Advances and Applications in Statistics
Volume 63, Issue 1, Pages 85 - 96
(July 2020) http://dx.doi.org/10.17654/AS063010085 |
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PERIODIC AUTOREGRESSIVE MODEL FOR TEMPERATURE DATA IN NUWARA ELIYA, SRI LANKA
H. N. A. M. Wijayawardhana and A. P. Hewaarachchi
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Abstract: Many climatological time series display interesting properties such as trend, seasonality and autocorrelation. Furthermore, some time series display periodic autocorrelation also. Time series, which depicts periodic correlation, are called periodic time series and they can be modeled using autoregressive moving average models with periodically varying parameters. The key objective of this study was to model monthly temperature data using a periodic autoregressive model and to predict under the periodic correlation. In this research, monthly mean minimum temperature series and monthly mean maximum temperature series in Nuwara Eliya district were considered. Fisher’s g test was used to detect periodic correlation. Fisher’s g test showed that only monthly mean minimum temperature series has a significant periodic correlation structure. The seasonally adjusted mean minimum temperature series was modeled using periodic autoregressive (PAR) model. Using the Akaike information criterion, PAR model of order 1 with zero mean was chosen as the best fitted model for the seasonally adjusted data. The parameters of the model were estimated using periodic Yule-Walker estimation. Further to check whether the periodic model was the best time series model for modeling and forecasting monthly mean minimum temperature data in Nuwara Eliya, different seasonal autoregressive integrated moving average models (SARIMA) were fitted. All models were compared using the forecast accuracy measurements such as mean error (ME), root mean squared error (RMSE) and mean absolute percentage error (MAPE). The best model was identified as the PAR (1) model, which showed a ME value of –0.0861, RMSE value of 0.613 and MAPE value of 4.664%. According to the comparison, the periodic autoregressive model of order 1 has the best forecasting accuracy among all fitted time series models. |
Keywords and phrases: periodic correlation, temperature, PAR models, forecasting.
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