Basic Secular Long Time Series, Business Mathematics and Statistics

Basic or secular or long-time trend: Basic trend underlines the tendency to grow or decline over a period of years. It is the movement that the series would have taken, had there been no seasonal, cyclical or erratic factors. It is the effect of such factors which are more or less constant for a long time or which change very gradually and slowly. Such factors are gradual growth in population, tastes and habits or the effect on industrial output due to improved methods. Increase in production of automobiles and a gradual decrease in production of foodgrains are examples of increasing and decreasing secular trend.
All basic trends are not of the same nature. Sometimes the predominating tendency will be a constant amount of growth. This type of trend movement takes the form of a straight line when the trend values are plotted on a graph paper. Sometimes the trend will be constant percentage increase or decrease. This type takes the form of a straight line when the trend values are plotted on a semi-logarithmic chart. Other types of trend encountered are “logistic”, “S-curyes”, etc.
Properly recognising and accurately measuring basic trends is one of the most important problems in time series analysis. Trend values are used as the base from which other three movements are measured.
Therefore, any inaccuracy in its measurement may vitiate the entire work. Fortunately, the causal elements controlling trend growth are relatively stable. Trends do not commonly change their nature quickly and without warning. It is therefore reasonable to assume that a representative trend, which has characterized the data for a past period, is prevailing at present, and that it may be projected into the future for a year or so.

The Components of Time Series
The factors that are responsible for bringing about changes in a time series, also called the components of time series, are as follows:

1. Secular Trends (or General Trends)
2. Seasonal Movements
3. Cyclical Movements
4. Irregular Fluctuations

Secular Trends
The secular trend is the main component of a time series which results from long term effects of socio-economic and political factors. This trend may show the growth or decline in a time series over a long period. This is the type of tendency which continues to persist for a very long period. Prices and export and import data, for example, reflect obviously increasing tendencies over time.

Seasonal Trends
These are short term movements occurring in data due to seasonal factors. The short term is generally considered as a period in which changes occur in a time series with variations in weather or festivities. For example,  it is commonly observed that the consumption of ice-cream during summer is generally high and hence an ice-cream dealer’s sales would be higher in some months of the year while relatively lower during winter months. Employment, output, exports, etc., are subject to change due to variations in weather. Similarly, the sale of garments, umbrellas, greeting cards and fire-works are subject to large variations during festivals like Valentine’s Day, Eid, Christmas, New Year’s, etc. These types of variations in a time series are isolated only when the series is provided biannually, quarterly or monthly.

Cyclic Movements
These are long term oscillations occurring in a time series. These oscillations are mostly observed in economics data and the periods of such oscillations are generally extended from five to twelve years or more. These oscillations are associated with the well known business cycles. These cyclic movements can be studied provided a long series of measurements, free from irregular fluctuations, is available.

Irregular Fluctuations
These are sudden changes occurring in a time series which are unlikely to be repeated. They are components of a time series which cannot be explained by trends, seasonal or cyclic movements. These variations are sometimes called residual or random components. These variations, though accidental in nature, can cause a continual change in the trends, seasonal and cyclical oscillations during the forthcoming period. Floods, fires, earthquakes, revolutions, epidemics, strikes etc., are the root causes of such irregularities.

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## FAQs on Basic Secular Long Time Series, Business Mathematics and Statistics - Business Mathematics and Statistics - B Com

 1. What is a long time series in business mathematics and statistics?
A long time series in business mathematics and statistics refers to a set of data points collected over a significant period of time, usually spanning several years or even decades. It helps to analyze and understand the trends, patterns, and fluctuations in various business variables such as sales, profits, or stock prices over an extended period. Long time series data is valuable for forecasting, identifying seasonality, and making informed business decisions based on historical trends.
 2. How is a long time series useful in business analysis?
A long time series is extremely useful in business analysis as it provides insights into the trends and patterns over an extended period. By analyzing a long time series, businesses can identify seasonality, cycles, and long-term trends in their data. This information is valuable for forecasting future sales, demand, or market behavior. It also helps in identifying the impact of external factors such as economic conditions or marketing campaigns on business performance. Overall, a long time series allows businesses to make data-driven decisions and formulate effective strategies based on historical data.
 3. What are the key components of a long time series analysis?
The key components of a long time series analysis include: 1. Trend analysis: Identifying the long-term direction or pattern in the data, whether it is increasing, decreasing, or stable over time. 2. Seasonality analysis: Identifying repeating patterns or cycles within a year, such as sales spikes during holidays or lower demand during certain months. 3. Cyclical analysis: Identifying longer-term cycles that occur over several years, such as economic boom and bust cycles. 4. Volatility analysis: Examining the degree of variation or fluctuation in the data over time, which can help assess risk and uncertainty. 5. Forecasting: Using historical data patterns to predict future values and trends, allowing businesses to plan and make informed decisions.
 4. How can businesses benefit from analyzing secular trends in a long time series?
 5. How can statistical analysis of a long time series help in risk management?
Statistical analysis of a long time series can play a crucial role in risk management for businesses. By analyzing historical data, businesses can: 1. Identify potential risks: Statistical analysis helps in identifying patterns of volatility, extreme events, or outliers in the long time series data. This helps businesses identify potential risks and take proactive measures to mitigate them. 2. Estimate risk probabilities: By analyzing the distribution of data points, businesses can estimate the probabilities of certain events or outcomes. This allows them to assess the likelihood of risks occurring and make informed decisions. 3. Optimize resource allocation: Statistical analysis helps businesses allocate resources effectively by identifying high-risk periods or areas. It allows them to prioritize risk management efforts and allocate resources where they are most needed. 4. Evaluate risk mitigation strategies: Statistical analysis enables businesses to evaluate the effectiveness of their risk mitigation strategies by comparing historical data with actual outcomes. This helps in refining and improving risk management practices. Overall, statistical analysis of a long time series helps businesses make informed decisions, minimize potential risks, and enhance their overall risk management framework.

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