The Components of a Time Series Analysis
Time series analyses are analysis tools used to evaluate data that has been collected over a period of time in order to uncover key patterns that can help predict the future. To understand how these analyses play out, we have to break them down into their four key components, as follows:
Trend
With each time series analysis, analysts look for trends, which are essentially the directions in which the data points move. Since trends are able to filter out the noise and spikes that result from short-term changes, they can inform analysts as to whether a variable is growing, declining, or stagnating. For example, a time series analysis may reveal that the inflation in country A has been growing at a rate of 5% a year, which would be a cause for concern for citizens whose purchasing power would be at risk.
Trends look different based on the data in question. For instance, where the growth or decline is at a constant absolute rate, the trends are linear. But when there are spikes or other such factors, the trends tend to be non-linear.
It is important to note that trends are influenced by underlying factors such as technological shifts, inflation, population growth, and more. As such, when analysts discover trends, they are also put to the task of determining the forces that are contributing to the changes, as this can help forecasters make long-term strategic decisions.
Seasonality
While trends reveal the general direction of changes, analysts also pay attention to patterns, particularly to those that repeat at fixed and predictable intervals. These are referred to as seasonality. But not all patterns fall into this category. Instead, analysts look for what is known as fixed periodicity, which hinges on the premise that they can predict when the pattern will take place because it does so at the same time every cycle. For example, they can predict that ice cream sales peak in July when it is summer, as this is a pattern that they can see in historical data.
But when the patterns are irregular, they are considered to be cyclical patterns or random variations. Say, for example, that a company has an increase in sales because of a viral social media reel; this would be a sudden and unpredictable change caused by a one-time event and would thus not be considered fixed periodicity. We will share more on these two aspects in the next two components.
Since there are many patterns that can show up in a trend, when we say that seasonality is key to time series analyses, our focus is on fixed periodicity, where analysts can tell what will happen and when it will happen. Usually, this seasonality is brought on by weather patterns (such as winter and summer), calendar events like holidays and school breaks, and routine human behavior like the rush hour after work.
Time series analyses allow analysts to isolate this component so as to determine whether the changes they are seeing are part of the trend or have been caused by something else.
Cycle
We mentioned that fixed periodicity is the marker of seasonality. We also stated that sometimes, there are changes that occur due to one-time events, like sales increases because of social media virality. But what happens when a change comes about and lasts for a long time yet does not have a fixed and predictable period?
Well, analysts refer to this as a cyclical variation, also known as a cycle. These are long-term changes that are visible around the trend line and which are not possible to predict. What’s more, they can last for as long as ten years, and the duration between one cycle and the next varies from one cycle to the next, which creates quite a conundrum.
A good example in this case would be real estate booms and busts. We know that real estate markets go through these cycles, and we have sufficient information to know when the bubble is about to burst. But even then, we never really have the assurance that these booms and busts will take place on a given day.
Much of the unpredictability of these cycles stems from the fact that they are heavily influenced by macroeconomic forces. But while that may be so, time series analysts must take note of these cycles as they can use them to prepare for economic changes, even if they cannot point to the exact moment the change will happen.
Noise
The last component that time series analysts consider is the noise, which is also referred to as the irregular component, the residual, or the error. Unlike fixed periodicity, which has a clear pattern, noise does not. It comprises the changes that show up after analysts have accounted for trends, seasonality, and cycles in the data. And given that these changes are random, they do not have identifiable patterns and are thus unpredictable.
Take the example of a natural disaster that negatively affects the tourism sector in a country. This type of change would be unforeseen, as this is not something that analysts could have predicted.
These one-time short-term events come in all shapes and forms, from political coups to sudden strikes and random human behavior. They can also show up due to errors in measurement.
Seeing as they are so random, why do time series analysts include these changes? It all comes down to what they represent, which is essentially pure uncertainty. While analysts are not able to predict this uncertainty, they use its variance to establish confidence levels. For example, when forecasting sales, the analysts can state that they think that sales will be X with a margin of error of plus or minus Y so as to account for random noise. Thus, it provides a much-needed buffer, seeing as we do not live in a world where we can predict everything that can happen.
How Do These Components Interact?
Time series analyses enable analysts to combine time series components based on how they behave in relation to the trend. Here, we have two options. The first is the additive model, where the components act independently of each other, such that the magnitude of the seasonal and cyclical fluctuations remains constant regardless of whether the trend changes. For example, a retail store analysis may reveal that the store always sells $20,000 more in February than its yearly average, regardless of whether its business is growing or declining.
The second option is the multiplicative model, where the components are interdependent. Here, you find that the cyclical and seasonal fluctuations change in relation to the trend, such that as the trend increases, the peaks and valleys become more pronounced. For instance, a retail store analysis may show that the store sells 10% more in February compared to its yearly average. However, if the business grows from a baseline of $300,000 to $350,000, then the spike in February increases based on this new baseline.
