Rolling Window Method Research Articles

Dynamic risk-based optimization on cryptocurrencies

PurposeIt is crucial to find a better portfolio optimization strategy, considering the cryptocurrencies' asymmetric volatilities. Hence, this research aimed to present dynamic optimization on minimum variance (MVP), equal risk contribution (ERC) and most diversified portfolio (MDP).Design/methodology/approachThis study applied dynamic covariances from multivariate GARCH(1,1) with Student’s-t-distribution. This research also constructed static optimization from the conventional MVP, ERC and MDP as comparison. Moreover, the optimization involved transaction cost and out-of-sample analysis from the rolling windows method. The sample consisted of ten significant cryptocurrencies.FindingsDynamic optimization enhanced risk-adjusted return. Moreover, dynamic MDP and ERC could win the naïve strategy (1/N) under various estimation windows, and forecast lengths when the transaction cost ranging from 10 bps to 50 bps. The researcher also used another researcher's sample as a robustness test. Findings showed that dynamic optimization (MDP and ERC) outperformed the benchmark.Practical implicationsSophisticated investors may use the dynamic ERC and MDP to optimize cryptocurrencies portfolio.Originality/valueTo the best of the author’s knowledge, this is the first paper that studies the dynamic optimization on MVP, ERC and MDP using DCC and ADCC-GARCH with multivariate-t-distribution and rolling windows method.

Research on Dynamic Path Planning Based on the Fusion Algorithm of Improved Ant Colony Optimization and Rolling Window Method

This paper focuses on the problem that the current path planning algorithm is not mature enough to achieve the expected goal in a complex dynamic environment. In light of the ant colony optimization (ACO) with good robustness and strong search ability, and the rolling window method (RWM) with better planning effect in local path planning problems, we propose a fusion algorithm named RACO that can quickly and safely reach the designated target area in a complex dynamic environment. This paper first improves the ant colony optimization, which greatly improves the convergence performance of the algorithm and shortens the global path length. On this basis, we propose a second-level safety distance determination rule to deal with the special problem of the research object encountering obstacles with unknown motion rules, in order to perfect the obstacle avoidance function of the fusion algorithm in complex environments. Finally, we carry out simulation experiments through MATLAB, and at the same time conduct three-dimensional simulation of algorithm functions again on the GAZEBO platform. It is verified that the algorithm proposed in this paper has good performance advantages in path planning and dynamic obstacle avoidance.

Time-varying properties of asymmetric volatility and multifractality in Bitcoin.

This study investigates the volatility of daily Bitcoin returns and multifractal properties of the Bitcoin market by employing the rolling window method and examines relationships between the volatility asymmetry and market efficiency. Whilst we find an inverted asymmetry in the volatility of Bitcoin, its magnitude changes over time, and recently, it has become small. This asymmetric pattern of volatility also exists in higher frequency returns. Other measurements, such as kurtosis, skewness, average, serial correlation, and multifractal degree, also change over time. Thus, we argue that properties of the Bitcoin market are mostly time dependent. We examine efficiency-related measures: the Hurst exponent, multifractal degree, and kurtosis. We find that when these measures represent that the market is more efficient, the volatility asymmetry weakens. For the recent Bitcoin market, both efficiency-related measures and the volatility asymmetry prove that the market becomes more efficient.

Rolling window VaR: an EVT approach

In this study, a method of estimating value-at-risk is proposed. This method combines elements of extreme value theory (EVT), the APARCH model (Ding et al. 1993) and the rolling window method. The research was conducted using 20 stock market indexes worldwide during 2006-2019. Value-at-risk was estimated via 12 competing models which were evaluated using 5 tests. The back testing results indicate that the best model was the one which takes into consideration the asymmetric character of financial data (APARCH with skewed normal distribution), the Generalized Pareto Distribution for modeling the tail of the financial returns distribution and the rolling window approach. The methodologies discussed in this paper could provide a useful tool for both financial entities and regulatory authorities.

