Cyclic variation

Cyclic variation is a type of variation that occurs in a cyclical pattern over a period of time. It is often seen in economic, social, and environmental factors and is often linked to seasonal changes. Cyclic variation can be seen in both a long-term and short-term timeline. Examples of cyclic variation include:

• Seasonal changes in temperature: As the seasons change, the average temperature of an area will rise and fall.
• Stock market fluctuations: The stock market is known to fluctuate in a cyclical pattern, often following a regular pattern of highs and lows throughout the year.
• Changes in population: Population levels tend to fluctuate in a cyclical pattern, with certain times of the year or certain times of the decade tending to be more populated than others.

"Cyclic variation is any change in economic activity that is due to some regular and/or recurring cause, such as the business cycle or seasonal influences" (Friedman J. 2012, p.60).

Example of Cyclic variation

The formula for cyclic variation is given by: $y=A+Bcos(2\pi ft+\phi )$

Where A is the mean of the data, B is the amplitude, f is the frequency and φ is the phase. This formula displays the cyclic variation in data points, showing how the data points will rise and fall over a set period of time. A is the average of the data points, B is the difference between the maximum and minimum values, f is the number of cycles per unit of time, and φ is the phase shift. This formula is used to calculate the cyclic variation in data points and can be used to predict how the data points will move in the future.

Formula of Cyclic variation

The formula for cyclic variation is y = A + Bsin(Cx + D), where A is the mean (average) value, B is the amplitude (maximum variation from the mean), C is the angular frequency (number of cycles per unit time), and D is the phase shift (the amount the graph is shifted from the original position).

Overall, the formula for cyclic variation is an equation that describes a sinusoidal pattern, with A, B, C, and D representing the mean, amplitude, angular frequency, and phase shift, respectively.

When to use Cyclic variation

Cyclic variation is typically used to analyze trends in data over a period of time, whether it is over a short-term or long-term timeline. It is often used in economics to analyze the stock market, in environmental sciences to analyze seasonal changes, and in the social sciences to analyze population trends. Cyclic variation can also be used to identify and measure the differences in a data set over a given period of time.

For example, economists can use cyclic variation to determine the performance of the stock market over a certain period of time, and ecologists can use it to measure the changes in temperature over the four seasons. In the social sciences, cyclic variation can be used to understand population trends over a certain period of time.

Overall, cyclic variation is used to analyze trends in data over a period of time and can be used to identify and measure the differences in a data set.

Types of Cyclic variation

There are two types of cyclic variation: short-term and long-term. Short-term cyclic variation includes changes that occur over a shorter period of time, such as daily or weekly variations in temperature. Long-term cyclic variation includes changes that occur over a longer period of time, such as seasonal changes in temperature. Additionally, long-term cyclic variation can also include changes in population or stock market fluctuations that occur annually or over a longer period of time.

Cyclical variation in statistic

It is said that the term cyclical variation refers to the recurrent variation in a time series which usually lasts for two or more years and is regular neither in amplitude nor in length.

These cyclical variations are also known as oscillating movements that take place due to ups and downs recurring after a period of greater than one year. These variations, though more or less regular are not necessarily, uniformly periodic. This means that they may not follow exactly similar pattern after equal intervals of time say 7 to 9 years. They may not always complete two years with a fixed duration of time.

• In the field of business and economy, they follow a well-determined pattern with four different phases, like the prosperity phase, businesses prosper, prices go up, and profits are multiplied. This causes overdevelopment, difficulties in transportation, an increase in wage rate, deficiency in labor, high rate of interest, the dearth of money in the market and price concession etc. leading to depression (slump). In the depression phase, as we know, there is pessimism in trade and industries, factories close down, businesses fail, unemployment spreads, the rate of wages and prices are low. This causes idleness of money, availability of money at low interest, increase in demand for goods of money at low interest, increase in demand for goods and services characterized by the situation of recovery which ultimately leads to prosperity, or boom.
• "Cyclical movements or variations refer to the long-term oscillations or swings about a trend line These cycles may or may not be periodic, i.e., they may or may follow exactly similar patterns after equal intervals of time. Such variations are of longer duration than a year and they do not show the type of regularity as observed in the case of seasonal variations. An important example of cyclical variations in the so-called business cycles representing intervals of prosperity, recession, depression, and recovery. Each phase changes gradually into the phase which follows it in the given order. In the business activity, these phases follow each other with steady regularity and the period from the peak of one boom to the peak of the next boom is called a complete cycle. The usual periods of a business cycle may be ranging between 5-11 years. Most of the economic and business series relating to income, investment, wages, production shows this tendency. The study of cyclical fluctuations is therefore very important for predicting the turning phases in a business activity which may greatly help in proper policy formation in the area" (Sharma K. 2006, p.397)
• Cyclic variations may not necessarily be periodic fluctuations activity over a period of years. No satisfactory method of measuring directly the cyclical swings in a time series has been developed. The irregular nature of fluctuations makes it impossible any attempt to find an average cycle that could be used to represent the effect of the cycle on the series. The best measuring the cyclical fluctuations in time series has been the indirect method of removing the variation in the series that results from seasonal forces of a secular trend. The remaining fluctuations are considered to be cyclical and erratic movements (Pillai R. 2008, p.624).

Steps of Cyclic variation

Cyclic variation has three steps which are:

• Measurement: The first step of cyclic variation is measuring the changes that are occurring in the environment or system. This can be done by collecting data over a certain period of time.
• Analysis: The next step is to analyze the data collected in order to identify patterns or trends in the changes that are occurring.
• Prediction: The final step of cyclic variation is to use the data and analysis to predict future changes that can be expected.

Advantages of Cyclic variation usage

Cyclic variation can be advantageous in several ways. Firstly, cyclic variation can help to identify patterns, which can be useful for predicting future trends. Secondly, cyclic variation can provide insights into how certain factors interact with each other, which can be useful for making decisions. Finally, cyclic variation can help to identify trends in data, which can be beneficial for understanding the overall picture.

Limitations of Cyclic variation

Despite being an important factor to consider in many aspects of life, cyclic variation can be limited in its application. For example, it does not always take into account external factors that could potentially affect the cycle such as a change in economic policy or a natural disaster. Additionally, cyclic variation does not always account for the long-term effects of certain changes, as cycles can be difficult to predict far into the future. Finally, cyclic variation is often too narrow a focus for certain applications, as it does not take into account other factors that could potentially influence the data.

Other approaches related to Cyclic variation

Another approach related to cyclic variation is the use of Fourier Analysis. This is a mathematical technique used to decompose a signal into its frequency components. This technique can be used to analyze cyclic patterns of data over a period of time. It can also be used to identify any underlying trends in the data. In addition, Fourier Analysis can be used to predict future values of the data based on the past fluctuations.

Cyclic variation — recommended articles

Moving average chart — Short run aggregate supply curve — Kondratiev cycle — Economic trend — Market condition — Net Volume — Chande Momentum Oscillator — Cross elasticity of demand — Continuation Pattern

References

• Friedman J. (2012), Dictionary of Business and Economic Term, Simon and Schuster,
• Pillai R. (2008), Statistics (Theory & Practice), S. Chand Publishing,
• Sharma K. (2006), Statistics in Management Studies, Krishna Prakashan Media.

Author: Monika Broszkiewicz