**Subject :**Math -3

**Unit :**Statistical Techniques - II

## Time Series and Forecasting

**Time Series and Forecasting:
**

Time series analysis is the basis for understanding past behaviour, evaluating current accomplishment, planning future operations. It is also used for comparing the components of different time series. It is used to determine the patterns in the data of the past over a period of time and extrapolate the data into the future. Previous performances are studied to forecast future activity. **Prof. W.Z. Hirsch** writes, A main objective in analyzing a time series is to understand, interpret and evaluate changes in economic phenomena in the hope of more correctly anticipating the course of the events.

In short, following are the use of Time Series Analysis:

**1**. **Analysis of past behaviour:** Time series analysis helps in understanding the past behaviour of the factors which are responsible for the variations.

**2**. **Estimates for the future:** The understanding of the past behaviour and projecting the past trends are extremely helpful in predicting the future behaviour.

**3**.** Forecasting**: Time series study helps in forecasting and planning future operations.

**4**. **Evaluation of performance:** Time series analysis helps in evaluating current accomplishments.

**5**.** Comparison:** Time series analysis help in comparison among various time series. Interpreting of the variations that how they are related with each other, net effect of their interaction and also with the similar changes in other time series data.

**6**. **Estimation of trade cycles:** Time series analysis helps in the estimation of trade cycles on the basis cyclical fluctuations which helps the businessman to plans and regulate their activities.

**Components of Time Series:**

The forces affecting time series data generate certain movements or fluctuations in a time series. Such characteristics movements or fluctuations of time series are called components of a time series. The components of a time series may be classified into different categories on the basis of the operations forces. There are four components of a time series.

**1**. Secular Trend or Trend (T)

**2**. Seasonal Variations (S)

**3**. Cyclic Variations (C)

**4**. Irregular (or Random) Variations (I)

The components of a time series may or may not occur at the same time.

**Trend or Secular Trend:**

The component of a time series which is responsible for its general behaviour (i.e. general long term movement) over a fairly long period of time as a result of some identifiable influences is called the secular trend or trend. It is a smooth, regular and long term tendency of a particularly activity to grow or decline. The trend may be upward as well as downward. If the series neither increases nor decreases over a long term (usually a minimum of 15 to 20 years) then series is said without trend (or nor-trend) or with a constant trend: It is not necessary that the trend should be in the same direction through out the given period. The time series may be increasing slowly or increasing fast or may be decreasing at various rates or may remain relatively constant. Some time series reverse their trend from growth to decline or from decline to growth over a period of time. In brief, the movements which exhibit persistent growth or decline in long period of time are known as secular trend. The term ‘long period of time’ is a relative concept which is influenced by the characteristic of the series. The formation of rocks is a particular example of secular trend. Declining death rate is an example of downward trend; population growth is an example of upward trend. Mathematically trend may be linear or nonlinear.

**Seasonal Variations:**

The movements that are regular and periodic in nature not exceeding a year are called seasonal variations. The movements that are regular and periodic in nature not exceeding a year are called seasonal variations. The forces that are responsible for seasonal variations are:

(**i**) Natural factors (or climate)

(**ii**) Man-made conventions (Holidays, Festivals, etc.)

For example, crops are sown and harvested at certain times every year and demand for labor goes up during sowing and harvesting seasons, demands of woolen cloths goes up in winter, prices increase during festivals, with draws from banks are heavy on first week of a month, the number of letters posted on Saturday is larger, etc.

**Cyclic Variations:**

The oscillatory movements (or swings or patterns) whose period of oscillation is more than one year are called cyclic variations one complete period is called a cycle. In economic and business series they correspond to the business cycle and take place as a result of economic booms or depressions. It is a matter of common knowledge that almost all economic and business activities have four distinct phases: Prosperity, Decline, Depressions, Recovery.

**Irregular (or Random) Variations:**

Irregular (or Random) Variations do not exhibit any definite pattern and there is no regular period of their occurrence. these are accidental changes which are purely random and unpredictable. For example, variations due to earthquake, war etc. Normally these variations are short term but sometimes their effects are severe.