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Characterizing and forecasting climate indices using time series models

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Abstract

The objective of the current study is to present a comparison of techniques for the forecasting of low-frequency climate oscillation indices with a focus on the Great Lakes system. A number of time series models have been tested including the traditional autoregressive moving average (ARMA) model, dynamic linear model (DLM), generalized autoregressive conditional heteroskedasticity (GARCH) model, as well as the nonstationary oscillation resampling (NSOR) technique. These models were used to forecast the monthly El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) indices which show the most significant teleconnection with the net basin supply (NBS) of the Great Lakes system from a preliminary study. The overall objective is to predict future water levels, ice extent, and temperature, for planning and decision making purposes. The results showed that the DLM and GARCH models are superior for forecasting the monthly ENSO index, while the forecasted values from the traditional ARMA model presented a good agreement with the observed values within a short lead time ahead for the monthly PDO index.

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Data availability

The climate indices data used in the current study is already available to public. The website is mentioned in the manuscript.

Code availability

Code is available upon request to the corresponding author.

Abbreviations

t :

Time index

X t :

Time-dependent variable

X t :

Vector of multivariate time-dependent variables

Z t :

Time-independent white noise variable or its square is time dependent in the representation of GARCH model

p, q :

Mode order of ARMA model

\(\theta\),\(\varphi\) :

Parameters of ARMA model

n, n par :

Number of observations and parameters, respectively

h :

Prediction lead time

\({\widehat{X}}_{n}(h)\) :

h-Step ahead forecast, Xn+h

L(.):

Likelihood

B :

Backward shift operator

\(\mu\),\({\sigma }^{2}\) :

Mean and variance

C:

Covariance matrix

\(\psi\) :

Parameter set of a model

\(\alpha ,\beta\) :

Parameters of GARCH model

\({\Lambda }_{t}\) :

M-dimensional state vector

\({V}_{t},{W}_{t}\) :

Mutually independent error sequences with normal distribution

\({F}_{t},{G}_{t}\) :

Parameter and evolution matrices in DLM

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Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (2023R1A2C1003850).The first author acknowledges that this research was partially supported by a grant (2022-MOIS63-001) of Cooperative Research Method and Safety Management Technology in National Disaster funded by Ministry of Interior and Safety (MOIS, Korea).

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Authors and Affiliations

  1. Department of Civil Engineering, Gyeongsang National University, 501 Jinju-Daero52828, Jinju, Gyeongsangnam-Do, 660-701, South Korea

    Taesam Lee

  2. Canada Research Chair in Statistical Hydro-Climatology, INRS-ETE 490, de La Couronne Québec, Québec, G1K 9A9, Canada

    Taha B. M. J. Ouarda

  3. Department of Civil Engineering, University of Ottawa, 161 Louis Pasteur Office A113, Ottawa, ON, K1N 6N5, Canada

    Ousmane Seidou

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  1. Taesam Lee
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Contributions

TS carried out selecting methods and programmed the models used as well as drafted the manuscript. TO supervised the study and edited the manuscript.

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Correspondence to Taesam Lee.

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Lee, T., Ouarda, T.B.M.J. & Seidou, O. Characterizing and forecasting climate indices using time series models. Theor Appl Climatol 152, 455–471 (2023). https://doi.org/10.1007/s00704-023-04434-z

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