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This review investigates the effects of temporal aggregation and systematic sampling on time-series analysis, focusing on their influence on data accuracy, interpretability and statistical properties. The purpose of the study is to synthesise existing literature on the topic and offer insights into the trade-offs between these data reduction techniques.

The research methodology is based on an extensive review of theoretical and empirical studies covering univariate and multivariate time series models, focusing on unit roots, ARIMA, GARCH, cointegration properties and Granger Causality.

The key findings reveal that while temporal aggregation simplifies data by emphasising long-term trends, it can obscure short-term fluctuations, potentially leading to biases in analysis. Similarly, systematic sampling enhances computational efficiency but risks information loss, especially in non-stationary data, and may result in biased samples if sampling intervals coincide with data periodicity. The review highlights the complexities and trade-offs involved in applying these methods, particularly in fields like economic forecasting, climate modelling and financial analysis.

The originality and value of this study lie in its comprehensive synthesis of the impacts of these techniques across various time series properties. It underscores the importance of context-specific applications to preserve data integrity, offering recommendations for best practices in the use of temporal aggregation and systematic sampling in time-series analysis.

The authors analyse the nature of nonlinear long-run causal dynamics between VIX futures and exchange-traded products (ETPs).

Nonlinear long-run causal relations between daily price movements in ETPs and futures are established through a Markov switching vector error correction model (MS-VECM).

The authors observe time variation in causality with the volatility of volatility. In particular, demand pressures for VIX ETNs and futures can change in different regimes. The authors observe two regimes where regime 1 is classified as low-mean low-volatility, while regime 2 is classified as high-mean high-volatility. The convergence to the long-run equilibrium in the low-mean low-volatility regime is faster than the high-mean high-volatility regime. The nature of the time varying lead lag relations demonstrates the opportunities for arbitrage.

The linear causal relations between VXX and VIX futures are well established, with leads and lags generally found to be short-lived with arbitrage relations holding. The authors go further to capture the time-varying causal relationships through a Markovian process. The authors establish the nonlinear causal relations between inverse and leveraged products where causal relations are not yet documented.

The authors analyse six actively traded VIX Exchange Traded Products (ETPs) including 1x long, −1x inverse and 2x leveraged products. The authors assess their impact on the VIX Futures index benchmark.

Long-run causal relations between daily price movements in ETPs and futures are established, and the impact of rebalancing activity of leveraged and inverse ETPs evidenced through causal relations in the last 30 min of daily trading.

High frequency lead lag relations are observed, demonstrating opportunities for arbitrage, although these tend to be short-lived and only material in times of market dislocation.

The causal relations between VXX and VIX Futures are well established with leads and lags generally found to be short-lived and arbitrage relations holding. The authors go further to capture 1x long, −1x inverse as well as 2x leveraged ETNs and the corresponding ETFs, to give a broad representation across the ETP market. The authors establish causal relations between inverse and leveraged products where causal relations are not yet documented.