SLBDD (version 0.0.4)

arimaID: Automatic Modeling of a Scalar Time Series

Description

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

Usage

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)).

Value

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

# NOT RUN {
data(TaiwanAirBox032017)
fit <- arimaID(TaiwanAirBox032017[,1])

# }