The rainfall series from the South African Astronomical Observatory in Cape Town, South Africa, is one of the longest known single site instrumental records in the southern hemisphere, spanning over 176 years. Rainfall data are analysed to determine trends and periodicity in the series for annual, seasonal and monthly time scales. Using the Mann Kendall test and Sen's slope, significant negative rainfall trends are recorded for the months of March and October, and for the spring season (from September to November). Using the Mann Kendall and its modified versions to account for serial correlation, as well as a multi‐temporal trend analysis, we demonstrate a positive rainfall trend during the first 60 years (i.e., 1841–1900), which thereafter changes to a long‐term (1900–2016) negative trend, but incorporating a shorter 40 years significant positive trend between 1930 and 1970. We identify cyclic patterns with recorded periods of 9–12 years, 16–30 years and 30–42 years for rainfall, the Southern annular mode (SAM) and Southern oscillation index (SOI). In addition to the notable 9–12 years rainfall cycle that is evidently associated with sunspot cycles, 20–30 years and longer 32–40 years rainfall, solar, SAM and SOI cycles are also identified.

This paper applies time series modeling methods to paleoclimate series for temperature, ice volume, and atmospheric concentrations of CO2 and CH4. These series, inferred from Antarctic ice and ocean cores, are well known to move together in the transitions between glacial and interglacial periods, but the dynamic relationship between the series is open to question. A further unresolved issue is the role of Milankovitch theory, in which the glacial/interglacial cycles are correlated with orbital variations. We perform tests for Granger causality in the context of a vector autoregression model. Previous work with climate series has assumed nonstationarity and adopted a cointegration approach, but in a range of tests, we find no evidence of integrated behavior. We use conventional autoregressive methodology while allowing for conditional heteroscedasticity in the residuals, associated with the transitional periods. Copyright © 2015 John Wiley & Sons, Ltd.

This study investigates an alternative modelling approach for empirical seasonal temperature forecasts over South America. Seasonal average temperatures are found to be non-stationary at most parts of South America over the 1949-2012 period. Simple persistence and lagged regression methods have considerable correlation skill in forecasting next season temperature using previous season temperature as predictor. However, the presence of trends in both predictor and predictand temperature variables can affect correlation skill. Models that can account for non-stationarity in these variables may do better in modelling and forecasting seasonal temperatures known to have trends. A novel method (cointegration), introduced here for empirical seasonal climate forecasting, is found to perform better than the traditional persistence and regression forecasts for places where the predictor and predictand temperatures have stochastic trends. Potential skill pairwise comparisons between temperature forecasts produced with cointegration and those produced using persistence and lagged regression have shown that the alternative cointegration method performs significantly better than the other two. One of the main reasons for the better performance of cointegration method is that the modelling procedure accounts for the existing non-stationarity in the process, and thus enables the estimated model to predict out of the range as efficiently as possible. Overall, this method appears to be ideal for modelling and predicting climate under the current global warming scenario. This is because most of the climatic variables including temperature in particular cannot be assumed to be stationary through time under such warming scenario.

Scaling factors in detection and attribution studies are typically estimated by performing a least squares regression of the observed trending variable, e.g. annual Global Mean Surface Temperature (GMST), on the equivalent variable simulated by a climate model. This study proposes instead to obtain the scaling factors by dynamically modelling the time series as a cointegrating Vector Auto-Regressive (VAR) time series process. It is shown that a 2nd order cointegrating VAR(2) model is theoretically justified if the observed and simulated variables can be represented as a one-box AR(1) response to a common integrated forcing. The VAR(2) model can be expressed as a Vector Error-Correction Model (VECM) and then fitted to the data to obtain the cointegration relationship, the stationary linear combination of the two variables, from which the scaling factor is then easily obtained. Estimates of the scaling factor from the VAR(2) model are critically compared to those from Ordinary Least Squares (OLS) and Total Least Squares (TLS) for GMST data simulated by a simple stochastic model of the carbon-climate system and for historical simulations from 16 climate models in the Coupled Model Intercomparison Project 5 (CMIP5) experiment. Results from the toy model simulations show that the slope estimates from OLS are negatively biased, TLS estimates are less biased but have high variance, and the VAR(2) estimates are unbiased and have lower variance and provide the most accurate estimates with smallest mean squared error. Similar behaviour is noted in the CMIP5 data. Hypothesis tests on the VAR(2) fits found strong evidence of a cointegrating relationship with the observations for all the CMIP5 simulations.

Adapting to human-induced climate change is becoming an increasingly important aspect of sustainable development. To be able to do this effectively, it is important to know how much human influence has contributed to observed climate trends. Climate detection and attribution (D&A) studies achieve this by estimating scaling factors usually obtained by performing a least squares regression of the observed trending climate variable on the equivalent variable simulated by a climate model. This study proposed instead to estimate scaling factors by using the econometric approach of dynamically modelling the time series as a cointegrating Vector Auto-Regressive (VAR) time series process. It is shown that a 2nd-order cointegrating VAR(2) model is theoretically justified if the observed and simulated variables can be represented as a one-box AR(1) response to a common integrated forcing. The VAR(2) model can be expressed as a Vector Error-Correction Model (VECM) and then fitted to the data to obtain the cointegration relationship, the stationary linear combination of the two variables, from which the scaling factor is then easily obtained. Estimates of the scaling factor from the VAR(2) model are critically compared to those from Ordinary Least Squares (OLS) and Total Least Squares (TLS) for annual Global Mean Surface Temperature (GMST) data simulated by a simple stochastic model of the carbon–climate system and for historical simulations from 16 climate models in the Coupled Model Intercomparison Project 5 (CMIP5) experiment. Results from the toy model simulations show that the slope estimates from OLS are negatively biased, TLS estimates are less biased but have high variance, and the VAR(2) estimates are unbiased and have lower variance and provide the most accurate estimates with smallest mean squared error. Similar behaviour is noted in the CMIP5 data. Hypothesis tests on the VAR(2) fits found strong evidence of a cointegrating relationship with the observations for all the CMIP5 simulations.