Prioritize...
After reading this section, you should be able to define trend and note the impacts a trend can have on a time series analysis.
Read...
Unlike the patterns we just discussed that are periodic, trends (I specifically mean linear trends, but from here on out will refer to them as trends unless otherwise noted) are a constant increase or decrease over time. As a reminder, trends and periodicity can and do occur at the same time. Again, when performing different time series analyses, you may have to account for trends, but the main goal right now is to know how to identify trends in a given dataset.
What is a trend?
Let’s start with the very basics. What is a trend? For this course, specifically this lesson, a trend is a monotonic increase or decrease in the dataset over a time period. Sometimes, you will have different trends over different time periods, where the rates of change are different. While other times, it will be one long steady increase or decrease. There are other types of trends, such as exponential, that exist in weather and climate data, but right now, we will focus on linear trends.
How to identify a trend?
You might think it should be pretty evident if your data has a trend, but it can be much trickier. When trying to identify a trend, there are two components to consider. The first is the long-term trend you are trying to identify, and the second is the short-term variability. The short-term variability is what makes it difficult to identify the trend. The short-term variability can come from natural variability (the natural fluctuation that occurs in the variable you are measuring) or errors (anything that is non-natural, such as errors from the instrument). The short-term variability can also include any periodicity we discussed previously, further complicating the problem. For the purpose of finding the trend, the trend is the signal and the short-term variability is the noise. This will change later in the course when we start analyzing periodicities.
Rarely will you be able to visualize a trend by simply plotting your data. Usually, there is too much short-term variability to pull out the long-term trend. Many times, we need to either smooth the data or transform it to pull out the trend. Smoothing data will average out the noise, reducing the jagged fluctuations you observe. Once you smooth the data, you are usually left with a dataset that is easier to detect a trend with. We will learn more about this topic later on.