# aar: Additive nonlinear autoregressive model In tsDyn: Nonlinear Time Series Models with Regime Switching

## Usage

 `1` ```aar(x, m, d=1, steps=d, series) ```

## Arguments

 `x` time series `m, d, steps` embedding dimension, time delay, forecasting steps `series` time series name (optional)

## Details

Nonparametric additive autoregressive model of the form:

x[t+steps] = mu + sum_j s_j(x[t-(j-1)d])

where s_j are nonparametric univariate functions of lagged time series values. They are represented by cubic regression splines. s_j are estimated together with their level of smoothing using routines in the mgcv package (see references).

## Value

An object of class `nlar`, subclass `aar`, i.e. a list with mostly internal structures for the fitted `gam` object.

## Author(s)

Antonio, Fabio Di Narzo

## References

Wood, mgcv:GAMs and Generalized Ridge Regression for R. R News 1(2):20-25 (2001)

Wood and Augustin, GAMs with integrated model selection using penalized regression splines and applications to environmental modelling. Ecological Modelling 157:157-177 (2002)

## Examples

 ```1 2 3 4 5 6``` ```#fit an AAR model: mod <- aar(log(lynx), m=3) #Summary informations: summary(mod) #Diagnostic plots: plot(mod) ```

### Example output

```Non linear autoregressive model

AAR model

Family: gaussian

Formula:
y ~ s(V1.0, bs = "cr") + s(V1..1, bs = "cr") + s(V1..2, bs = "cr")

Estimated degrees of freedom:
2.85 3.39 2.55  total = 9.79

GCV score: 0.2408534

Residuals:
Min         1Q     Median         3Q        Max
-1.2439386 -0.2666732  0.0047851  0.2853675  1.0369893

Fit:
residuals variance = 0.195,  AIC = -130, MAPE = 5.666%

Family: gaussian

Formula:
y ~ s(V1.0, bs = "cr") + s(V1..1, bs = "cr") + s(V1..2, bs = "cr")

Parametric coefficients:
Estimate Std. Error t value  Pr(>|t|)
(Intercept)  6.70683    0.04448  150.78 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Approximate significance of smooth terms:
edf Ref.df       F p-value
s(V1.0)  2.8491 3.5678 54.3269 < 2e-16 ***
s(V1..1) 3.3873 4.2096  7.9558 7.5e-06 ***
s(V1..2) 2.5519 3.2274  1.7656  0.1489
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R-sq.(adj) =  0.869   Deviance explained =   88%
GCV = 0.24085  Scale est. = 0.21961   n = 111
```

tsDyn documentation built on Jan. 23, 2018, 1:01 a.m.