timsac (version 1.3.0)

mlomar: Minimum AIC Method of Locally Stationary Multivariate AR Model Fitting

Description

Locally fit multivariate autoregressive models to non-stationary time series by the minimum AIC procedure using the householder transformation.

Usage

mlomar(y, max.order=NULL, span, const=0)

Arguments

y

a multivariate 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 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.

Value

• mean
  mean.
• var
  variance.
• ns
  the number of local spans.
• order
  order of the current model.
• aic
  AIC of the current model.
• arcoef
  AR coefficient matrices of the current model. arcoef[[m]][i,j,k] shows the value of $i$-th row, $j$-th column, $k$-th order of $m$-th 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.
• npre
  data length of the preceding stationary block.
• nnew
  data length of the new block.
• order.mov
  order of the moving model.
• aic.mov
  AIC of the moving model.
• order.const
  order of the constant model.
• aic.const
  AIC of the constant model.

Details

The data of length $n$ are divided into $k$ locally stationary spans, $$|<-- n_1 -->|<-- n_2 -->|<-- n_3 -->| ..... |<-- n_k -->|$$ where $n_i$ $(i=1,\ldots,k)$ denoted 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(Amerikamaru)
  mlomar(Amerikamaru, max.order=10, span=300, const=0)