data in such a way that the areas above or below the trend are equal.
MERITS:1. Time and labour is saved. 2. More flexible than rigid mathematical function. 3. It makes possible rapid approximations of trend i.e. reliable.
DEMERITS:1. It is highly subjective. 2. It has little value as a bias of projection for future.
3. 4.
B. METHOD OF AVERAGES a. SEMI AVERAGE METHOD:- this methods employed when a straight line appears to be an adequate expression of trend. In this, data are divided into two equal halves, and simple arithmetic mean of each half is computed. b. MOVING AVERAGES METHOD:- like semi averages, this method also employs arithmetic means of items. But in this, there are so many averages as there are items in the series, except as averages may be calculated for 3,4,5,7,8,9 yearly periods. Averages are taken from overlapping periods. a. b.
FITTING THE LINEAR TREND BY THE LEAST SQUARE METHOD
THE WAY TO DESCRIBE SECULAR TREND BY LENEAR METHOD OR STRAIGHT LINE METHOD IS FOLLOWS:-
EQUATION TO ESTIMATING A STRAIGHT LINE:-
Ye =a +bX
Where, = Estimated value of the dependent variable. Ye X= independent variable.(time in tend analysis) a= y-intercept(where the value of y=0). b= slop of the trend line.
2. CYCLIC VARIATION It tends to move above and below the secular trend line for periods longer than 1 year. The most common example of this, is cyclic fluctuation in business cycle. The procedure used to identify cyclical variations is the residual method. Percent of trend= y / ye 100
*
Where Y= actual time series And y=eestimated trend value from the same point in he time series.
CALCULATION OF RELATIVE CYCLIC RESIDUALS X YEAR 1988
Y ACTUAL Ye=ESTIMA PERSCENT OF Y / Ye *1 0 0 BUSHELS T-ED TREND= BUSHELS 7.5 7.6 98.7
CYCLIC RESIDUA L=P.T*100 -1.3
1989
7.8
7.8
100.0
0.0
1990
8.2
8.0
102.5
2.5
1991
8.2
8.2
100.0
0.0
1992
8.4
8.4
100.0
-1.2
1993
8.5
8.6
98.8
-1.2
1994
8.7
8.8
98.9
-1.1
1995
9.1
9.0
101.1
1.1
3. SEASONAL VARIATION
SEASONAL VARIATION IS DEFINED THAT REPETITIVE AND PREDICTABLE MOVEMENT AROUND THE TREND LINE IN ONE YEAR OR LESS.IN ORDER TO DETECT SEASONAL VARIATIN, TIME INTERVALS MUST BE MEASURED IN SMALL UNITS, SUCH AS DAYS, WEEKS, MONTHS, OR QUARTERS. IT GENERALLY REFER TO THE ANNUAL PATTERNS OF ECONOMIC ACTIVITY.
FOLLOWING ARE THE MAIN REASONS TO STUDYING SEASONAL VARIATION:1. we can establish the pattern of past change. 2. To aid in short term forecasting and planning. 3. To compare changes in seasonal patterns, year after year. 1.
USES OF THE SEASONAL INDEX 1.It allows us to identify seasonal variation in a time series. 2.It is used to remove the effect of seasonality from a time series. 3.Once we have removed the seasonal variation, we can compute a deseasonalized trend line, which we can then project into the future. 4.
4. IRREGULAR VARIATION It is the final component of a time series. It represents the residual variation after trend. It occurs over short intervals and follows a random pattern. Because of the unpredictability of irregular variation, we do not attempt to explain it mathematically.
WE STUDY IRREGULAR VARIATION UNDER FOLLOWING HEADS 1. planning for the future is facilitated. 2. For time analysis and determination of the statistical position of an enterprise. 3. For time series analysis and control. 4. Reduction of undesirable variation. 5. For analysis of time series and economic.
TIME SERIES ANALYSIS IN FORECASTING
We must realize that the mechanical approach of time series is subject to considerable error ad change. It’s necessary for management to combine these simple procedures with knowledge of other factors in order to develop workable forecast. Analyst are constantly revising, updating, and discarding their forecasts. If we wish to cope successfully with the future, we must do the same.
When using the procedures, we should pay particular attention to two problems:1. In forecasting, we project past trend and seasonal variation into the future. We must ask, ” how regular and lasting were the past trends? What are the chances that these patterns are changing? 2. How accurate are the historical data we use in time series analysis?
REFERENCE
BY THE BOOK OF STATICS FOR MANAGEMENT.
WRITTEN BY:- 1.RICHARD I. LEVIN 2. DAVID S. RUBIN
THANK
YOU
Success is the ability to go from one failure to another with no loss of enthusiasm.
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