# Resid: Compute residuals In itsmr: Time Series Analysis Using the Innovations Algorithm

## Description

Compute residuals

## Usage

 `1` ```Resid(x, M = NULL, a = NULL) ```

## Arguments

 `x` Time series data `M` Data model `a` ARMA model

## Details

The data model can be `NULL` for none. Otherwise `M` is a vector of function names and arguments.

Example:

`M = c("log","season",12,"trend",1)`

The above model takes the log of the data, then subtracts a seasonal component of period 12, then subtracts a linear trend component.

These are the available functions:

 `diff` Difference the data. Has a single argument, the lag. `hr` Subtract harmonic components. Has one or more arguments, each specifying the number of observations per harmonic. `log` Take the log of the data, has no arguments. `season` Subtract a seasonal component. Has a single argument, the number of observations per season. `trend` Subtract a trend component. Has a single argument, the order of the trend (1 linear, 2 quadratic, etc.)

At the end of the model there is an implicit subtraction of the mean operation. Hence the resulting time series always has zero mean.

## Value

Returns a vector of residuals the same length as `x`.

`test`
 ```1 2 3 4 5``` ```M = c("log","season",12,"trend",1) e = Resid(wine,M) a = arma(e,1,1) ee = Resid(wine,M,a) ```