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Table 3 Regression statistics for ARIMA time series modeling of percent of high-severity fire per year for yellow pine-mixed conifer forests, for 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) 0.0079 0.0080 0.0082 0.0083 0.0087 0.0086 0.0092
Intercept 0.3018 0.2996 0.3014 0.3038 0.3060 0.3024 0.3030
Linear trend 0.0027 0.0030 0.0028 0.0025 0.0023 0.0027 0.0026
Autoregressive function (AR) 1 −0.9501 −0.9185 −0.9380 −0.9674 −0.9373 −0.9526 −0.9509
AR 2 −0.7800 −0.7314 −0.7777 −0.7702 −0.7352 −0.7505 −0.7429
AR 3 −0.6472 −0.5725 −0.5748 −0.5695 −0.5489 −0.5933 −0.5933
AR 4 −0.5099 −0.4937 −0.4812 −0.4897 −0.4648 −0.4707 −0.4718
P (linear) <0.001 <0.001 0.002 0.008 0.031 0.017 0.036
P (AR 1) <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001
P (AR 2) 0.006 0.011 <0.001 0.011 0.019 0.017 0.022
P (AR 3) 0.014 0.038 0.041 0.045 0.060 0.044 0.052
P (AR 4) 0.016 0.021 0.026 0.025 0.041 0.038 0.046
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 6
Mean square error 0.007 0.007 0.007 0.007 0.007 0.007 0.007
Root mean square error 0.081 0.081 0.082 0.082 0.083 0.082 0.084
Mean absolute percent error 20.124 19.560 19.703 19.825 20.263 18.924 19.640
Mean absolute error 0.066 0.065 0.066 0.067 0.068 0.064 0.066
R2 0.561 0.561 0.566 0.582 0.540 0.560 0.561
adjusted R2 0.456 0.452 0.452 0.465 0.405 0.423 0.415
Akaike information criterion −123.514 −118.436 −113.120 −108.025 −102.520 −97.849 −91.927