Introduction to Time Series

What is Time Series?

According to Ya-Lun-Chou: “A time series may be defined as a collection of readings belonging to different time periods, of some economic variable or composite of variables”.

Less formally, time series is a set of ordered observations taken at successive & equally spaced points in time. It may be recorded in terms of days, months, years, and so on.

For instance, let us look at an example :

Difficult to find a pattern? Let’s try plotting the above points.

Now we can easily say there is a decreasing pattern present in the dataset. But we all know it won’t be always decreasing.

Then what all patterns can we expect?

To answer this let us first try to understand what are the four different components of time series.

Components of the Time Series :

1. Secular or Long term Trend (T)
2. Seasonal Variation (S)
3. Cyclical Variation (C)
4. Irregular or Random Movements (I/R)

Secular/Long-term Trend :

Data that has the general tendency to increase, decrease or remain constant for a long period of time is said to possess a secular trend.

Examples: Number of smartphone users, deaths due to covid-19, etc.

The above graph shows the number of smartphone users in India from 2013 to 2020. Since there is an increasing trend present we say it possesses secular trend.

Seasonal Variations :

It is a short-term periodic movement that occurs regularly over a span of one year or shorter and has an almost similar pattern year after year. The major factors that cause seasonal variations are due to nature and due to man-made customs.

Examples: Sales of mangoes in summer, Sales of electronic items before festivals, etc.

The above graph shows the monthly sales of a company. As we can see a similar pattern is getting repeated after each quarter hence we can say it has seasonal variations.

Cyclical Variations :

It is a long-term periodic movement that occurs over a period of two or more years. The cyclic movements are referred to as ‘Business Cycle’ or a ‘Four phase cycle’. The four phases consist of prosperity, recession, depression, and recovery.

Irregular or Random Movements :

These are purely random in nature and are unpredictable. These fluctuations do not have a definite pattern.

Examples: Covid-19 pandemic, floods, earthquakes, etc

Reference: Fundamentals of Applied Statistics by S. C. Gupta & V. K. Kapoor.

Thanks for reading !!