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Lecture

Time Series

In course

MATH-342: Time series

A first course in statistical time series analysis and applications. ...

Description

This lecture by the instructor covers the topic of Time Series, focusing on model specification, diagnostics, and forecasting. The lecture delves into identifying ARMA models, model checking, and comparing models using information criteria. It also explores forecasting methods, including mean square error and prediction errors for autoregressive and moving average processes.

Instructor

Sofia Charlotta Olhede

Sofia Olhede is a professor of Statistics at EPFL in Switzerland. She joined UCL prior to this in 2007, before which she was a senior lecturer of statistics (associate professor) at Imperial College London (2006-2007), a lecturer of statistics (assistant professor) (2002-2006), where she also completed her PhD in 2003 and MSci in 2000. She has held three research fellowships while at UCL: UK Engineering and Physical Sciences Springboard fellowship as well as a five-year Leadership fellowship, and now holds a European Research Council Consolidator fellowship. Sofia has contributed to the study of stochastic processes; time series, random fields and networks. Sofia was part of the multi-institutional team that set up the UK national data science institute, the Alan Turing Institute. She organised and served as chair of the science committee that developed the initial 500 000 pounds scientific programme of the institute; peer-reviewing over 100 workshop proposals and hosting over 30. She also chaired the first recruitment wave of the institute hiring 13 data scientists as a multi-university recruitment drive. Sofia was a member of the Royal Society and British Academy Data Governance Working Group, and the Royal Society working group on machine learning. Most recently she was one of 3 commissioners on a law society commission on the usage of algorithms in the justice system.

Official source

Ontological neighbourhood

Statistics

Data analysis: Time series

Related concepts (32)

Forecasting

Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results creating a variance actual analysis. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself.

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).

Autoregressive–moving-average model

In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA). The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins.

Moving-average model

In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable. Together with the autoregressive (AR) model, the moving-average model is a special case and key component of the more general ARMA and ARIMA models of time series, which have a more complicated stochastic structure.

Weather forecasting

Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th century. Weather forecasts are made by collecting quantitative data about the current state of the atmosphere, land, and ocean and using meteorology to project how the atmosphere will change at a given place.

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Covers ARMA models for time series forecasting, discussing implications, properties of forecast error, challenges with predictions, and covariance models.

Residuals & Forecasting: MATH-342 Time Series

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