Time series are particularly useful to track variables such as revenues, costs, and profits over time. Time series models help evaluate performance and make predictions. Consider the following and respond in a minimum of 175 words: Time series decomposition seeks to separate the time series (Y) into 4 components: trend (T), cycle (C), seasonal (S), and irregular (I). What is the difference between these components

Trend (T): This is a secular trend, which refers to the movement across time.

Cycle (C): These are cyclical swings that correspond to seasonal but not periodical variations.

Seasonal (S): These are seasonal shifts represented by seasonal variations.

Irregular (I): These are irregular variations, which are a different type of nonrandom cause of series variations.

Explanation:

A time series is a collection of data points that have been indexed (or listed or graphed) in chronological sequence.

The difference between the components can explained as follows:

Trend (T): This is a secular trend, which refers to the movement across time. A trend in data is a pattern that demonstrates the movement of a series to progressively higher or lower values over time. To put it another way, a trend can be seen when the time series has a rising or decreasing slope. A trend usually lasts for a short period of time before dissipating; it does not occur again.

Cycle (C): These are cyclical swings that correspond to seasonal but not periodical variations. The term cycle refers to recurring fluctuations in time series that persist longer than a year, sometimes up to 15 or 20 years. In terms of amplitude and length, these variations aren't regular. The majority of business time series show some form of cyclical or oscillatory fluctuation.

Seasonal (S): These are seasonal shifts represented by seasonal variations. Seasonal fluctuation may be present in time series data. Seasonal variation, often known as seasonality, refers to cycles that occur on a regular basis over time. Seasonal variation refers to a recurring pattern within each year, though it can also refer to patterns that repeat across any specified period.

Irregular (I): These are irregular variations, which are a different type of nonrandom cause of series variations. The polar opposite of a regular time series is an irregular time series. The data in the time series is organized in a chronological order, however measurements may not occur at regular intervals. The operator may produce unexpected or suboptimal results if the time series is erratic.