Time Series Analysis

Time series data is ubiquitous in research, from economic indicators to climate measurements. This page demonstrates various techniques for analyzing and visualizing temporal data[1].

Climate Data Analysis

Temperature Anomalies Over Time

Seasonal Decomposition

Time series often contain trend, seasonal, and irregular components[2]. Here we decompose the signal:

Economic Indicators

Multiple Time Series Comparison

Forecasting

Time Series Forecasting with Confidence Intervals

Event Timeline

Using our custom Timeline component to show research milestones[3]:

Autocorrelation Analysis

ACF and PACF Plots

Autocorrelation helps identify patterns and dependencies in time series data[4].

Volatility Analysis

Rolling Standard Deviation

Change Point Detection

Identifying structural breaks in time series[5]:

Summary Statistics by Period

Methods and Applications

Time series analysis is crucial for understanding temporal patterns in data[6]. Key applications include:

  1. Climate Science: Analyzing temperature trends and detecting climate change signals
  2. Economics: Forecasting GDP, inflation, and market indicators
  3. Epidemiology: Tracking disease spread and seasonal patterns
  4. Engineering: Monitoring system performance and detecting anomalies

  1. Time series analysis involves statistical techniques for analyzing time-ordered data points. Box, G.E.P., Jenkins, G.M., Reinsel, G.C., & Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ↩︎

  2. Seasonal decomposition separates a time series into trend, seasonal, and residual components. The STL (Seasonal and Trend decomposition using Loess) method is particularly robust. Cleveland, R.B., Cleveland, W.S., McRae, J.E., & Terpenning, I. (1990). STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6(1), 3-73. ↩︎

  3. Timeline visualizations help communicate the temporal sequence of events in research projects. They are particularly useful for project management and presenting research progress to stakeholders. ↩︎

  4. The Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) are essential tools for identifying the order of ARIMA models. Ljung, G.M., & Box, G.E.P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297-303. ↩︎

  5. Change point detection identifies times when the statistical properties of a time series change. The CUSUM (Cumulative Sum) method is one of the simplest approaches. Page, E.S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100-115. ↩︎

  6. For comprehensive coverage of modern time series methods, see: Hyndman, R.J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts. Available online at https://otexts.com/fpp3/ ↩︎