The time-varying causal relationship between oil price and unemployment: Evidence from the U.S. and China (EGY 118745)

This study detects the relationship between the crude oil price (COP) and unemployment rate (UR) to explore whether the efficiency-wage model is consistent for the United States (U.S.) and China. It is unstable to use full-sample data in the long-run nexus with the consideration of structural changes, implying that causality is unreliable. Instead, the dynamic causal relationship is examined by a time-varying rolling-window method. In certain sub-periods, the existence of time-varying positive bidirectional causality between the COP and UR is illustrated by the empirical findings, supporting the efficiency-wage model indicating that these two variables can interact through supply, demand and inflation channels. For the U.S., deviations between the COP and UR can be explained by geopolitical events, monetary policy, financial crises and the shale oil revolution. In addition, the end of double-digit economic growth, financial crises and high oil demand lead to fluctuations in China for certain sub-periods. Hence, for the government, these empirical findings have significant implications for identifying factors that bring about the causal link between the COP and UR and moreover lead to policy suggestions for U.S. and China.

Resources or development first: An interesting question for a developing country

Natural resource-based income or wealth should be a blessing and catalyst for growth in any country. However, paradoxically it has been suggested by many researchers that the countries rich in natural resources tend to transfer resource-based income to the non-productive sectors, resulting in slower investment and sluggish economic growth and financial development. This study employs the bootstrap Granger full-sample and rolling window estimation for sub-sample to explore the time-varying property between financial development and natural resources in Pakistan from 1971Q1 to 2017Q4. In view of structural changes, we analyze parameter stability and identify the relationship between the two estimated variables that are unstable. This outcome shows that full-sample causality checks can not be counted upon. Instead, we use a bootstrap-based rolling window method to revisit the complex causal link, and we find that both the positive and negative impacts of financial development (FD) on natural resources (NR) over many sub-periods, while NR having the same implications for FD in Pakistan. Our analysis confirms the resource-curse and the resource-blessing hypothesis exist in a different sub-stages. These significantly bi-directional changes in FD and NR, indicating the importance of stabilize resources and the financial market and give new insight for policymakers to ensure the effective management of natural resources.

Exchange Rate Return and Volatility Spillover across Major Trading Partners of India

ABSTRACTWe examine the connectedness among the series of four exchange rates with respect to the Indian Rupee. The results of Diebold and Yilmaz method which measures time-domain connectedness, show that the overall connectedness of the system is 30.15%. The results of Baruník and Křehlík approach which measures frequency-domain connectedness, exhibit that in the total connectedness the maximum contribution is from highest frequency (14.27%) and the lowest contribution is made by the second-lowest frequency (2.03%). Finally, the dynamic connectedness is also examined with rolling window methods. These results are very critical in understanding the connectedness among various exchange rate markets.

Analyzing time-varying volatility spillovers between the crude oil markets using a new method

Abstract The spillover effect is an important factor affecting the volatility of crude oil price. Basing on the study of Diebold and Yilmaz (2009, 2012, 2014), we propose a new method that calculates the time-varying volatility spillover indexes by the generalized forecast error variance decomposition of TVP-VAR-SV model. Then, using the new method, we study the time-varying volatility spillovers between four major crude oil markets (WTI, Brent, Oman, Tapis) from November 29, 2002 to July 13, 2018. By comparing the results of our new method and traditional rolling window method, we verify the superiority of our new method. The results show that the volatility spillovers calculated by the new method are clearer, more stable and not outlier sensitive. From the estimated results of time-varying volatility spillovers, we find that the volatility spillover between crude oil markets is slowly increasing, but there are obvious cyclical changes. And from the correlation analysis and the Granger causality test, we find that the volatility and volatility spillovers are positively correlated and are two-way Granger causality, which supported for the market infection hypothesis of King and Wadhwani (1990).

