Trends, time series and the types of analysis

Why this matters

Much of what an analyst reports is change over time: sales up this month, complaints down this quarter, traffic growing year on year. Time series data has features that make naive comparisons misleading, such as seasons, calendar effects and random noise, and a percentage change quoted without them can describe nothing real.

The exam also asks you to classify analyses by their purpose: describing what happened, explaining it, predicting it, or recommending action. This lesson covers the four types of analysis, the components of a time series, moving averages and period-over-period change, exploratory against confirmatory analysis, and matching the analysis to the question.

The lesson

Descriptive, diagnostic, predictive and prescriptive analysis

Analyses are commonly grouped into four types by the question they answer.

• Descriptive analysis asks what happened: total sales last quarter, average response time, the number of new customers. Most reporting is descriptive.
• Diagnostic analysis asks why it happened: sales fell because one region lost a major customer; response times rose after a system change. It uses drill-down, comparison between segments and correlation.
• Predictive analysis asks what is likely to happen: next month's demand, which customers are likely to cancel. It uses forecasting and models trained on history.
• Prescriptive analysis asks what should be done: how much stock to order, which customers to offer a discount. It combines predictions with constraints and goals, often using optimisation or simulation.

The types build on each other, in increasing complexity and value, and each depends on the one before being right: a prediction built on a misdescribed history inherits its errors.

Trend, seasonality and noise in a time series

A time series is a sequence of values recorded at regular intervals: daily orders, monthly revenue, hourly temperature. Its movements are usually described as a combination of components.

• The trend is the long-term direction: steady growth, decline, or flat.
• Seasonality is a pattern that repeats at a fixed period: higher retail sales every December, more web traffic on weekdays, higher temperatures every afternoon.
• Cyclical movements rise and fall over longer, irregular periods, such as economic cycles.
• Noise, or irregular variation, is what remains: random fluctuation with no pattern.

The practical danger is mistaking noise or seasonality for trend. The course's practice orders were generated at a steady random rate through 2025, so there is no real trend in them at all. Even so, monthly totals move between 147 and 178, and February to March shows an apparent 19.7% increase. Part of that is simply the calendar: February has 28 days and March 31. Per day, the increase is about 8%, and the rest is noise. A report headlined "orders up 20%" would be describing a short month and chance.

Moving averages and period-over-period change

Two tools help separate signal from noise.

A moving average replaces each value with the average of it and its neighbours over a window, such as the last seven days. It smooths out noise and short-term swings so the underlying trend is easier to see. A seven-day window also removes the weekly pattern, because every window contains each weekday once. The cost is lag: a moving average responds to a real change later than the raw data does, and a longer window smooths more and lags more.

Period-over-period comparisons express change relative to an earlier period.

• Month over month compares consecutive months. It is sensitive to noise and to differing month lengths.
• Year over year compares a period with the same period a year earlier: December with last December. It removes seasonality, which is why it is standard in retail and finance.
• Year to date accumulates from the start of the year, for comparison with the same point last year.

Percentage change is (new − old) ÷ old. It is asymmetric: a fall of 50% followed by a rise of 50% does not return to the start, and percentage changes on small bases produce dramatic numbers from tiny movements. Reporting the absolute change alongside the percentage guards against both.

Exploratory analysis against confirmatory analysis

Analyses also differ by whether they are looking for questions or answering them.

Exploratory data analysis (EDA) looks at data without a fixed hypothesis: profiling, plotting distributions, comparing segments, looking for patterns and surprises. It is where most ideas come from, and it is flexible by design.

Confirmatory analysis tests a specific hypothesis stated in advance, using a planned method, such as an A/B test or a pre-specified statistical test.

The distinction matters because exploration looks at many things, and some patterns found that way will be chance. A pattern discovered during exploration is a hypothesis, not a finding. Treating it as confirmed, then testing it on the same data that suggested it, produces conclusions that do not hold up. The sound sequence is to explore, form a hypothesis, and then confirm it on new data or with a designed test.

Choosing the analysis type the question actually needs

Much wasted analytical effort comes from answering a different question from the one asked. Before starting, it helps to classify the request.

"How many customers did we lose last quarter?" is descriptive, and needs an accurate count with a clear definition of "lost". "Why are we losing customers?" is diagnostic, and needs comparison between those who left and those who stayed. "Which customers are likely to leave next quarter?" is predictive, and needs a model. "What should we do to keep them?" is prescriptive, and needs predictions combined with the costs and effects of possible actions.

Matching the type sets expectations about effort, data and certainty. A descriptive answer can be exact; a predictive one is a probability; a prescriptive one depends on assumptions that should be stated. And a request that sounds prescriptive often needs a good descriptive answer first, because the decision may be obvious once the facts are clear.