# ARMA Model-Based Prediction (Advanced Signal Processing Toolkit)

LabVIEW 2010 Advanced Signal Processing Toolkit Help

Edition Date: June 2010

Part Number: 371419D-01

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The ARMA model is a general model that includes both the AR and the MA models. This section describes time series value predictions based only on ARMA models. You can apply ARMA model-based prediction to AR or MA model-based prediction by converting an AR or MA model to an ARMA model.

Use the TSA ARMA Prediction VI to predict the future values of univariate or multivariate time series based on the estimated ARMA or VARMA models.

The following figure shows an example of predicting the monthly temperatures for the following year based on the ARMA model of the monthly temperatures during the previous eleven years.

 Note  The data source in the previous figure is from the Time Series Data Library.

In the previous figure, the Original graph contains the monthly average temperatures for twelve consecutive years. Before predicting future values, this example estimates the AR model for the temperature time series of the first eleven years. With the estimated AR model coefficients and by specifying the MA model coefficients to one, this example predicts the monthly temperatures for the twelfth year using the TSA ARMA Prediction VI.

The Prediction Result graph in the previous figure compares the predicted temperatures with the original temperatures of the twelfth year by plotting them together. The prediction may bias from the true values but the true values fall into the estimated confidence range. The Upper Limit and Lower Limit plots in the Prediction Result graph indicate the confidence range of the prediction. You can see in the Confidence Level indicator that the prediction result falls into the estimated confidence range with the confidence level of 99.73% (3σ).

Refer to the ARMA Prediction VI in the labview\examples\Time Series Analysis\TSAGettingStarted.llb for an example that demonstrates how to obtain ARMA model parameters of a univariate time series by using the Time Series Analysis VIs.

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