Dynamic spillovers and connectedness between oil returns and policy uncertainty

ABSTRACT This article investigates the dynamic connectedness and spillover effects between category policy uncertainty and WTI crude oil returns for oil-importing countries. To overcome the shortcomings of the traditional rolling-window method and obtain rigorous results, we adopt the TVP-VAR-based connectedness approach, apply it to full samples, and then estimate the dynamic spillovers between the series. Regarding the whole sample, the results reveal that economic policy uncertainty is as a net transmitter, and by employing four categorical policy uncertainty indices we reach the same conclusions. In particular, spillovers of fiscal policy uncertainty on crude oil returns are the most dominant ones, followed by exchange rate policy uncertainty, then monetary policy uncertainty, and finally trade policy uncertainty. And it is noteworthy that the network plots are employed by our article, which provides clearer evidence for the connectedness between variables. On a final note, Brent crude oil returns are utilized to increase the robustness of our conclusion.

Detrended moving average partial cross-correlation analysis on financial time series

Cross-correlations between nonlinear time series widely exist in complex systems. It is of great importance to accurately measure the correlations between time series. In this work, we suggest a combination methodology of Detrended Moving Average Processing and Partial Cross-correlation Analysis to quantify the correlations between different time series, which we call as Detrended Moving Average Partial Cross-correlation Analysis (DMPCCA). This novel approach combines the advantages of Detrended Moving Average Processing and Partial Cross-correlation Analysis, not only exploring power-law cross-correlations between two signals but removing underlying impacts of other signals on those two signals. To demonstrate the advantages of this approach, we carry out experiments with synthetic data generated by correlated processes and compare the performance of this measurement to traditional cross-correlation techniques. It is found that this method can reveal the real cross-correlations between systems even when the indirect cross-correlations established by other common factors exist. Then we go further study into the application of DMPCCA to financial time series in order to report its performance in stock markets and investigate cross-correlations between different stock indices. Furthermore, the rolling windows method is used in conjunction with DMPCCA to capture the changes of cross-correlations between stock indices as time goes on. We notice that there is a special period when DMPCCA coefficients between stock indices are obviously different from those of other periods.

Exploring the time and frequency domain connectedness of oil prices and metal prices

This paper explores the time and frequency domain connectedness between oil prices and metal prices for the period of 1980M1-2017M5. We employ DECO-GARCH model for equi-correlation among commodity under consideration, Diebold and Yilmaz (2014), for time domain, and Barunik and Krehlik (2017), for frequency domain (i.e., frequencies considered are: 1–4 months, 4–8 months, 8–15 months and more than 15 months) connectedness measures. The dynamic connectedness is examined by applying a rolling window method in time and frequency domain. Besides, network plots are also made based on the pair-wise net connectedness between the variables. The results for time domain analysis show that the overall connectedness of the system has been just 3.39%. The empirical results of frequency domain connectedness show that total connectedness varies at different frequencies. The maximum contribution is observed at short-term frequency, (1–4 months; 1.65%) and the lowest contribution at medium-term frequency (8–15 months; 0.45%.). The contribution from the highest frequency, which corresponds to more than 15 months’ period, is just 0.56%. The network analysis shows that Zinc is net receiver.

Connectedness Between Natural Gas Price and BRICS Exchange Rates: Evidence from Time and Frequency Domains

In this paper, we investigate the connectedness between natural gas and BRICS (Brazil, Russia, India, China, and South Africa)’s exchange rate in terms of time and frequency. This empirical work is based on the approach of connectedness proposed by Diebold and Yilmaz, who provided an effective way of valuing how much variation in one variable is responsible for the value of other variables, and the method proposed by Baruník and Křehlík, who decomposed the results from Diebold and Yilmaz into different frequencies. We also use the rolling-window method to conduct time-varying analysis. The data used in this paper are from 23 August 2010 to 20 June 2019. We find that the natural gas price hardly influences BRICS’s exchange rates, which provides an important practical implication for policymakers, especially in oil-dependent countries.