So, how do analysts decide the best option? It boils down to the behavior of the seasonal and cyclical swings. If these do not change with the trend, they go for additive models, and if these change based on the trend, they use the multiplicative model.
The Time Series Analysis in Action
Now that we have covered the key components of a time series analysis, let us break down the general steps of the process so we can see how analysts move from raw data to actionable insights. They are as follows:
Defining the Problem
Before conducting a time series analysis, researchers must always define the goal of their research, as this informs them of the kind of data they need to collect.
Let us consider some examples. A problem may look like a hedge fund manager who wants to predict the future daily closing price of a technology stock so that they can get the most out of their new trading strategy. It can also look like the central bank collecting monthly consumer price indices so as to determine whether it needs to review its current monetary policies. Or it could look like the Bureau of Labor Statistics compiling data on monthly payroll so as to keep track of the unemployment rate.
These are all instances where time series analyses would serve as the ideal statistical tools. But the data collected would differ based on the varying goals.
Collecting Data
Once an organization has clearly defined its problem, the next step hinges on collecting data that can address the said gap. For example, if an e-commerce marketplace wants to run a sales event and wants to plan server capacity for that period, it would need to collect data relating to daily website traffic and transaction volumes.
With time series data, the data collection period can be as short as a few seconds to years. For instance, with macroeconomic trends, researchers aim for at least 10 years of data collection to establish long-term trends. But when studying short-term trends such as shifts in consumer behavior, newer data tends to be more accurate, such that data collection can take a few weeks or months. Once again, it all depends on the context.
Cleaning and Preprocessing the Data
Time series models are often highly sensitive to missing periods, irregular intervals, and other such omissions and irregularities, because the sequence matters. To account for this, analysts must find ways to handle missing values, such as by forward filling, resampling, or adjusting for calendar effects. The technique chosen varies based on the reason behind the missing or erroneous data. For example, if a stock exchange closes on public holidays, the analyst may have to carry the previous day’s price over to maintain the sequence.
Performing the Exploratory Data Analysis
Analysts use this step to inspect the data so as to understand the components we discussed earlier. They can do this by plotting the data to reveal the trends and seasonality, or by using autocorrelation functions to measure how data correlates with past values, to name but a few options.
From here, they check the data for stationarity using tests like the augmented Dickey-Fuller test, as this allows them to apply methods such as first-order differencing and log transformations to stabilize mean, variance, and autocorrelation, as these change over time with time series data, unlike in traditional models, where these remain constant.
Choosing a Model
Based on the patterns uncovered during the exploratory data analysis, the analyst must then select an analysis model that best suits their data.
The first option is statistical models, such as ARIMA and SARIMA, which work very well with linear and structured data. For example, when tracking inflation, most analysts use SARIMA which is seasonal ARIMA, as this model accounts for the fact that inflation changes smoothly and often has predictable patterns.
The second option applies to data sets with complex and non-linear data. And here, analysts turn to machine learning and deep learning models as these are able to pick up on nuances that traditional models may miss. Take the example of a finance firm that wants to find non-linear trading signals across multiple correlated stocks. Using a network to do this would allow them to get through millions of data points.
Training the Model
Before a model can be trusted to predict future outcomes, it has to be tested on data that it has not encountered in the past. And since time series follow a strict sequence, analysts cannot use traditional random cross-validation. So, they often use time series splitting.
For example, if the Bureau of Statistics is tracking unemployment rates, it can train the model based on monthly unemployment data from 2000 to 2023. Then, it can validate those results against the data from 2024 and 2025 to gauge its accuracy. But that is not all.
Analysts must also compare the forecasts from their models with historical outcomes through measures such as the mean absolute percentage error and the root mean squared error, as this can show them how accurate their predictions are.
Training involves a lot of back and forth as analysts must address the errors in the model. And before deploying the final models, they must check the residuals we talked about earlier, which are also known as the noise. These errors should have a mean of zero, constant variance, and zero remaining autocorrelation. If not, analysts must continue adjusting their model parameters until they achieve this to ensure that their models capture these random events.
Forecasting the Future
Once analysts have run all the necessary tests and are sure that the model can produce accurate results, they can use it to project the future. However, these forecasts are not presented as single and fixed numbers and must instead include confidence levels because, as we said, there is uncertainty to consider.
For example, the Bureau of Labor Statistics cannot present a report stating that they forecast the unemployment rate will sit at 4% in the next month. Instead, they would present something in the lines of ‘we are 95% confident that the unemployment rate will fall between 4% and 4.5% in the next month.
Beyond accounting for uncertainty, analysts must continuously retrain their models with new data as it becomes available to them so as to account for real-world changes.