Table 4 Regression statistics for ARIMA time series modeling of percent of high-severity fire per year for yellow pine-mixed conifer forests, fires ≥400 ha 1984 to 2010.

Parameter estimates

Model variance (sigma squared)

0.0079

0.0078

0.0081

0.0084

0.0090

0.0088

0.0096

Intercept

0.3064

0.2986

0.3020

0.3055

0.3085

0.3009

0.3015

Linear trend

0.0028

0.0034

0.0031

0.0028

0.0026

0.0033

0.0032

Autoregressive function (AR) 1

−0.8560

−0.7972

−0.8108

−0.8302

−0.8031

−0.8228

−0.8169

AR 2

−0.6782

−0.5829

−0.6183

−0.6108

−0.5812

−0.5924

−0.5816

AR 3

−0.5713

−0.4404

−0.4414

−0.4403

−0.4232

−0.4638

−0.4583

AR 4

−0.5686

−0.5388

−0.5272

−0.5345

−0.5170

−0.5196

−0.5161

P (linear)

0.011

0.008

0.019

0.046

0.110

0.056

0.096

P (AR 1)

<0.001

0.001

0.002

0.002

0.004

0.004

0.005

P (AR 2)

0.023

0.053

0.051

0.057

0.086

0.079

0.099

P (AR 3)

0.039

0.127

0.135

0.140

0.174

0.139

0.160

P (AR 4)

0.008

0.012

0.016

0.016

0.026

0.026

0.035

Statistics of fit

Number of observations

27

26

25

24

23

22

21

Number of missing actuals

3

3

3

3

3

3

3

Number of model parameters

6

6

6

6

6

6

6

Mean square error

0.008

0.007

0.008

0.008

0.008

0.008

0.009

Root mean square error

0.088

0.086

0.088

0.089

0.091

0.090

0.092

Mean absolute percent error

25.924

24.491

25.293

26.260

27.334

26.154

27.500

Mean absolute error

0.074

0.071

0.073

0.075

0.078

0.074

0.078

R²

0.379

0.386

0.376

0.386

0.303

0.331

0.330

adjusted R²

0.207

0.205

0.182

0.182

0.054

0.074

0.050

Akaike information criterion

−104.805

−100.641

−94.900

−89.444

−83.796

−79.534

−73.745