# ar1: Estimation of an AR(1) model In Rfast: A Collection of Efficient and Extremely Fast R Functions

## Description

Estimation of an AR(1) model.

## Usage

 ```1 2``` ```ar1(y, method = "cmle") colar1(y, method = "cmle") ```

## Arguments

 `y` For the case of ar1 this is a vector of time series. For the case of colar1 this is a matrix where weach column represents a time series. `method` This can be either "cmle" for conditional maximum likelihood or "yw" for the Yule-Walker equations.

## Details

Instead of the classical MLE for the AR(1) model which requires numerical optimsation (Newton-Raphson for example) we estimate the parameters of the AR(1) model using conditional maximum likelihood. This procedure is described in Chapter 17 in Lee (2006). In some, it assumes that the first observation is deterministic and hence conditioning on that observation, there is a closed form solution for the parameters. The second alternative is to use the method of moments and hence the Yule-Walker equations.

## Value

 `param` For the case of ar1 this is a vector with three elements, the constant term, the φ term (lag coefficient) and the variance. For the case of colar1 this is a matrix with three columns, eahc of which carries the same aforementioned elements.

Michail Tsagris

## References

http://econ.nsysu.edu.tw/ezfiles/124/1124/img/Chapter17_MaximumLikelihoodEstimation.pdf

``` rm.lines, varcomps.mle, rm.anovas ```

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```y <- as.vector(lh) ar1(y) ar(y, FALSE, 1, "ols") ar1(y, method = "yw") ar(y, FALSE, 1, "yw") a1 <- colar1(cbind(y, y) ) b1 <- colar1(cbind(y, y), method = "yw") ```

### Example output

```Loading required package: Rcpp
constant       phi     sigma
0.7859809 0.6710498 0.2039206

Call:
ar(x = y, aic = FALSE, order.max = 1, method = "ols")

Coefficients:
1
0.586

Intercept: 0.006234 (0.06551)

Order selected 1  sigma^2 estimated as  0.2016
mean       phi     sigma
2.4000000 0.5755245 0.2079007

Call:
ar(x = y, aic = FALSE, order.max = 1, method = "yw")

Coefficients:
1
0.5755

Order selected 1  sigma^2 estimated as  0.2079
```

Rfast documentation built on May 18, 2021, 1:07 a.m.