fittestArima function

Automatic ARIMA fitting, prediction and accuracy evaluation

The function predicts and returns the next n consecutive values of a univariate time series using an automatically best fitted ARIMA model. It also evaluates the fitness of the produced model, using AICc, AIC, BIC and logLik criteria, and its prediction accuracy, using the MSE, NMSE, MAPE, sMAPE and maximal error accuracy measures.

fittestArima(
  timeseries,
  timeseries.test = NULL,
  h = NULL,
  na.action = stats::na.omit,
  level = c(80, 95),
  ...
)

Arguments

• timeseries: A vector or univariate time series which contains the values used for fitting an ARIMA model.

• timeseries.test: A vector or univariate time series containing a continuation for timeseries with actual values. It is used as a testing set and base for calculation of prediction error measures. Ignored if NULL.

• h: Number of consecutive values of the time series to be predicted. If h is NULL, the number of consecutive values to be predicted is assumed to be equal to the length of timeseries.test. Required when timeseries.test is NULL.

• na.action: A function for treating missing values in timeseries

  and timeseries.test. The default function is na.omit, which omits any missing values found in timeseries or timeseries.test.

• level: Confidence level for prediction intervals.

• ...: Additional arguments passed to the auto.arima modelling function.

Returns

A list with components: - model: A list of class "ARIMA" containing the best fitted ARIMA model. See the auto.arima

function in the `forecast` package. - **parameters**: A list containing the parameters of the best fitted ARIMA model. See the `arimaparameters` function. - **AICc**: Numeric value of the computed AICc criterion of the fitted model. - **AIC**: Numeric value of the computed AIC criterion of the fitted model. - **BIC**: Numeric value of the computed BIC criterion of the fitted model. - **logLik**: Numeric value of the computed log-likelihood of the fitted model. - **pred**: A list with the components `mean`, `lower` and `upper`, containing the predictions and the lower and upper limits for prediction intervals, respectively. All components are time series. See the `forecast`

function in the `forecast` package. - **MSE**: Numeric value of the resulting MSE error of prediction. - **NMSE**: Numeric value of the resulting NMSE error of prediction. - **MAPE**: Numeric value of the resulting MAPE error of prediction. - **sMAPE**: Numeric value of the resulting sMAPE error of prediction. - **MaxError**: Numeric value of the maximal error of prediction.

Details

The ARIMA model is automatically fitted by the auto.arima function and it is used for prediction by the forecast function both in the forecast

package.

The fitness criteria AICc, AIC (AIC), BIC (BIC) and log-likelihood (logLik) are extracted from the fitted ARIMA model. Also, the prediction accuracy of the model is computed by means of MSE (MSE), NMSE (NMSE), MAPE (MAPE), sMAPE (sMAPE) and maximal error (MAXError) measures.

Examples

data(CATS,CATS.cont)
fArima <- fittestArima(CATS[,1],CATS.cont[,1])
#predicted values
pred <- fArima$pred$mean
#model information
cbind(AICc=fArima$AICc, AIC=fArima$AIC, BIC=fArima$BIC,
 logLik=fArima$logLik, MSE=fArima$MSE, NMSE=fArima$NMSE, 
 MAPE=fArima$MSE, sMAPE=fArima$MSE, MaxError=fArima$MaxError)

#plotting the time series data
plot(c(CATS[,1],CATS.cont[,1]),type='o',lwd=2,xlim=c(960,1000),ylim=c(0,200),
 xlab="Time",ylab="ARIMA")
#plotting the predicted values
lines(ts(pred,start=981),lwd=2,col='blue')
#plotting prediction intervals
lines(ts(fArima$pred$upper[,2],start=981),lwd=2,col='light blue')
lines(ts(fArima$pred$lower[,2],start=981),lwd=2,col='light blue')

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

fittestArimaKF, fittestLM, marimapred

Author(s)

Rebecca Pontes Salles