Introduction to Time Series Analysis

“ A Time Series is a set of statistical observations arranged in chronological order”- Morris Hamburg.

Dr. Hamburg was a renowned econometrician at University of Pennsylvania. He studied economic problems in and around the U.S.A. and that led to his foray into time series and forecasting.  In the study of economic problems the chronological variation plays a vital role in the study of supply and demand, the rise and fall of a price of commodities, etc.  Time series are most pertinent to economic situations but that in no way means that it is limited to only that. For example, in geography, the study of atmospheric pressure, humidity, rainfall, etc are mostly related with time.

So, in essence, studies which relate the analysis of a variable with a specific period of time (either long or short) come under the ambit of Time Series Analysis. The analytical study of a Time Series is important so as to forecast regarding the fluctuation of the data in future, on the basis of the trend studied from the data. So, Time Series analysis may be regarded as a decision making factor of any concern, for their future plan and estimate.

Now, let’s make an attempt to have a close look at the components of Time Series. The major components are-

• Secular trend
• Seasonal variations
• Cyclical fluctuations
• Irregular variations

A brief discussion may be done regarding the components for further clarification.

1. Secular trend –  The word trend means ‘tendency’. So, secular trend is that component of the time series which gives the general tendency of the data for a long period. It is smooth, regular and long-term movement of a series. The steady growth of the same status for a particular commodity of a company or the fall of demand for a certain article for long years can be studied through secular trend. Do note that rapid fluctuations cannot give the trend. Growth of population in a locality over decades is a good example of secular trend.
2. Seasonal variation– If we observe the sale structure of clothes in the market we will find that the sale curve is not uniform throughout the year. It shows different trend in different seasons. It depends entirely on the locality and the people who reside there.  It can also be seen that each and every year, sale structure is more or less same as the previous year in those periods. So, this component occurs uniformly and regularly. This variation is periodic in nature and regular in character.
3. Cyclical fluctuations– Apart from seasonal variations, there is another type of fluctuation which usually lasts for more than a year. This fluctuation is the effect of business cycles. In every business there are four important phases- i) prosperity, ii) decline, iii) depression, and v) improvement or regain. The time from prosperity to regain is a complete cycle. So, this cycle will never show regular periodicity. A period of a cycle may differ but, importantly, the sequence of changes should be more or less regular and it is this fact of regularity which enables us to study cyclical fluctuations.
4. Irregular variations– These are, as the name suggests, totally unpredictable. The effects due to flood, draughts, famines, earthquakes, etc are known as irregular variations. All variations excluding trend, seasonal and cyclical variations are irregular. Sometimes cyclical fluctuations too can get generated from natural calamities, though.

Essentially, what we need to do is to isolate the factors which are responsible for the ups and downs, i.e., we need to take care of the seasonality, the stationary and the interactions among the components before we can get a meaningful series of data which can be used for forecasting future trends and variations.

Look out for the continuation of this series.
Related Reads:

Initial Preparation of the Data for Time Series Analysis

Measurement of Trend- Graphic Model