Is inflation driven by survey-based, VAR-based or myopic expectations? An empirical assessment from US real-time data

The relative importance of survey-based, VAR-based or myopic expectations is evaluated in accounting for US inflation dynamics in a New Keynesian Phillips Curve (NKPC) setting. Our contribution is threefold. First, we estimate the NKPC with both final and real-time vintage data in order to control for large revisions in the real GDP data. Second, we distinguish between two different series for VAR-based inflation forecasts—derived by a recursive or rolling-window method—to account for changes in the conduct and transmission mechanisms of US monetary policy after World War II. Third, joint restrictions are tested in the NKPC to assess whether one of the expectational variables is able, on its own, to capture inflation dynamics. On a statistical basis, we find that there is no clear-cut winner between VAR- and survey-based inflation expectations. Most of our estimated NKPC variants conclude that survey inflation expectations tend to have the largest numerical weight. Nevertheless, the difference between VAR- and survey-based expectations’ estimated coefficients is not statistically significant. Moreover, myopic expectations do not play any significant role in the majority of the estimated NKPC variants.

Predictive power of Markovian models: Evidence from US recession forecasting

AbstractThis paper provides extensions to the application of Markovian models in predicting US recessions. The proposed Markovian models, including the hidden Markov and Markov models, incorporate the temporal autocorrelation of binary recession indicators in a traditional but natural way. Considering interest rates and spreads, stock prices, monetary aggregates, and output as the candidate predictors, we examine the out‐of‐sample performance of the Markovian models in predicting the recessions 1–12 months ahead, through rolling window experiments as well as experiments based on the fixed full training set. Our study shows that the Markovian models are superior to the probit models in detecting a recession and capturing the recession duration. But sometimes the rolling window method may affect the models' prediction reliability as it could incorporate the economy's unsystematic adjustments and erratic shocks into the forecast. In addition, the interest rate spreads and output are the most efficient predictor variables in explaining business cycles.

Causal Change Detection in Possibly Integrated Systems: Revisiting the Money–Income Relationship*

AbstractThis paper re-examines changes in the causal link between money and income in the United States over the past half century (1959–2014). Three methods for the data-driven discovery of change points in causal relationships are proposed, all of which can be implemented without prior detrending of the data. These methods are a forward recursive algorithm, a rolling window algorithm, and a recursive evolving algorithm all of which utilize subsample tests of Granger causality within a lag-augmented vector autoregressive framework. The limit distributions for these subsample Wald tests are provided. Bootstrap methods are developed to control family-wise size in the implementation of the recursive testing algorithms. The results from a suite of simulation experiments suggest that the recursive evolving window algorithm provides the most reliable results, followed by the rolling window method. The forward expanding window procedure is shown to have the worst performance. Both the rolling window and recursive evolving approaches find evidence of Granger causality running from money to income during the Volcker period in the 1980s. The forward algorithm does not find any evidence of causality over the entire sample period.

Dynamic relationship between carbon price and coal price: perspective based on Detrended Cross-Correlation Analysis

Unlike the European Union market, the main driver of CO2 price in China seems to be coal price rather than oil and gas prices, considering the coal-dominant energy structure in this country. This study analyzes the interrelationship between coal and carbon prices in both time and time-scale interval perspectives by using the Detrended Cross-Correlation Analysis method. China’s seven pilot carbon markets are taken as the sample. Results show a weak correlation between coal and carbon prices in short time scales (shorter than a quarter) but medium in long time scales (longer than a quarter). For short time scales, the correlation is negative in Chongqing and Shanghai, undetermined in Hubei, and positive for other pilots. For long time scales, Shenzhen pilot remains a negative correlation, Chongqing a positive while others a varying correlation. Results from rolling window method show a dominant weak cross-correlation during the development period of these pilot markets. However, the direction of correlation varies a lot during their developing periods both for the short and the long time scales except for Beijing market. Correlation is enhanced in Shenzhen but weakened in Hubei. In general, there exists a positive cross-correlation in Chinese carbon market and coal market. Such cross-correlation between coal and carbon prices is not usually seen in the European market. China’s coal-dominant energy structure may be the reason behind this phenomenon.

