What are the four 4 main components of a time series?

What are the four 4 main components of a time series?

Trading & Investing

Time series analysis occurs when individuals utilize historical data to predict future outcomes. Ancient civilizations like the Greeks, Romans, and Mayans studied and mastered the art of using recurring occurrences like weather, agriculture, and astronomy to predict the future. For instance, the Maya priests believed that astronomical occurrences followed cycles. As a result, they carefully watched and documented such incidents, which enabled them to compile an in-depth time series table of earlier occurrences, finally enabling them to predict upcoming ones. In modern society, technological development actualizes modern time series analysis because computers facilitate the processes of statistical modeling and complex calculations. Used effectively in stock market analysis, especially when automated trading algorithms become used.

Components of Time Series 

There are four components of time series, as listed below:

  • Secular Trend (T)
  • Seasonal Variations (S)
  • Cyclical Variations (C)
  • Irregular Variations (I)

Based on these four components; two models are frequently used to describe their relationships to the dependent variable Y:

  • Additive Model: Y = T + S + C + I

Each factor’s effect is independent of the others, and their total effects become added to the data. Generally, the data represents a linear trend because the changes consistently occur over time.

  • Multiplicative Model: Y = T * S * C * I

Where the effects are multiplied by one another, which gives the data a non-linear trend; like exponential or quadratic, and it may have an increasing or decreasing amplitude and frequency over time.

The additive model is chosen when cyclical and seasonal variations are relatively constant, and their levels do not impact the tendency; the multiplicative model, on the other hand, is selected when cyclical and seasonal variations have an amplitude almost proportional to that of the secular trends.

For long-term analysis, the secular trend becomes more likely to become considered and does not take cyclical variations into account; for medium-term analysis, cyclical variations become included, where the secular trend has to become adjusted based on the possible influences of cyclical variations; furthermore, for short-term analysis, irregular variations are not contained in the prediction, and both the cyclical and seasonal variations impact the secular trend.

Secular Trend (T)

The secular trend illustrates the long-term movement of a time series, which can be linear or nonlinear. To observe the secular trend preliminarily, it is best to graph data first. 

To estimate the linear relationship, there are two methods: the first method is the least-squares method. Aimed to discover the best linear relationship between two variables. In the time series, the independent variable t is the time, and the dependent variable Yt is the value of a time series. The formula Yt=a+bt becomes utilized to estimate the secular trend of a time series where the predicted line is the secular trend. 

The second method is the moving-average method. It is the primary technique to smooth a time series to see its pattern, and it is also fundamental to measure seasonal variations. To apply the moving-average method, the data should be fairly linear and have a repeating pattern over a certain number of years, usually three, five, or seven years. Because the data are recorded yearly, there are no seasonal variations; moreover, the function of the moving-average method is to average out cyclical variations (C) and irregular variations (I). According to the formula, what is left out is the last component, the secular trend (T). 

When data increase or decrease by equal percentages or proportions; the trend equation of a time series does represent more like a curvilinear trend.

The general equation for the curvilinear trend is the logarithmic equation, log Yt =log a +log bt . The output can be calculated from data through the least-squares method, thereby determining the secular trend.

The secular trend analysis aims to construct a model that describes previous circumstances; produces forecasts with a consistent framework, and examines additional time series elements while secular trends are eliminated.

Seasonal Variations (S)

Seasonal variations are variations of a periodic nature that can recur frequently. Several factors, including climatic conditions, customs appropriate for a population, and religious holidays can cause seasonal variations. Thus, it is crucial to comprehend the impact of seasonal variations. The technique to capture the seasonal variations is to create a seasonal index, where the ratio-to-moving-average method is employed. It eliminates the secular trend (T), cyclical variations (C), and irregular variations (I). The data may be categorized monthly or quarterly.

Moreover, a seasonal index should have an average value of 1. For instance, if the first quarter sales seasonal index is 1.5, it means that in this quarter, the sales are 50% higher than the average sales in the year. After calculating the seasonal index, it is also necessary to deseasonalize data by dividing the amount by the seasonal index so seasonal variations will be removed from the time series, thereby using deseasonalized data to forecast.

Cyclical Variations (C)

After determining the secular trend (T) and seasonal variations (S), according to the equation, cyclical variations can be represented as Y – T – S = C + I in the additive model and YT*S=C*I in the multiplicative model. To calculate cyclical variations, irregular variations needed to become eliminated; thus, the weighted average moving average method becomes employed. It allows rendering more weight to central values and less weight to extreme values aiming to recreate the cyclical variations more precisely. 

The cyclical variations analysis can help discover the maximum and minimum values a time series can achieve, perform medium- or short-term forecasting, and identify the cyclical components.

Irregular Variations (I)

For the components to be classified as irregular variations; they should become isolated from the influence of the secular trend (T), seasonal variations (S), and cyclical variations (C). Some incidents can become categorized as irregular variations; for instance, strikes, economic busts, natural disasters, etc. Irregular variations are generally unpredictable: they follow a random pattern and occur during a short period. However, in practice, irregular variations tend to follow a normal distribution and may counteract each other. Thus, it is possible to have a time series free of irregular variations for analysis.

What are the four 4 main components of a time series? Written by Boyu Yang