R: The AR-1 Autoregressive Process

dAR1 {VGAM} | R Documentation

## The AR-1 Autoregressive Process

### Description

Density for the AR-1 model.

### Usage

    dAR1(x, drift = 0, var.error = 1, ARcoef1 = 0.0,
         type.likelihood = c("exact", "conditional"), log = FALSE)

### Arguments

`x,` | vector of quantiles.
`drift` | the scaled mean (also known as the drift parameter), mu^*. Note that the mean is mu^* / (1-rho). The default corresponds to observations that have mean 0.
`log` | Logical. If `TRUE` then the logarithm of the density is returned.
`type.likelihood, var.error, ARcoef1` | See `AR1`. The argument `ARcoef1` is rho. The argument `var.error` is the variance of the i.i.d. random noise, i.e., sigma^2. If `type.likelihood = "conditional"` then the first element or row of the result is currently assigned `NA`—this is because the density of the first observation is effectively ignored.

### Details

Most of the background to this function is given in `AR1`. All the arguments are converted into matrices, and then all their dimensions are obtained. They are then coerced into the same size: the number of rows is the maximum of all the single rows, and ditto for the number of columns.

### Value

`dAR1` gives the density.

### Author(s)

T. W. Yee and Victor Miranda

### See Also

`AR1`.

### Examples

    nn <- 100; set.seed(1)
    tdata <- data.frame(index = 1:nn,
                        TS1 = arima.sim(nn, model = list(ar = -0.50),
                                        sd = exp(1)))
    fit1 <- vglm(TS1 ~ 1, AR1, data = tdata, trace = TRUE)
    rhobit(-0.5)
    coef(fit1, matrix = TRUE)
    (Cfit1 <- Coef(fit1))
    summary(fit1)  # SEs are useful to know
    logLik(fit1)
    sum(dAR1(depvar(fit1), drift = Cfit1[1], var.error = (Cfit1[2])^2,
             ARcoef1 = Cfit1[3], log = TRUE))

    fit2 <- vglm(TS1 ~ 1, AR1(type.likelihood = "cond"), data = tdata, trace = TRUE)
    (Cfit2 <- Coef(fit2))  # Okay for intercept-only models
    logLik(fit2)
    head(keep <- dAR1(depvar(fit2), drift = Cfit2[1], var.error = (Cfit2[2])^2,
                      ARcoef1 = Cfit2[3], type.likelihood = "cond", log = TRUE))
    sum(keep[-1])

[Package VGAM version 1.0-3 Index]