Time Series Analysis


Introduction:
 A time series is a set of statistical observations arranged is chronological order. Time series may be defined as collection of magnitudes of some variables belonging to different time periods. It is commonly used for forecasting.

Utilities of time series analysis
1. It helps in understanding past behaviour and is useful for prediction of future.
2. It facilitates comparison.
3. The various components of time series are useful to study the effective change under each component.
4. The reasons for variation can be studied by comparing actual with expected results.
 
Components of time series
1. Secular trend: - Secular trend is a long term trend which has the basic tendency to grow or decline over a period of time. It may be due to population change technological progress, large scale shifts in consumer tastes, discovery of new things, etc.

2. Seasonal variation: - Seasonal variations are those periodic movements in business activity, which occur regularly every year and have their origin in the nature of the year itself. It may be due to climate weather conditions, customs, traditions and habits, festivals, etc.

3. Cyclical variation: - The term cycle refers to the recurrent variations in time series that usually last longer than a year and are regular neither in amplitude nor in length. Cyclical fluctuations are long-term movements that represent consistently recurring rises and declines in activity. It has four important characteristics:
i) Prosperity
ii) Decline
i)     Depression
ii)    Improvement

4. Irregular variation or irratic movement: - It is the variation in business activities, which do not repeat in a
definite pattern. Floods, earthquakes, strikes and wars cause it.

Models of time series:
In Traditional time series analysis, it is ordinarily assumed that there is a multiplicative relationship between the components of time series.
                                Symbolically, Y=T X S X C X I
                                Where T= Trend
                                                S= Seasonal component
                                                C= Cyclical component
                                                I= Irregular component
                                                Y= Result of four components.
Another approach is to treat each observation of a time series as the sum of these four components
Symbolically, Y=T + S+ C + I

Methods of measuring trend and seasonal variation:
The following four methods are commonly used for measuring trends:-
i)        Graphic method
ii)       Semi-average method
iii)     Moving average method
iv)     Method of least squares.

Again, The following methods are commonly used for measuring seasonal variation:-
i)        Method of simple averages
ii)       Ratio to trend method
iii)     Ratio to moving average
iv)     Link relative method.

i) Graphic method: - This is the simplest method of studying trend. The procedure of obtaining a straight line trend is:
                a) Plot the time series on a Graph.
                b) Examine the direction of the trend based on the plotted information.
                c) Draw a straight line which shows the direction of the trend.
The trend line thus obtained can be extended to predict future values.

Merits:-
i) This method is simplest method of measuring trend.
ii) This method is very flexible. I can be used regardless of whether the trend is a straight line or curve.

Demerits:-
i)  This method is highly subjective because it depends on the personal judgement of the investigator.
ii)  Since this method is subjective in nature it cannot be used for predictions.
                                             
ii) Semi-average method: - Under this method, the given data is divided into two parts. After that an average of each part is obtained which gives two points. Each point is plotted at the mid-point of the class interval covered by the respective part and then the two points are joined by a straight line which gives the required trend line.

Merits:-
i) This method is simple to understand as compared to the moving average method and the method of least square.
ii) This is an objective method of measuring trend as everyone who applies this method gets the same result.

Demerits:-
i) It is affected by extreme values.
                ii) This method assumes straight relationship between the plotted points whether this exist or not.

iii) Method of moving average: - Under this method the average value for a certain time span is secured and this average is taken as the trend value for the unit of time falling at the middle of the period covered in the calculation of the average. While using this method it is necessary to select a period for moving average.

Merits:-
i) This method is simple to understand and apply.
ii) It is particularly effective if the trend of a series is very irregular.
iii) It is a flexible method of measuring trend because all figures are not changed if a few figures are added to the data.
Demerits:-
                i) Trend values cannot be computed for all years.
                ii) No there is no hard and fast rule for selecting the period of moving average.
                iii) this method is not appropriate if the trend situation is not linear.

iv) Method of Least Square: - This method is most commonly used method of measuring trend. It is a mathematical method and a trend line is fitted to the data in such a manner that the following two conditions are satisfied:-
                                i) the sum of deviation of the actual values from their respective mean is zero.
                                ii) the sum of square of the deviations of the actual and compute values is least from this line. That is why this method is called method of least square.
                                The straight line trend is represented by the equation:
                                                Y = a + bx
                                Where, y = denotes the trend values
                                                a = represents the intercept on y axis.
                                                b= represents slope of the trend line.

Merits:-
                i) This is a mathematical method of measuring trend.
                ii) Trend values can be obtained for all the given time periods in the series.

Demerits:-
                i) This method is more tedious and time consuming.
                ii) This method cannot be used to fit the growth curves.

Shifting of trend origin and Deseasonalised data
 Shifting:-Shifting of trend origin means replacing the origin with new base. Shifting can be done by using the following formula:
                                Y = a + b (X + k)
Where k is the number of time units shifted. If the origin is shifted forward in time, k is positive and if shifted backward in time, k is negative.

Deseasonalised Value: - The value which show how things would have been or would be if there were no seasonal fluctuations is called Deseasonalised data. In order to obtain Deseasonalised data, the effect of seasonal variations have to be removed. For this purpose, the actual data is divided by the appropriate seasonal indices.    

0/Post a Comment/Comments

Kindly give your valuable feedback to improve this website.