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This paper searches for stochastic trends and returns predictability in key energy asset markets in Europe over the last decade. The financial assets include Intercontinental Exchange Futures Europe (ICE-ECX) carbon emission allowances (the main driver of interest), European Energy Exchange (EEX) Coal ARA futures and ICE Brent oil futures (reflecting the two largest energy sources in Europe), Stoxx600 Europe Oil and Gas Index (the main energy stock index in Europe), EEX Power Futures (representing electricity), and Stoxx600 Europe Renewable Energy index (representing the sunrise energy industry). This paper finds that the Moving Average (MA) technique beats random timing for carbon emission allowances, coal, and renewable energy. In these asset markets, there seems to be significant returns predictability of stochastic trends in prices. The results are mixed for Brent oil, and there are no predictable trends for the Oil and Gas index. Stochastic trends are also missing in the electricity market as there is an ARFIMA-FIGARCH process in the day-ahead power prices. The empirical results are interesting for several reasons. We identified the data generating process in EU electricity prices as fractionally integrated (0.5), with a fractionally integrated Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) process in the residual. This is a novel finding. The order of integration of order 0.5 implies that the process is not stationary but less non-stationary than the non-stationary I(1) process, and that the process has long memory. This is probably because electricity cannot be stored. Returns predictability with MA rules requires stochastic trends in price series, indicating that the asset prices should obey the I(1) process, that is, to facilitate long run returns predictability. However, all the other price series tested in the paper are I(1)-processes, so that their returns series are stationary. The empirical results are important because they give a simple answer to the following question: When are MA rules useful? The answer is that, if significant stochastic trends develop in prices, long run returns are predictable, and market timing performs better than does random timing.

Purpose This paper aims to examine the integration of housing markets in Canada by examining housing price data (1999–2016) of six metropolitan areas in different provinces, namely, Calgary, Vancouver, Winnipeg, Toronto, Montreal and Halifax. The authors test for cointegration, driver cities of long-run relationships, long-run Granger causality and instantaneous causality in light of the global financial crisis (GFC) (2007–2008). Design/methodology/approach The authors use Johansen’s system cointegration approach with structural breaks. Moving average representation is used for common stochastic trend(s) analysis. Finally, the authors apply vector error correction model-based Granger causality and instantaneous causality. Findings Cities’ housing prices are in long-run equilibrium. Post-crisis Canadian housing markets became more integrated. The Calgary, Vancouver, Toronto and Montreal markets drive the Canadian housing market, leading all cities toward long-run equilibrium. Strong long-run Granger causality exists, but the authors observe no instantaneous causality. Price information takes time to disseminate, and long-run price adjustments play a significant role in causation. Practical implications The findings of cointegration increasing after the GFC and strong lead–lag can be used by investors to arbitrage and optimize portfolios. This can also help national and local policymakers in mitigating risk. Incorporating these findings can lead to better price forecasting. Originality/value This study presents many novelties for the Canadian housing market: it is the first to use repeat-sales regional pricing indices to test long-run behaviors, conduct common stochastic trend analyzes and present causality relations.

This study investigates the statistical significance of the trends of station temperature time series from the European Climate Assessment & Data archive poleward of 60°N. The trends are identified by different methods and their significance is assessed by three different null models of climate noise. All stations show a warming trend but only 17 out of the 109 considered stations have trends which cannot be explained as arising from intrinsic climate fluctuations when tested against any of the three null models. Out of those 17, only one station exhibits a warming trend which is significant against all three null models. The stations with significant warming trends are located mainly in Scandinavia and Iceland. Key Points I am using a novel method to test the significance of temperature trends In the Eurasian Arctic region only 17 stations show a significant trend I find that in Siberia the trend signal has not yet emerged

Criminological research is often based on time-series data showing some type of trend movement. Trending time-series may correlate strongly even in cases where no causal relationship exists (spurious causality). To avoid this problem researchers often apply some technique of detrending their data, such as by differencing the series. This approach, however, may bring up another problem: that of spurious non-causality. Both problems can, in principle, be avoided if the series under investigation are “difference-stationary” (if the trend movements are stochastic) and “cointegrated” (if the stochastically changing trendmovements in different variables correspond to each other). The article gives a brief introduction to key instruments and interpretative tools applied in cointegration modelling.

This article shows how new time series models can be used to track the progress of an epidemic, forecast key variables and evaluate the effects of policies. The univariate framework of Harvey and Kattuman (2020, Harvard Data Science Review, Special Issue 1—COVID-19, https://hdsr.mitpress.mit.edu/pub/ozgjx0yn) is extended to model the relationship between two or more series and the role of common trends is discussed. Data on daily deaths from COVID-19 in Italy and the UK provides an example of leading indicators when there is a balanced growth. When growth is not balanced, the model can be extended by including a non-stationary component in one of the series. The viability of this model is investigated by examining the relationship between new cases and deaths in the Florida second wave of summer 2020. The balanced growth framework is then used as the basis for policy evaluation by showing how some variables can serve as control groups for a target variable. This approach is used to investigate the consequences of Sweden’s soft lockdown coronavirus policy in the spring of 2020.

Technical change is generally seen as a major source of growth, but usually cannot be observed directly and measurement can be difficult. With only aggregate data, measurement puts further demands on the empirical strategy. Structural time series models and the state-space form are well suited for unobserved phenomena, such as technical change. In fisheries, technical advance often contributes to increased fishing pressure, and improved productivity measures are important for managers concerned with efficiency or conservation. I apply a structural time series model with a stochastic trend to measure technical change in a Cobb-Douglas production function, considering both single equation and multivariate models. Results from the Norwegian Lofoten cod fishery show that the approach has both methodological and empirical advantages when compared with results from the general index approach, which has been applied in the literature. JEL Codes: C22, O39, Q22.

The article provides an analysis of the development of NAIRU and the economic cycle in the labour market at the level of the economy and in selected sectors in the Czech Republic and Slovakia. The analysis focuses on estimation of the time-varying NAIRU with the use of the method of the stochastic trend. The difference between the estimated NAIRU values and the real unemployment rates is used for characterisation of the economic cycle in the labour market. The estimated phases of the cycle are compared with the development of the basic real economy indicators. Unstable periods on the labour market in the economy and in selected sectors of the two countries are localised. The identified leading indicators are used for prediction of the development in the following period.

This study investigates the linearity test of smooth transition autoregressive models when the true data generating process is a stochastic trend process. Results show that, under the null hypothesis of linearity, the asymptotic distribution of the W statistic proposed by Teräsvirta (J Am Stat Assoc 89:208–218, 1994) follows the χ2 distribution, whereas the finite sample distribution does not. A maximized Monte Carlo simulation-based test is used to perform the linearity test, and the results show good performance.

This study investigates the degree of co-integration between five major European stock markets and five major non European stock markets. The results show that all five major European stock markets are co-integrated either positively or negatively, while among the five major non European the Canadian, the Japanese and the Singapore are non co-integrated with the others.