bfa.ls {bifurcatingr} R Documentation

## Least Squares Estimation of Bifurcating Autoregressive Models

### Description

This function performs Least Squares estimation of bifurcating autoregressive (BFA) models of any order as described in Zhou & Basawa (2005).

### Usage

```bfa.ls(
z,
p,
x.data = FALSE,
y.data = FALSE,
resids = FALSE,
error.cor = TRUE,
error.var = FALSE,
cov.matrix = FALSE,
conf = FALSE,
conf.level = 0.95,
p.value = FALSE
)
```

### Arguments

 `z` a numeric vector containing the tree data `p` an integer determining the order of bifurcating autoregressive model to be fit to the data `x.data` a logical that determines whether the x data used in fitting the model should be returned. Defaults to FALSE. `y.data` a logical that determines whether the y data used in fitting the model should be returned. Defaults to FALSE. `resids` a logical that determines whether the model residuals should be returned. Defaults to FALSE. `error.cor` a logical that determines whether the estimated correlation between pairs of model errors (e_{2t}, e_{2t+1}) should be returned. Defaults to TRUE. `error.var` a logical that determines whether the estimated variance of the model errors should be returned. Defaults to FALSE. `cov.matrix` a logical that determines whether the estimated variance-covariance matrix of the least squares estimates should be returned. Defaults to FALSE. `conf` a logical that determines whether confidence intervals for model coefficients should be returned. Defaults to FALSE. If TRUE, normal confidence intervals are calculated using `cov.matrix`. `conf.level` confidence level to be used in computing the normal confidence intervals for model coefficients when `conf=TRUE`. Defaults to `0.95`. `p.value` a logical that determines whether p-values for model coefficients should be returned. Defaults to FALSE. If TRUE, p-values are computed from normal distribution using estimated coefficients and `cov.matrix`.

### Value

 `coef` a matrix containing the least squares estimates of the autoregressive coefficients `error.cor` the least squares estimate of the correlation between pairs of model errors (e_{2t}, e_{2t+1}). Only returned if `error.cor=TRUE` `x` a matrix containing the x data used in fitting the model. Only returned if `x.data=TRUE` `y` a vector containing the y data used in fitting the model. Only returned if `y.data=TRUE` `resids` the model residuals. Only returned if `resids=TRUE` `error.var` the estimated variance of the model errors. Only returned if `error.var=TRUE` `cov.matrix` the estimated variance-covariance matrix of the least squares coefficients. Only returned if `cov.matrix=TRUE` `conf` a matrix of normal confidence intervals for model coefficients. Only returned if `conf=TRUE` `p.value` a matrix of two-sided p-values for testing the significance of model coefficients. Computed from normal distribution and using the estimated covariance matrix `cov.matrix`. Only returned if `p.value=TRUE`

### References

Zhou, J. & Basawa, I. V. (2005). Least squares estimation for bifurcating autoregressive processes. Statistics & Probability Letters, 74(1):77-88.

### Examples

```z <- bfa.tree.gen(127, 1, 1, 1, -0.9, -0.9, 0, 10, c(0.7))
bfa.ls(z, p=1)
bfa.ls(z,p=1,conf=TRUE,cov.matrix = TRUE,conf.level = 0.9,p.value=TRUE)
```

[Package bifurcatingr version 1.0.0 Index]