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Time Series Analysis - Univariate Box-Jenkins ARIMA Models

[Home] [Up] [Transfer Function] [Multiple Time Series] [Bayesian Models] [Univariate Models]

[Identification] [ARIMA Estimation] [ARIMA Checking] [ARIMA Forecasting] [ARIMA Extensions]

A great reference for scientists. A classic in time series literature.

An absolute MUST for serious researchers. We recommend this excellent textbook !

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Models in Time Series Analysis enable the user to generate: forecasts of a (dependent) time series that is based upon the information of its own past, explain events that occurred in the past, and provide insight into the dynamical interrelationships between variables.

In the following sections we describe the development of Autoregressive Integrated Moving Average models (short: ARIMA), Transfer Function-Noise models, and Multivariate Time Series Models according to the methodologies proposed by Box and Jenkins and many other scientists.

For obvious reasons these methodologies can only apply to time series. Above that, the steps or intervals of the time series under investigation are always supposed to be equally spaced in time (which is an important restriction).

Furthermore we assume that each observation of the time series has the same expectation function, standard deviation, and probability distribution function.

Since the Box-Jenkins methodology uses Maximum Likelihood Estimation (MLE), it is obvious that a distribution has to be assumed about the error term. In practice we will assume a white noise error component, which is a sequence of uncorrelated stochastic variables with a fixed (normal) distribution, a mathematical expectation of zero, and constant variance.
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Transfer Function
Multiple Time Series
Bayesian Models
Univariate Models
Identification
ARIMA Estimation
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ARIMA Extensions
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