Time Series Analysis

We have already used moving averages to find the trend on the graph of a time series.
Here are some notes on Time Series Analysis:
Many graphs arising from data gathered over a period of time will show several types of variation.
These generally include:
Seasonal Variation - this shows a more-or-less regular variation over a "season". Note that a season is not always a year (divided into quarters or months), but it might also be a week (divided into days) or even a day (divided into hours) or some other repeating period. For example, we might have a graph of temperatures at a certain location taken each hour. In such a case we would expect the temperature to show a decrease during the night and increase again during daylight hours.
Cyclical Variation - this is a similar up and down change in values of a variable, but generally for periods that are greater than a year. For example, the boom and bust variation of a national economy over a longer period of years.
Irregular Variation - this refers to variation caused by unusual or unexpected events, that disturbs the regular patterns of the other types of variation. For example, some natural disaster may disturb the pattern of data of rainfall or temperature, or a pandemic might disturb the pattern of the data for economic activity in a national economy.
Secular Variation
- this is just another phrase meaning "Trend". In other words, the Secular Variation shows the general change in value of a variable quantity over the whole period of our graph.

A Time Series Graph to show Advance Bookings for a Hotel in a Certain Country

In the example illustrated by the sketch graph above, the quarterly data (in black) shows a fairly regular seasonal variation, as we would expect. But over a period of years, the popularity of the hotel also varies (this is the cyclical variation overlaid in red). The overall trend is shown as a blue line. Notice the irregular variation in the bookings for the 2nd Quarter of 2020, in which bookings usually increase, but unusual events (a pandemic) have caused the bookings to go down instead.