Time Series Analysis: Patterns in Your Data

Most statistical data is cross-sectional—a snapshot in time. But what happens when you measure the same thing over and over again? Stock prices, weather, heart rates, website traffic—these are all examples of Time Series Data.

Time Series Analysis is the set of statistical techniques used to analyze these temporal sequences. It helps us understand the underlying structure of the data and forecast future values.

If you need help decomposing your time series or building a predictive model, our statistical consulting service is here to assist.

What is Time Series Analysis?

Time series analysis is the process of using statistical models to understand the underlying forces that structure the data. It is distinct from standard regression because the data points are not independent; they are chronologically ordered.

The primary goals are:

• Description: identifying patterns like trends or seasonal cycles.
• Explanation: understanding *why* the data changes (e.g., did a policy change affect sales?).
• Forecasting: predicting future values based on past behavior.

The Four Components of a Time Series

We can decompose most time series into four distinct parts:

1. Trend (T): The long-term direction of the data (increasing, decreasing, or stable).
2. Seasonality (S): Regular, repeating patterns within a fixed period (e.g., monthly, quarterly).
3. Cyclicality (C): Long-term fluctuations that are not of a fixed period (e.g., economic boom/bust cycles).
4. Irregularity (I): Random noise or “residuals” left after removing the other components.

The Concept of Stationarity

A time series is stationary if its statistical properties (mean, variance) do not change over time. This is a critical assumption for many models.

If your data has a trend or seasonality, it is non-stationary. You must “stationarize” it using techniques like:

• Differencing: Subtracting the previous value from the current value.
• Log Transformation: Stabilizing the variance of the series.

We use the Augmented Dickey-Fuller (ADF) test to check for stationarity. For a detailed explanation, see the Duke University guide to stationarity.

Autocorrelation (ACF & PACF)

Autocorrelation measures the relationship between a variable’s current value and its past values. We use correlograms to visualize this:

• ACF (Autocorrelation Function): Shows the correlation between the series and its lags.
• PACF (Partial Autocorrelation Function): Shows the correlation between the series and its lags *after* removing the effects of intermediate lags.

Common Forecasting Models

There are several ways to model time series data:

Moving Average (MA)

Uses the average of the last *n* data points to predict the next one. Good for smoothing out noise.

Exponential Smoothing (ETS)

Assigns exponentially decreasing weights to past observations. Recent data matters more than old data.

ARIMA (AutoRegressive Integrated Moving Average)

The most popular model for stationary time series. It combines Autoregression (AR), Differencing (I), and Moving Average (MA). For seasonal data, we use SARIMA. For technical details, refer to the NIST handbook on Box-Jenkins models.

Get Help with Your Forecast

Time series analysis is mathematically intense. Identifying the correct order of differencing or selecting the right ARIMA parameters (p, d, q) requires expertise. Our team of data scientists can help you build, validate, and interpret predictive models.