# ARMA

ARMA, or Auto-Regressive Moving-Average, is a method for error prediction. It predicts future errors between model results and reality using recorded errors between past model outputs and observations.

A model in which future values are forecast purely on the basis of past values of the time series is called an autoregressive (AR) process. A model in which future values are forecast purely on the basis of past shocks (or noise or random disturbances) is called a moving average (MA) process. A model that uses both past values of the time series and past shocks is called an autoregressive-moving average (ARMA) process.

In InfoWorks ICM, ARMA is used to:

- Calculate the difference between actual observed flows from a subcatchment and the runoff predicted by a model.
- Post-processing forecast predictions.

Both these operations use an ARMA model which defines the type of error calculation (linear or logarithmic) to be performed and the autoregressive (AR) and the moving average (MA) coefficients to be used in the ARMA predictions.

## Calculating the difference between actual observed flows and predicted runoff

In order to calculate the difference between actual observed flows and predicted runoff, an ARMA model must be referenced by the subcatchment for which the runoff is modelled. A TVD connector can be setup to either connect a TSDB data stream or another TVD connector, from which the observed flow can be obtained, to the subcatchment. This allows the observed and predicated values to be calculated during a simulation.

The simulation results for the subcatchment will include the raw or unmodified runoff result as well as the ARMA-modified outflow result. The results can be shown on the relevant subcatchment's graph or grid view.

A brief description of how to use ARMA to calculate the difference between observed flows and the predicted runoff is outlined in the topic, Using ARMA in InfoWorks ICM.

## Post-processing forecast predictions

A TVD connector can be used for post-processing the model output. Using observed data, either from a TSDB data stream or another TVD connector, and the relevant ARMA model, the model output can be corrected for any of the following types of objects that the TVD connector is connected to:

- node – using the comparison result level
- network results point 1D – using the comparison results flow, depth or velocity
- network results point 2D – using the comparison results depth or speed

When a simulation is complete, the TVD connector results can be displayed on the graph or grid view.

A brief description of how to use ARMA to post-process the forecast predictions is outlined in the topic, Using ARMA in InfoWorks ICM.

Further information about ARMA models in general can be found in:

- Box, G.E.P. and Jenkins, G.M. (1970) Time Series Analysis, Forecasting and Control. Holden-Day.
- Chatfield, C. (1980) The Analysis of Time Series; An Introduction. Chapman & Hall, 2nd Ed., 268 pp.