arimaID function

Automatic Modeling of a Scalar Time Series

Automatic selection and estimation of a regular or possibly seasonal ARIMA model for a given time series.

arimaID(
  zt,
  maxorder = c(5, 1, 3),
  criterion = "bic",
  period = c(12),
  output = TRUE,
  method = "CSS-ML",
  pv = 0.01,
  spv = 0.01,
  transpv = 0.05,
  nblock = 0
)

Arguments

• zt: T by 1 vector of an observed scalar time series without any missing values.
• maxorder: Maximum order of $(p,d,q)$ where $p$ is the AR order, $d$ the degree of differencing, and $q$ the MA order. Default value is (5,1,4).
• criterion: Information criterion used for model selection. Either AIC or BIC. Default is "bic".
• period: Seasonal period. Default value is 12.
• output: If TRUE it returns the differencing order, the selected order and the minimum value of the criterion. Default is TRUE.
• method: Estimation method. See the arima command in R. Possible values are "CSS-ML", "ML", and "CSS". Default is "CSS-ML".
• pv: P-value for unit-root test. Default value is 0.01.
• spv: P-value for detecting seasonality. Default value is 0.01.
• transpv: P-value for checking non-linear transformation. Default value is 0.05.
• nblock: Number of blocks used in checking non-linear transformations. Default value is floor(sqrt(T)).

Returns

A list containing:

• data - The time series. If any non-linear transformation is taken, "data" is the transformed series.
• order - Regular ARIMA order.
• sorder - Seasonal ARIMA order.
• period - Seasonal period.
• include.mean - Switch concerning the inclusion of mean in the model.

Details

The program follows the following steps:

• Check for seasonality: fitting a multiplicative ARIMA(p,0,0)(1,0,0)_s model to a scalar time series and testing if the estimated seasonal AR coefficient is significant.
• Check for non-linear transformation: the series is divided into a given number of consecutive blocks and in each of them the Mean Absolute Deviation (MAD) and the median is computed. A regression of the log of the MAD with respect to the log of the median is run and the slope defines the non-linear transformation.
• Select orders: maximum order of $(p,d,q)$.

Examples

data(TaiwanAirBox032017)
fit <- arimaID(TaiwanAirBox032017[,1])