In: Finance

# Time series

The various reasons or the forces which affect the values of an observation in a time series are the components of a time series. Explain briefly any four components of time series.

## Solutions

##### Expert Solution

The chronological arrangement of statistical data with respect to time of an economic variable or composite of variable is called time series. So time series is a collection of reading belongs into different time periods of some economic variable or composite of variable.

for example- The data relating to deposits in a bank on various days is a time series.

Time series plays an important role in the field of economic and business statistics. If t1,t2,..,tn are n periods f(t1), f(t2),..,f(tn) be their respect to time series values. Time series values $\mu_{t}$ is a function of time (i.e.) $\mu_{t}$= f (t).Time series in a bi variate data one is time another one is function of time.

MAIN COMPONENT OF TIME SERIES:

-The variations in the time series values due to so many factors, the main factors are;

1. Long term fluctuations or Secular trend or trend.
2. Short term fluctuations or Periodic fluctuations : a) Seasonal Variations b) Cyclic Variations
3. Irregular fluctuations or Random fluctuations

1. Long term fluctuations:        The variations in the time series with span of long period are called long term fluctuations. It is also called secular trend or trend. The general smooth long term average tendency in the data to increase or decrease is called trend. Trends are three types. They are

• Upward trend
• Downward trend
• Stable trend

Upward trend: If time increases time series values also increases then the     trend    is called upward trend.

Example: population growly, agriculture production.

Downward trend: If time increase time series values decrease then the trend is called down ward trend

Example: epidemics, utilization of agriculture land

Stable trend: If the time increase (even) though there is neither increase nor decrease in the time series values then the trend is called stable trend. No time series data shows stable trend in long period. If the data shows stable trend after that it converts into either upward or downward trend.

2. Periodic fluctuations:

The variations in the time series with span short period and which operate in a regular spasmodic manner. These are two types.

• Seasonal variations
• Cycle variations

Seasonal variations- The variation in the time series are due to rhythmic forces which operate in regular and periodic manner over a span of less than one year is called seasonal variations. The data are recorded quarterly, monthly, weekly, daily, hourly and so on. These are same or almost same pattern year after year. Most of economic time series are influenced by seasonal swings. Seasonal variations may be further classified into

Natural made forces- Various seasons or weather conditions and climatic changes play an important role in seasonal movements.

Example: Sales of umbrellas pick up very fast in rainy season, the sale of ice and ic-cream increases very much in summer, the sales of woolens go up in winter.

Man made conventions- These variations are due to habits, fashions, customs and conventions of the people in the society.

Example: Sales of jewelers and ornaments goes up in marriages, the sales and profits in departmental stores go up during marriages and festivals like Diwali, Dushehra and Christmas etc.

Cyclic variation - The oscillator moments in a time series with a period of oscillation more than one year are called cyclic variations. One complete period is called a cycle. The cyclic moments in time series are generally observed in business. In business generally there are four phases namely;

• Prosperity(starting stage)
• Recession (progress)
• Depression
• Recovery

For the completion of these four phases in business generally requires 7 to 11 years.

3. Random fluctuations: - The variation in the time series which are not due to any trend, seasonal, cyclic variations are called Random fluctuations or irregular fluctuations. There fluctuations are purely Random manner. These variations are unpredictable and undetectable. These variations are the beyond the control of human hand.

These variations are due to earthquakes, wars, floods, revolution, etc are irregular fluctuations. It is also called has episodic fluctuations

MAIN COMPONENT OF TIME SERIES:

-The variations in the time series values due to so many factors, the main factors are;

1. Long term fluctuations or Secular trend or trend.
2. Short term fluctuations or Periodic fluctuations : a) Seasonal Variations b) Cyclic Variations
3. Irregular fluctuations or Random fluctuations