Time-varying character for short-term capital flow from the interest rate aspect in China

This study investigates the causal link between short-term capital flow and interest rate differential with the bootstrap Granger full-sample causality and sub-sample rolling-window methods. The empirical results indicate that there is a unidirectional link from interest rate differential to short-term capital flow. However, when considering structural breaks in the above series, the full-sample causality test cannot be relied on. Hence, the time-varying rolling-window method is employed to examine the dynamic causal nexus. Being influenced by the U.S. monetary, world economic situation, Chinese intervention policies and other factors, interest rate differential has influences on short-term capital flow in some periods, but the reverse effect does not exist. Therefore, it is important for authorities to focus on specific backgrounds (e.g., economic situation, monetary policies) and further utilise interest rate and capital control to alleviate negative effects from violent fluctuation of short-term capital flow on the Chinese economy.

Information linkage, dynamic spillovers in prices and volatility between the carbon and energy markets

Abstract The European Union Emissions Trading System (EU ETS) has strengthened the information flow and connection between carbon market and energy markets, which makes the carbon-energy system more complicated. This paper investigates information linkages and dynamic spillover effects between the carbon and energy markets. We adopt a systemic time-series approach to study connectedness in both returns and volatility in the carbon-energy system. Moreover, a rolling-windows method is used to show the dynamic features. Empirical results show that Brent oil prices play an important role in affecting carbon price changes and risks. Feedback exists from the carbon market to other energy markets, and electricity prices are shown to be the biggest information receiver in the system. It is also shown that the level of connectedness in the volatility system is substantially higher than that in the returns system. Our results can provide useful implications for policymakers to design market mechanisms and market investors to manage their portfolios.

Scanner Data-Based Panel Price Indexes.

We construct panel price indexes using retail scanner data that allow comparisons of consumption cost across space and time. Two types of panel indexes are examined: the rolling-window panel extensions of the multilateral Cave-Christensen-Diewert (CCD) index with the Törnqvist index as its elements, and of the multilateral Gini-Eltetö-Köves-Szulc (GEKS) index using the Fisher ideal index as its elements. The rolling window method maintains the nonrevisability of published index numbers while it allows index numbers for new periods and locations be calculated and the basket of items be updated. Meanwhile, the multilateral structure of price comparison eliminates significant downward drift in standard chained indexes. Using county-level bilateral and panel indexes based on retail beverage scanner data, we experimentally adjust for purchasing parity the portion of Supplemental Nutrition Assistance Program (SNAP) benefits that participants spend on beverages. Accounting for temporal and spatial cost differences causes over 2% of SNAP allotment spent on beverages be reallocated, or approximately a 5% change in allotment on average for a county. About 90% of the relocated SNAP fund is to adjust for spatial differences in food cost. We also compare SNAP allotments implied by the retail scanner data indexes with those implied by indexes based on the USDA Quarterly Food-at-Home Price Database (QFAHPD). The treatment of unit values and product quality may have contributed to the significant differences observed between the retail scanner data indexes and the QFAHPD indexes.

Multifractal Detrended Cross‐Correlation Analysis of the Return‐Volume Relationship of Bitcoin Market

We investigate the cross‐correlations of return‐volume relationship of the Bitcoin market. In particular, we select eight exchange rates whose trading volume accounts for more than 98% market shares to synthesize Bitcoin indexes. The empirical results based on multifractal detrended cross‐correlation analysis (MF‐DCCA) reveal that (1) the nonlinear dependencies and power‐law cross‐correlations in return‐volume relationship are found; (2) all cross‐correlations are multifractal, and there are antipersistent behaviors of cross‐correlation for q = 2; (3) the price of small fluctuations is more persistent than that of the volume, while the volume of larger fluctuations is more antipersistent; and (4) the rolling window method shows that the cross‐correlations of return‐volume are antipersistent in the entire sample period.