Updated March 8, 2023

## Definition of Components of time series analysis

Components of time series analysis are defined as parts or elements of a larger whole time series algorithm which when bundled together attributes to the working of the algorithm for its true intent. In our normal conversations, we do talk about changes in prices of gold or petrol or any other commodities with respect to time. What do we do there? We compare the prices at some other period of time to the other comparable period of the same commodity. The sets of observations that are ordered in successive time periods is known as a time series and the components that are a vital part to derive the trends and behavior from the data are the components of the time series analysis. In this article, we will look at the different components that constitute the time series analysis.

### Components of time series analysis

Now that we already know that arrangement of data points in agreement to the chronological order of occurrence is known as a time series. And also, the time series analysis is the relationship between 2 variables out of which one is the time and the other is the quantitative variable. There are varied uses of time series, which we will just glance at before we know the components of the time series analysis so that while we study the time series, it becomes evident on to how the components is able to solve the time series analysis.

- Time series analysis is performed to predict the future behavior of any quantitative variable on the basis of the past behavior. For example, umbrellas getting sold on mostly rainy seasons than other seasons, although umbrellas still get sold in other time periods. So maybe in order to predict the future behavior, more umbrellas will be sold during the rainy seasons!
- While evaluating the performance of the business with respect to the expected or planed one, time series analysis helps a great deal in order to take informed decisions to make it better.
- Time series also enables business analysts to compare changes in different values at different times or places.

Keeping these applications of time series, we now look at the different components that gets involved in this analysis. They are:

#### 1. Long term movements or Trend

This component looks into the movement of attributes at a long-term window of time frame and mostly tries to understand the increment or decrement of the quantitative value that is attached to the behavior. This is more like an average tendency of the parameter that is in measurement. The tendencies that are observed can be increasing, decreasing or stable at different sections of the time period. And on this basis, we can make the trend a linear one and a non-linear one. In the linear trend we just talk about continuously increasing or continuously decreasing whereas in the non-linear we can segment the time period into different frames and populate the trend! There are many ways by which non-linear trends can be included in the analysis. We can either take higher order of the variable in hand, which is realistically non-interpretable or a better approach than that is the piecewise specification of the function, where each of the piecewise function has a linear and collectively makes a non-linear trend at an overall level.

#### 2. Short term movements

In contrast to the long-term movements, this component looks into the shorter period of time to get the behavior of the quantitative variable during this time frame. This movement in the time series sometimes repeats itself over certain period of time or even in regular spasmodic manner. These movements over a shorter time frame give rise to 2 sub-components namely,

**Seasonality**: These are the variations that are seen in the variable in study for the forces than spans over for lesser than a year. These movements are mainly present in the data where the record in with a shorter duration of difference, like daily, weekly, monthly. The example we talked about the sale of umbrella is more during the rainy season is a case of seasonality. Sale of ACs during the summertime is again a seasonality effect. There are some man-made conventions that affect seasonality like festivals, occasions etc.**Cyclic Variations**: Even though this component is a short-term movement analysis of time series, but it is rather longer than the seasonality, where the span of similar variations to be seen is more than a year. The completion of all the steps in that movement is crucial to say that the variation is a cyclic one. Sometimes we even refer them to as a business cycle. For example, the product lifecycle is a case of cycle variation, where a product goes through the steps of the life cycle, that is Introduction, growth, maturity, decline and just before the product reaches below a threshold of decline, we look for re-launch of the product with some newer features.

#### 3. Irregular variation or Random variations

This component is one of the most non-regular versions of variations and hence the most unpredictable one. The fluctuation or variation in the movement we see in these components are mostly unforeseen, non-controllable. The ones which falls under this component are natural disasters like earthquakes, floods, famines, man made disasters like war and even pandemics like Covid-19. During the time frame of Covid-19, there was an irregular variation in the tourism, which ought to be seen may be just once in someone’s lifetime. Mostly, these random fluctuations are what are known as residuals in statistical terms.

Finally, we now know that the Trend, seasonality, cyclic and residuals totally constitutes of the time series analysis and these components may take form of additive model or multiplicative model, depending on the use cases!

### Conclusion

With this, we come to an end of the components of time series analysis article, where in we looked at each of these components in great details and got familiar with them before moving to the usage of these components in a time series analysis!

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