# acov2ma: Convert Autocovariances to Coefficients of a Moving Average In tsdecomp: Decomposition of Time Series Data

## Description

Convert autocovariances to coefficients of a moving average.

## Usage

 ```1 2``` ```acov2ma.init(x, tol = 0.00001, maxiter = 100) acov2ma(x, tol = 1e-16, maxiter = 100, init = NULL) ```

## Arguments

 `x` a numeric vector containing the autocovariances. `tol` numeric, convergence tolerance. `maxiter` numeric, maximum number of iterations. `init` numeric, vector of initial coefficients.

## Details

`acov2ma.init` is based on procedure (17.35) described in Pollock (1999). `acov2ma` is the Newton-Raphson procedure (17.39) described in the same reference.

## Value

A list containing the vector of coefficients and the variance of the innovations in the moving average model; convergence code and number of iterations.

## References

Pollock, D. S. G. (1999) A Handbook of Time-Series Analysis Signal Processing and Dynamics. Academic Press. Chapter 17. doi: 10.1016/B978-012560990-6/50002-6

## Examples

 ```1 2 3 4 5 6 7 8``` ```set.seed(123) x <- arima.sim(n=200, model=list(ma=c(0.7,-0.3))) #sample autocovariances a <- c(var(x), cov(x[-1], x[-200]), cov(x[-c(1,2)], x[-c(199,200)])) #inferred coefficients and variance acov2ma(a, init=acov2ma.init(a, maxit=10)\$macoefs) #compare with maximum-likelihood arima(x, order=c(2,0,0), include.mean=FALSE) ```

tsdecomp documentation built on May 1, 2019, 9:15 p.m.