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- data used. 
of STARFM 
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acted for the 
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s (Armston, et 
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n a per pixel 
r the common 
of analysis is 
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regressed are 
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lated residual 
he assumption 
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ponents were 
nomalies were 
distributed lag 
anomalies as 
r estimation: 
  
  
  
NDI =a+bRE+J,RE +... +b RF_„+& 
where t is the time, a is the, b; are the regression coefficients at 
lag i. 
In a second step an autoregressive moving average (ARMA) 
model is fitted to the error term & to assess the temporal 
autocorrelation structure of the series. The next step is to filter 
the original time-series (NDVI and rainfall anomalies) using the 
identified ARMA-model. The last step is to repeat the OLS- 
regression of the anomalies. This results in a distributed lag 
model in which the residuals are "white noise" and to an 
unbiased assessment of the significance of the regression 
coefficients (Udelhoven et al., 2009). 
A Durbin-Watson test was applied to detect the presence of a 
remaining autocorrelation in the time series. 
3. RESULTS 
A time series plot of rainfall and NDVI in a forested area (open 
woodland) displays the seasonality within the NDVI data. 
  
  
  
  
  
Figure 3: Time series of rainfall (blue line) and NDVI (black 
line) for a location in an open woodland. 
3.1 Simple lagged correlation 
A smoothing filer with a window length of 5 was applied to 
both time series. The maximum correlation at the respective lag 
Was reported on a per pixel basis (Figure 4). 
  
Correlation Lag “(orange=0, yellow=1, 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
  
red=2, white =4, black=neg.) 
Figure 4: Lagged correlation between rainfall and NDVI. 
The response times lag times appear to have very little spatial 
pattern with generally quick vegetation response with a lag of 0. 
In the forested areas appear a lag of 1 and a lag of 2 along the 
riparian areas. 
3.2 Distributed lag model 
Raster layers of the 5% significance level demonstrate the 
difference in the response times in the different land types. In 
this 14 day aggregation it appears that no significant response 
of the NDVI exists after a lag period of 4 (56 days). In the 
grasslands or open woodlands with low tree cover appears a 
significant response at lag times of 0 to 3. The distinct pattern 
visible in Figure 3 between forest and grasslands are less 
pronounced, but visible in Figure 5 (TO to T3). 
  
  
  
  
  
  
   
   
  
  
    
eo : Á 
    
i not sig. 
eese 
E sig. (5%, neg. irends) 
  
Figure 5: NDVI vs Rainfall anomalies significance (t-test) at the 
5% significance level of the regression coefficients at times TO 
to T5. 
3.3 Test for autocorrelation 
A simple test for temporal autocorrelation in the residual is the 
Durbin-Watson (DW) statistics. The outcome of this test is 
shown in Figure 6. A series without serial no autocorrelation 
results in a DW-value of 2.0. Smaller values (0 in the 
minimum) indicate positive autocorrelation whereas higher 
values (4.0 in the maximum) indicate negative autocorrelation. 
Figure 6 demonstrates that the residuals of the distributed lag 
model are indeed white noise using GLS-parameter estimation, 
except for singular, scattered pixels.