Time-series modelling: AR, MA, ARIMA, SARIMA and VAR
Learn how time-series models describe patterns in data collected over time. This one-hour recorded course from MCC Economics & Finance introduces AR and MA models, AIC/BIC model selection, ACF/PACF interpretation, and the extensions to ARIMA, SARIMA and VAR.
Econometrics 115 is provided by MCC Economics & Finance, whose work includes economic analysis, financial modelling and data science.
Course provider
MCC Economics & Finance
Economic analysis, modelling and data science
MCC Economics provides independent economic analysis for policy, regulation and investment decisions. Its training includes econometrics and forecasting. Contact the team for the named lecturer for this recording.
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Quick Answer
Econometrics 115 is an on-demand course on time-series model specification and forecasting. It explains autoregressive (AR), moving average (MA) and ARMA models; how AIC/BIC and ACF/PACF support model selection; and how ARIMA, SARIMA and vector autoregression (VAR) extend the framework. Registration gives immediate access to a one-hour lecture video, presentation slides, a transcript and a knowledge quiz. There is no live meeting.
Key takeaways
Autoregressive models use a series’ earlier values; moving average models use current and earlier error terms.
AIC and BIC help compare model fit against complexity when choosing a suitable specification.
ACF and PACF show relationships across lags and help identify candidate AR and MA structures.
ARIMA adds differencing, SARIMA adds seasonal structure, and VAR models several related time series together.
What will you be able to do after the course?
The course is designed to help you explain time-series specifications and interpret the tools used to compare them. Its topics support three learning outcomes.
Explain model structure. Distinguish AR, MA and ARMA models and describe how past observations and shocks enter a time-series specification.
Interpret selection tools. Explain how AIC/BIC comparisons and ACF/PACF patterns inform choices about model structure and lag length.
Recognise the extensions. Explain what ARIMA, SARIMA and VAR add, and identify the types of time-series questions each framework addresses.
What does the course cover?
The ten-topic outline follows the Eventbrite agenda, progressing from AR models to seasonal and multivariate frameworks. The summaries explain each topic in plain English.
Introduction: what time-series analysis studies and why the order of observations matters for economic and financial modelling.
Autoregressive Models: how AR models relate a series to its own earlier observations and what the lag order represents.
Information Criteria: how Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) help compare candidate specifications.
Moving Average Models: how MA models describe the influence of current and earlier shocks on a series.
ARMA Models: how autoregressive and moving average components combine in one model.
ACF and PACF: how autocorrelation and partial autocorrelation plots help interpret dependence at different lags.
ARIMA Models: how differencing extends the ARMA framework for series that require a change in level or trend treatment.
SARIMA Models: how seasonal terms extend ARIMA to account for patterns that repeat at regular intervals.
VAR Models: how vector autoregression describes the joint dynamics of several related time series.
References and Useful Links: resources for reviewing the concepts and continuing your study of time-series econometrics.
What do the key terms mean?
These definitions explain the model families and selection tools used in Econometrics 115. They also clarify the stationarity and differencing concepts needed to understand ARIMA.
Term
Meaning
Time series
Observations of a variable recorded in time order, such as monthly inflation or quarterly GDP.
Lag
An earlier observation or error term. Lag 1 refers to the preceding period.
Autoregressive model (AR)
A model that relates the current value of a series to its own past values and a current error term.
Moving average model (MA)
A model expressed using current and past error terms. It differs from moving-average smoothing of observations.
ARMA
Autoregressive moving average: a model combining AR and MA components, usually for a stationary series.
AIC and BIC
Akaike Information Criterion and Bayesian Information Criterion. Both balance fit against model complexity; lower values are preferred among comparable models fitted to the same response and observations.
ACF
Autocorrelation function: the correlation between a series and its lagged values at different lags.
PACF
Partial autocorrelation function: correlation at a given lag after accounting for the intervening lags.
Stationarity
For covariance stationarity, the mean and variance do not change over time and covariance depends on lag rather than calendar date.
Differencing
Subtracting an earlier value from the current value. It can help remove changes in level or seasonal patterns.
ARIMA
Autoregressive integrated moving average. In ARIMA(p,d,q), p is the AR order, d is the differencing order and q is the MA order.
SARIMA
Seasonal ARIMA: adds seasonal AR, differencing and MA terms to the non-seasonal model, with a specified seasonal period.
VAR
Vector autoregression: a system in which each variable is modelled using past values of itself and the other variables.
Who is the course for?
Econometrics 115 suits learners who use data observed over time and want to understand the specifications behind forecasting models. Examples include economic indicators, financial data and policy monitoring series.
Economists, analysts and researchers
Students of econometrics and time series
Finance and policy forecasting professionals
Consultants developing quantitative skills
Which courses should you take first?
Econometrics 115 focuses on time-series specification within MCC’s wider econometrics training. Familiarity with basic statistics and regression is useful preparation. The courses below are related options, rather than a mandatory sequence; check each outline before choosing.
MCC Economics applies economic theory, quantitative modelling and data analysis to policy, regulation and investment questions. Econometrics 115 introduces the time-series frameworks used to describe dynamic data and support forecasting decisions. Explore MCC’s economic analysis services, research publications and team profiles for the wider context of its work.
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Questions buyers ask before registering
What is Econometrics 115 about?
Econometrics 115 introduces time-series model specification. It covers AR, MA and ARMA models, information criteria, ACF/PACF, ARIMA, SARIMA and VAR.
Is there a live session or a meeting to attend?
No. This listing is for on-demand course material only. You study the recorded lecture and supporting resources without attending a live meeting.
How long is the course, and what do I receive?
The recorded lecture lasts one hour. Registration includes the lecture video, presentation slides, a transcript and a knowledge quiz. Allow additional time to review the resources and complete the quiz.
How do I access the course materials?
Register through the Eventbrite listing to get immediate access to the materials. Follow the access instructions provided with your registration.
Who delivers Econometrics 115?
The course is provided by MCC Economics & Finance. For the named lecturer for this recording, contact MCC Economics before registering.
What is the difference between AR and MA models?
An AR model uses past observations of the series. An MA model uses current and past error terms. ARMA combines both components.
What is the difference between ARIMA, SARIMA and VAR?
ARIMA combines autoregressive and moving average components with differencing. SARIMA adds seasonal terms. VAR models a system of related time series using lags of the variables in that system.
How do ACF, PACF, AIC and BIC help select a model?
ACF and PACF reveal dependence across lags and suggest candidate structures. AIC and BIC compare fit against complexity. These tools inform selection; they do not guarantee forecast accuracy.
Do I need prior knowledge of econometrics?
Familiarity with regression, basic statistics and time-series data will help you follow the material. This is suggested preparation; the listing does not specify a formal entry requirement.
Which software or certificate is included?
The listing does not specify a required software package or a completion certificate. Contact MCC Economics if either is important to your training plans.
Can my team take the course together?
Contact MCC Economics through the consultation page to discuss team access or training tailored to your organisation.