Time Series

 Time series

 Introduction:-

        We see the many variables are changes over period of time that are population (I.e. population are changes over time means population increase day by day), monthly demand of commodity, food production, agriculture production increases and that can be observed over period of times known as time series.

Time series is defined as a set of observation arranged according to time is called time series. Or a time Series is a set of statistical observation arnging chronological order. ( Chronological order means it is arrangements of variable according to time) and it gives information about variable. 

Also we draw the graph of time series to see the behaviour of variable over time. It can be used of forecasting. The analysis of time series is helpful to economist, business men, also for scientist etc. Because it used to forecasting the future, observing the past behaviour of that variable or items. Also planning for future, here time series use past data hence it is called historical series. 

There is no nay variable is stable in the world.  They are changes due to place and time,, we know that the value of any variable is not constant in a year or period of time. That are changes (they increase or decrease the price of commodity) due to some causes. We Need to study this fluctuations. 

In the Time series we study the factor's are responsible of fluctuations are classified into many four type that are:-

1. Secular trend

2. Seasonal variation

3. Cyclic variation

4. Irregular variation

these four elements are called components of time Series.

Now let's see what is the use of time Series

The analysis of time series is very useful to economist and business man. Because time series help to understand the past behaviour. forecasting future behaviour like demand and controlling present. 

1. Controlling present:- the analysis of time series help to compare the present situation with the past performance and taking necessary steps to controlling present situation e.g. if we analysing past data and estimating current performance of one of the production is 2000 units but the actual production is 900 then we take immediate action as increasing the working force to achieving estimated production units. And improving performance.

2.to understand past behaviour.:- analysing the variable to get information about variable in past behaviour. It helps to getting idea about future behaviour of variable. 

3. It help to plan future:- using the analysis of time series we are able to forecasting the future requirement. And according to requirement plan for future. 

Semi- Average Method                   

Semi- Average Method:

semi-average method is one of the method to measuring the trend. 

Semi-Average Method: 

In the semi-average method, the time series is divided into two halves. then finding the average of these two half of the series and this average value is write corresponding to the central value of each half od series. and for drawing the trend line we plot the average value against the central value corresponding to each half of series on graph, then joining the two plotted point to get trend line. using the trend line we understand the trend in time series. the direction of the trend line indicates the trend is rising, falling or constant trend of the corresponding time series.

following are the example based in the semi-average method there are to situation to used this method if the years in time series is odd or even. therefore calculating the semi-average for both as follows.

There are two  situations:

1. when the number of years in time series is even:  the number of years in a series is even like 4,6,8,10 etc, then the given series is easily divided into two parts.  For this situation following example refer.

Ex 1. Fit a trend line by method of semi-average to the given data. (production in lakhs)

Years	2000	2001	2002	2003	2004	2005	2006	2007
Production	410	421	438	456	490	485	456	501

Solution: -

For calculating Semi - average method

Year	Production	Semi-Average	Middle Year
2000 2001 2002 2003	410 421 438 456	=(410+421+438+456)/4 =1725/4 =431.25	2001.5
2004 2005 2006 2007	490 485 456 501	=(490+485+456+501)/4 =1932 =483	2005.5

 

Trend line semi-average method

black line is trend line and red- orange is actual value.

2. when the number of years in time series is odd:  the number of years in a series is odd like 3,5,7,9 etc, then there will be a problem in dividing the series into  two parts.  For this situation we delete the middle year. For example if the given years is 1971 to 1975 (i.e. 5 years) in this year we delete the middle year 1973 form data, then we get two part of 2 years (i.e. 1971, 1972 and 1974, 1975) then remaining procedure is same.

For example :  2. Fit a trend line by method of semi-average to the given data. (production in lakhs)

Years	1978	1979	1980	1981	1982	1983	1984
Production	20	22	29	30	28	26	27

Solution: - in this example there are 7 years so we delete middle year (i.e. 1981).

For calculating Semi - average method

Year	Production	Semi-Average	Middle Year
1978 1979 1980	20 22 29	=(20+22+29)/2 =23.66	1979
1982 1983 1984	28 26 27	=(28+26+27)/2 =26	1983

 Trend line semi-average method

black line is trend line and red- orange is actual value.

Merits:

1)This is an easy method.

2) this method is free from bias.

3)trend values thus obtained are define.

4) less time and efforts is involved in drawing the trend line.

Demerits:

1) this methods is based on straight line trend assumption which does not always hold true.

2)this method is affected by extreme values.

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Semi- Average Method