`rwf()`

returns forecasts and prediction intervals for a random walk
with drift model applied to `y`

. This is equivalent to an ARIMA(0,1,0)
model with an optional drift coefficient. `naive()`

is simply a wrapper
to `rwf()`

for simplicity. `snaive()`

returns forecasts and
prediction intervals from an ARIMA(0,0,0)(0,1,0)m model where m is the
seasonal period.

## Usage

```
rwf(
y,
h = 10,
drift = FALSE,
level = c(80, 95),
fan = FALSE,
lambda = NULL,
biasadj = FALSE,
...,
x = y
)
naive(
y,
h = 10,
level = c(80, 95),
fan = FALSE,
lambda = NULL,
biasadj = FALSE,
...,
x = y
)
snaive(
y,
h = 2 * frequency(x),
level = c(80, 95),
fan = FALSE,
lambda = NULL,
biasadj = FALSE,
...,
x = y
)
```

## Arguments

- y
a numeric vector or time series of class

`ts`

- h
Number of periods for forecasting

- drift
Logical flag. If TRUE, fits a random walk with drift model.

- level
Confidence levels for prediction intervals.

- fan
If TRUE, level is set to seq(51,99,by=3). This is suitable for fan plots.

- lambda
Box-Cox transformation parameter. If

`lambda="auto"`

, then a transformation is automatically selected using`BoxCox.lambda`

. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.- biasadj
Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.

- ...
Additional arguments affecting the forecasts produced. If

`model=NULL`

,`forecast.ts`

passes these to`ets`

or`stlf`

depending on the frequency of the time series. If`model`

is not`NULL`

, the arguments are passed to the relevant modelling function.- x
Deprecated. Included for backwards compatibility.

## Value

An object of class "`forecast`

".

The function `summary`

is used to obtain and print a summary of the
results, while the function `plot`

produces a plot of the forecasts and
prediction intervals.

The generic accessor functions `fitted.values`

and `residuals`

extract useful features of the value returned by `naive`

or
`snaive`

.

An object of class `"forecast"`

is a list containing at least the
following elements:

- model
A list containing information about the fitted model

- method
The name of the forecasting method as a character string

- mean
Point forecasts as a time series

- lower
Lower limits for prediction intervals

- upper
Upper limits for prediction intervals

- level
The confidence values associated with the prediction intervals

- x
The original time series (either

`object`

itself or the time series used to create the model stored as`object`

).- residuals
Residuals from the fitted model. That is x minus fitted values.

- fitted
Fitted values (one-step forecasts)

## Details

The random walk with drift model is

$$Y_t=c + Y_{t-1} + Z_t$$

where \(Z_t\) is a normal iid error. Forecasts are given by

$$Y_n(h)=ch+Y_n$$

If there is no drift (as in
`naive`

), the drift parameter c=0. Forecast standard errors allow for
uncertainty in estimating the drift parameter (unlike the corresponding
forecasts obtained by fitting an ARIMA model directly).

The seasonal naive model is

$$Y_t= Y_{t-m} + Z_t$$

where \(Z_t\) is a normal iid error.