Lecture

Autocorrelation and Periodicity

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In course

ENV-400: Air pollution and climate change

A survey course describing the origins of air pollution and climate change ...

Description

This lecture covers the analysis of relationships among observations in time series data, focusing on autocovariance, autocorrelation, and periodicity. It explores the correlogram, power spectrum, and cross-correlations, illustrating how to interpret patterns in sequential observations. The instructor demonstrates R code for calculating autocorrelation coefficients and correlograms, emphasizing the importance of understanding the underlying processes in time series data. Additionally, the lecture discusses the concept of spurious correlations and provides examples to caution against misinterpretation. Practical applications include examining relationships between variables like ozone concentration and radiation intensity, showcasing the significance of understanding autocorrelation in environmental data analysis.

Instructors (2)

Julia Schmale

Expertise atmospheric science, aerosol-cloud interactions, climate change in polar regions Mission Extreme environments are particularly sensitive to climate change and are transforming at accelerated rates. This can have important global repercussions. EERL aims to create integrated process understanding by investigating interactions between the atmosphere, cryosphere, biosphere, ocean, land and anthroposphere. The goal is to characterize climate-change relevant and vertically-resolved processes that are d

Satoshi Takahama

Curriculum Vitae (pdf)

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis, Time series

Related concepts (32)

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

Intraclass correlation

In statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures, it operates on data structured as groups rather than data structured as paired observations.

Correlation coefficient

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement.

Cross-correlation

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.

Time series

In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart).

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