Prospects for Improving the Operational Seasonal Prediction of Tropical Cyclone Activity in the Southern Hemisphere - Monitoring and Prediction of Tropical Cyclones in the Indian Ocean and Climate Change - page 125

3.2 Multiple Regression Models

We modified the simple linear regression model developed earlier (Kuleshov
et al., 2009) by adding a temporal trend variable ( T ) as one of the predictors.
The candidate models are:
Model 1

AR = E 0 + E 1 T + E 2 5VAR + °

Model 2

AR = E 0 + E 1 T + E 2 NINO 3.4 + °

Model 3

AR = E 0 + E 1 T + E 2 SOI + °
where ° denotes the noise variable, assumed to be normally distributed with
mean 0 and variance V 2 , i.e., ° ~ N (0,V 2 ).
All the model fittings were carried out using R software (http://www.r-
project.org/). The estimated regression model results are presented in Table 2.

Table 2: Multiple linear regressions with both time trend and the September 5VAR
(model 1), the August-September NIÑO3.4 (model 2) and the July-August-
September SOI (model 3) respectively

Model 1 Model 2 Model 3

Coefficients p-value Coefficients p-value Coefficients p-value

T -0.054 0.13 -0.056 0.13 -0.067 0.058

5VAR -2.240 4e-06 - - - -

NINO3.4 - - -2.561 2e-05 - -

SOI - - - - +0.233 5e-06

Residual s.e 2.592 2.711 2.605

Adj R 2

0.452 0.401 0.446

All three models have significant coefficients for the three indicial
predictors. The assumptions of randomly and normally distributed residuals
are also satisfied. Although the temporal predictor is not statically significant
for the first two models (although not far from being statistically significant),
the adjusted values R 2 for all three models have increased by comparing with
our earlier model without the temporal trend. The adjusted values R 2 for the
model with the 5VAR as a predictor has increased from 0.432 to 0.452, while
R 2 increased from 0.3791 to 0.4005 for the NIÑO3.4 models. As for the model
with SOI as a predictor, the temporal predictor is marginally significant at the
10% significance level, the percentage of explained variation has increased
from 0.4063 to 0.4462. As in our earlier study, the regression model with 5VAR
as the predictor surpasses the other two models with SOI or NIÑO3.4 as the
predictors.