estimate {aTSA} R Documentation

## Estimate an ARIMA Model

### Description

Estimates an ARIMA model for a univariate time series, including a sparse ARIMA model.

### Usage

```estimate(x, p = 0, d = 0, q = 0, PDQ = c(0, 0, 0), S = NA,
method = c("CSS-ML", "ML", "CSS"), intercept = TRUE, output = TRUE, ...)
```

### Arguments

 `x` a univariate time series. `p` the AR order, can be a positive integer or a vector with several positive integers. The default is `0`. `d` the degree of differencing. The default is `0`. `q` the MA order, can be a positive integer or a vector with several positive integers. The default is `0`. `PDQ` a vector with three non-negative integers for specification of the seasonal part of the ARIMA model. The default is `c(0,0,0)`. `S` the period of seasonal ARIMA model. The default is `NA`. `method` fitting method. The default is `CSS-ML`. `intercept` a logical value indicating to include the intercept in ARIMA model. The default is `TRUE`. `output` a logical value indicating to print the results in R console. The default is `TRUE`. `...` optional arguments to `arima` function.

### Details

This function is similar to the ESTIMATE statement in ARIMA procedure of SAS, except that it does not fit a transfer function model for a univariate time series. The fitting method is inherited from `arima` in `stats` package. To be specific, the pure ARIMA(p,q) is defined as

X[t] = μ + φ*X[t-1] + ... + φ[p]*X[p] + e[t] - θ*e[t-1] - ... - θ[q]*e[t-q].

The `p` and `q` can be a vector for fitting a sparse ARIMA model. For example, `p = c(1,3),q = c(1,3)` means the ARMA((1,3),(1,3)) model defined as

X[t] = μ + φ*X[t-1] + φ*X[t-3] + e[t] - θ*e[t-1] - θ*e[t-3].

The `PDQ` controls the order of seasonal ARIMA model, i.e., ARIMA(p,d,q)x(P,D,Q)(S), where S is the seasonal period. Note that the difference operators `d` and D = `PDQ` are different. The `d` is equivalent to `diff(x,differences = d)` and D is `diff(x,lag = D,differences = S)`, where the default seasonal period is `S = frequency(x)`.

The residual diagnostics plots will be drawn.

### Value

A list with class "`estimate`" and the same results as `arima`. See `arima` for more details.

### Note

Missing values are removed before the estimate. Sparse seasonal ARIMA(p,d,q)x(P,D,Q)(S) model is not allowed.

Debin Qiu

### References

Brockwell, P. J. and Davis, R. A. (1996). Introduction to Time Series and Forecasting. Springer, New York. Sections 3.3 and 8.3.

### See Also

`arima`, `identify`, `forecast`

### Examples

```estimate(lh, p = 1) # AR(1) process
estimate(lh, p = 1, q = 1) # ARMA(1,1) process
estimate(lh, p = c(1,3)) # sparse AR((1,3)) process

# seasonal ARIMA(0,1,1)x(0,1,1)(12) model
estimate(USAccDeaths, p = 1, d = 1, PDQ = c(0,1,1))
```

[Package aTSA version 3.1.2 Index]