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Time series analysis and forecasting with applications to climate science

Al Marhoobi, Safia Amur Ali 2022. Time series analysis and forecasting with applications to climate science. PhD Thesis, Cardiff University.
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Abstract

Singular spectrum analysis (SSA) is the popular tool for analysing and forecasting time series. SSA can be used for parametric estimation, forecasting and gap filling amongst many other tasks. SSA was used for the extraction of seasonality, simultaneous extraction of cycles with small and large periods and finding structure in short time series. This thesis aims to study the application of singular spectrum analysis which is supported by empirical evidence to further promote the value, effectiveness and applicability of strengthening SSA’s quality in the field of time series analysis and forecasting. We investigate the hourly, daily and monthly temperature and humidity time series collected at meteorological stations in Oman from 2009 to 2018. This data is provided by the Directorate General of Meteorology of Oman. Our investigation cover missing value imputation, splitting the hourly time series in the sum of several components corresponding to different frequencies and detection of trends. We investigated three methods of imputation: SSA-based iterative approach, regression methods and regression with lagging. We found that imputation by regression with lagging is a more reliable and reasonable method and provides natural results for filling gaps for any length of time series. We applied SSA to hourly time series for extracting the annual oscillations and the daily periodicities. SSA was able to extract these components very effectively. Moreover, we may use SSA for obtaining more refined decompositions with larger number of components and also for forecasting. We applied three commonly used tests for detecting trends in time series: the Mann-Kendall test, Spearman’s rho test and the Sen’s innovative trend method test. We found that there are no monotonic trends in the annual oscillations and the daily periodicities over the period of ten years. Also we did not find trends in the monthly variability of daily periodicities. We provide a statistical framework on studying which SSA forecasting algorithm is best on the example of real data representing monthly temperature and humidity in Oman. We demonstrated that the sensitivity of the root mean squared errors (RMSE) for retrospective forecasts is rather small to parameters the window length L and the number of singular values r. We shown that the efficiency of SSA forecasts with the automatic choice of parameters is rather high. We also found that SSA-R and SSA-V forecasts are more similar to each other with a slight dominance of SSA-V forecasts. Last part of thesis focuses on the performance of the application of SSA to daily time series of humidity and temperature in Oman. We apply SSA forecasting algorithms: recurrent SSA (SSA-R) forecasting, recurrent SSA original (SSA-R (original)) forecasting and vector SSA (SSA-V) forecasting algorithms based on SSA with double projection and SSA without projection. We have also studied the effect of series length and choice of parameters on the performance of the aforementioned algorithms. The findings show that SSA with double projection improve the accuracy of short term forecast using smaller set of observations.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Mathematics
Date of First Compliant Deposit: 25 May 2022
Last Modified: 25 May 2022 14:31
URI: https://orca.cardiff.ac.uk/id/eprint/150013

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