Lecture

Time Series: Common Models

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In course

MATH-342: Time series

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

Description

This lecture covers simple time series models, differencing, and trend removal. The instructor explains common models like moving average (MA), autoregressive (AR), and autoregressive moving average (ARMA) processes. The lecture also delves into trend removal and seasonality adjustment techniques, showcasing examples and calculations to understand the concepts better.

Instructor

Sofia Charlotta Olhede

I am a professor of Statistics at EPFL. I did my PhD in Mathematics at Imperial College London, and graduated in 2003. I was an assistant professor (lecturer) at Imperial College London 2002-2006, and an associate professor (senior lecturer) 2006-2007. In 2007 I moved to University College London and became a full professor. I moved to EPFL in 2019, and in 2018 I became an Institute of Mathematical Statistics Fellow with citation “For seminal contributions to the theory and application of large and heteroge

Official source

Ontological neighbourhood

Statistics

Data analysis: Time series

Related concepts (32)

Autoregressive model

In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation).

Autoregressive integrated moving average

In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. To better comprehend the data or to forecast upcoming series points, both of these models are fitted to time series data. ARIMA models are applied in some cases where data show evidence of non-stationarity in the sense of mean (but not variance/autocovariance), where an initial differencing step (corresponding to the "integrated" part of the model) can be applied one or more times to eliminate the non-stationarity of the mean function (i.

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.

Autocorrelation

Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.

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.

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