• autocorrelation;
  • autoregressive model;
  • stationary;
  • trend;
  • Yule-Walker equation;
  • autoregressive neural network;
  • modular neural network


The present paper has adopted an autoregressive approach to inspect the time series of monthly maximum temperature (Tmax) over northeast India. Through autocorrelation analysis the Tmax time series of northeast India is identified as non-stationary, with a seasonality of 12 months, and it is also found to show an increasing trend by using both parametric and non-parametric methods. The autoregressive models of the reduced Tmax time series, which has become stationary on removal of the seasonal and the trend components from the original time series, were generated through Yule–Walker equations. The sixth order autoregressive model (AR(6)) is identified as a suitable representative of the Tmax time series based on the Akaike information criteria, and the prediction potential of AR(6) is also established statistically through Willmott's indices. Subsequently, autoregressive neural network models were generated as a multilayer perceptron, a generalized feed forward neural network and a modular neural network. An autoregressive neural network model of order four (AR-NN(4)), in the form of a modular neural network (MNN), has performed comparably well with that of AR(6) based on the high values of Willmott's indices and the low values of the prediction error. Therefore, AR-NN(4)-MNN will be a better option than AR(6) to forecast a time series, i.e. the monthly Tmax time series of northeast India, because AR-NN(4)-MNN requires fewer predictors for a superior forecast of a time series. Copyright © 2010 Royal Meteorological Society