 # 4.6 Model Building For Monthly Temperature Series Case Study

4.6 Model building for monthly temperature series
According to Takele (2012), the process of model fitting involves data plotting, data transformation if necessary, identification of dependence order, estimation of parameter, diagnostic analysis and choosing appropriate model. In this section, a univariate SARIMA methodology is used to model maximum and minimum monthly temperatures of Nairobi.

4.7 Model Identification
ACF and PACF plots are used in the identification of the values p, q, P and Q. For the non-seasonal part, spikes of the ACF at low lags are used to identify the value of q while the value of p is identified by observing the spikes at low lags of the PACF. For the seasonal part the value of Q is observed from the ACF at lags that are multiples of S
Its AIC was -930.17. The Box – Ljung test yielded a chi square of 1.6412 with a p value equal to 0.9496. From Box – Ljung test, the p value of 0.9496 > 0.05 and this confirms that SARIMA (0, 0, 2) (0, 1, 1) is adequate for forecasting.
Minimum temperature time series-SARIMA (1, 0, 0) (0, 1, 1)12
Parameter Estimate Standard error ar1 0.4153 0.0534 sma1 -1.0000 0.0309
Table 11: Parameter estimates for SARIMA (1, 0, 0) (0, 1, 1)12
SARIMA (1, 0, 0) × (0, 1, 1)12 has an estimated variance of 0.004611 with a log likelihood of 346.57. Its AIC was -687.14. The Box – Ljung test yielded a chi square of 3.3259 with a p value of 0.767. From the Box – Ljung test, the p value of 0.767 > 0.05 and this confirms that SARIMA (1, 0, 0) (0, 1, 1) is adequate for forecasting.

4.1.0 Diagnostic Analysis
For a well fitted model, the standardized residuals estimated from the model should behave as an independent and identically distributed sequence with zero mean and constant variance.

4.1.1 Diagnostic analysis for Maximum temperature