If you’ve ever modeled two time series that each wander all over the place but somehow never drift too far apart, you’ve run into cointegration. It shows up everywhere: finance, energy, macroeconomics, even climate data. In this guide, we’ll walk through **examples of cointegration in time series: 3 practical examples** that analysts actually use on the job, not just in textbooks. Along the way, we’ll pull in several other real examples so you can see the pattern in different domains. Instead of abstract theory, we’ll focus on how cointegration behaves in real data: stock pairs that move together, interest rates locked by policy, and commodity prices tied by physical or regulatory links. These **real examples of cointegration** are the ones that motivate techniques like the Engle–Granger test, Johansen test, and pairs trading strategies. If you already know the basics of time series but want to understand when and why cointegration matters in practice, you’re in the right place.
When you first hear “stationarity,” it sounds like something only a math PhD should care about. In reality, if you work with time series at all—finance, forecasting, A/B testing, sensor data—you live or die by whether your data is stationary. In this guide, we’ll walk through examples of stationarity in time series: 3 practical examples that show how it appears in real data, how to recognize it, and what to do when your series isn’t stationary. Rather than staying abstract, we’ll look at real examples from finance, web analytics, and environmental monitoring, and then contrast them with non‑stationary behavior like trends and seasonality. Along the way, we’ll connect these examples of stationarity in time series to the models you actually use—ARIMA, regression with time series errors, and even modern forecasting tools. If you’ve ever run an Augmented Dickey–Fuller test “because the tutorial said so,” this is the article that finally makes stationarity click.
If you learn time series by seeing it in action, you’re in the right place. This guide walks through real, data-driven examples of autocorrelation function (ACF) behavior instead of staying stuck in theory. We’ll look at how ACF shows up in finance, weather, healthcare, and more, and why analysts rely on it to understand patterns over time. When people search for examples of examples of autocorrelation function (acf), they usually want to know what different ACF shapes actually *mean* in practice. Is that slow decay a sign of a trend? Does that spike at lag 12 really point to seasonality? And how does this help with forecasting or model selection? Here we’ll unpack those questions with concrete, well-explained scenarios. By the end, you’ll recognize classic ACF signatures in at least eight real examples, see how they connect to ARIMA-style models, and know how to interpret those vertical bars in an ACF plot with far more confidence.
If you work with data over time, you don’t just want a line chart—you want to understand what’s hiding under that line. That’s where looking at real examples of examples of time series decomposition becomes so valuable. Instead of staring at noisy curves, you separate a series into trend, seasonality, and irregular components, and suddenly the story becomes obvious. In this guide, we walk through practical examples of time series decomposition from finance, public health, energy, retail, climate, and tech. These examples include classic additive and multiplicative models, as well as newer STL and model-based approaches that are common in 2024–2025 analytics stacks. The goal is simple: show you how decomposition actually looks and why analysts keep coming back to it. If you’ve ever wanted a clear example of how to isolate seasonal patterns, detect structural breaks, or improve forecasts, the following cases will feel very familiar—and very usable in your own work.
If you work with data over time, you run into moving averages constantly, even if you don’t call them that. Weather reports, stock charts, COVID dashboards, and sales forecasts all hide moving averages under the hood. In this guide, we’ll walk through practical, real examples of moving averages in time series analysis, showing how they smooth noisy data, highlight trends, and support better decisions. We’ll start with concrete examples of examples of moving averages in time series analysis from finance, public health, climate data, and business operations. Along the way, we’ll compare simple, weighted, and exponential moving averages, and explain when each one actually helps instead of just making your plots look prettier. If you’ve ever wondered how analysts pick a 7‑day average for infections, a 50‑day average for stock prices, or a 12‑month rolling average for inflation, this is the walkthrough that connects the formulas to real-world practice.
If you work with time series, you eventually bump into the partial autocorrelation function and wonder what it actually looks like in practice. Abstract definitions are fine, but most people learn faster from concrete, real-world examples of partial autocorrelation function (PACF) behavior. This guide focuses on exactly that: how PACF behaves in different time series and how to read those patterns. We’ll walk through several realistic examples of examples of partial autocorrelation function (PACF): financial returns, daily temperatures, hospital admissions, web traffic, and more. Along the way, we’ll connect these patterns to ARIMA modeling decisions, show what a “good” PACF plot looks like for different processes, and point you to external resources if you want to go deeper into the theory. If you already know the definition of PACF and just want to see how it plays out in real data, you’re in the right place.
If you’re hunting for real, practical examples of R time series analysis examples instead of vague textbook talk, you’re in the right place. This guide walks through concrete, data-driven use cases that analysts actually work on in 2024–2025: forecasting retail sales, modeling electricity demand, tracking hospital admissions, and more. These examples of R time series analysis examples are written with working analysts, data scientists, and grad students in mind—people who care less about theory for its own sake and more about getting forecasts that don’t embarrass them in front of their boss. We’ll look at how to set up time series objects in R, why ARIMA and exponential smoothing still matter, and where newer tools like `fable` and `prophet` fit in. Along the way, you’ll see real examples, code-style snippets, and references to open datasets you can download today. Think of this as a practical tour of the best examples of R time series analysis, not a math lecture.