timsac (version 1.3.0)

mlocar: Minimum AIC Method of Locally Stationary AR Model Fitting; Scalar Case

Description

Locally fit autoregressive models to non-stationary time series by minimum AIC procedure.

Usage

mlocar(y, max.order=NULL, span, const=0, plot=TRUE)

Arguments

y

a univariate time series.

max.order

upper limit of the order of AR model. Default is $2 \sqrt{n}$, where $n$ is the length of the time series y.

span

length of the basic local span.

const

integer. 0 denotes constant vector is not included as a regressor and 1 denotes constant vector is included as the first regressor.

plot

logical. If TRUE (default) spectrums pspec are plotted.

Value

• mean
  mean.
• var
  variance.
• ns
  the number of local spans.
• order
  order of the current model.
• arcoef
  AR coefficients of current model.
• v
  innovation variance of the current model.
• init
  initial point of the data fitted to the current model.
• end
  end point of the data fitted to the current model.
• pspec
  power spectrum.
• npre
  data length of the preceding stationary block.
• nnew
  data length of the new block.
• order.mov
  order of the moving model.
• v.mov
  innovation variance of the moving model.
• aic.mov
  AIC of the moving model.
• order.const
  order of the constant model.
• v.const
  innovation variance of the constant model.
• aic.const
  AIC of the constant model.

Details

The data of length $n$ are devided into $k$ locally stationary spans, $$|<-- n_1 -->|<-- n_2 -->|<-- n_3 -->| ..... |<-- n_k -->|$$ where $n_i$ ($i=1,\ldots,k$) denotes the number of basic spans, each of length span, which constitute the $i$-th locally stationary span. At each local span, the process is represented by a stationary autoregressive model.

References

G.Kitagawa and H.Akaike (1978) A Procedure for The Modeling of Non-Stationary Time Series. Ann. Inst. Statist. Math., 30, B, 351--363. H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

Examples

data(locarData)
  z <- mlocar(locarData, max.order=10, span=300, const=0)
  z$arcoef