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Table 5 Regression statistics for ARIMA time series models of area of high-severity fire per year in yellow pine-mixed-conifer forests, fires ≥80 ha, 1984 to 2010.

From: Trends in Wildfire Severity: 1984 to 2010 in the Sierra Nevada, Modoc Plateau, and Southern Cascades, California, USA

  Last year in model
Model statistic 2010 2009 2008 2007 2006 2005 2004
Parameter estimates        
Model variance (sigma squared) 0.8409 0.8014 0.8165 0.8117 0.8221 0.8726 1.0163
Intercept 2.2390 2.1572 2.1088 2.1729 2.2357 2.2204 2.2177
Linear trend 0.0450 0.0531 0.0580 0.0508 0.0436 0.0455 0.0501
Autoregressive function (AR) 1 −0.2960 −0.3018 −0.2734 −0.3108 −0.2875 −0.2949 −0.3796
AR 2 0.1720 0.2303 0.2719 0.2857 0.3211 0.3159  
AR 3 −0.1589 −0.0998 −0.1117 −0.0676 −0.0636 −0.0628  
AR 4 −0.4137 −0.4334 −0.4715 −0.4652 −0.4556 −0.4443  
P (linear) 0.008 0.005 0.005 0.018 0.063 0.078 0.083
P (AR 1) 0.151 0.134 0.186 0.143 0.181 0.190 0.096
P (AR 2) 0.424 0.284 0.228 0.206 0.168 0.189  
P (AR 3) 0.465 0.644 0.609 0.762 0.778 0.787  
P (AR 4) 0.059 0.043 0.035 0.037 0.043 0.060  
Statistics of fit        
Number of observations 27 26 25 24 23 22 21
Number of missing actuals 0 0 0 0 0 0 0
Number of model parameters 6 6 6 6 6 6 3
Mean square error 0.673 0.639 0.649 0.635 0.634 0.661 0.873
Root mean square error 0.820 0.799 0.806 0.797 0.796 0.813 0.934
Mean absolute percent error 24.994 24.125 24.038 23.570 22.365 23.334 30.171
Mean absolute error 0.668 0.654 0.649 0.639 0.612 0.633 0.734
R2 0.338 0.391 0.400 0.402 0.383 0.384 0.221
adjusted R2 0.180 0.239 0.241 0.236 0.202 0.191 0.134
Akaike information criterion 1.305 0.343 1.211 1.114 1.507 2.886 3.137