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not in the same manner. For Sweden we find a negative impact in accordance with the Holland hypothesis, whereas for Germany and the Netherlands we find the opposite in support of the Cukierman–Meltzer hypothesis. In a sensitivity analysis we show that an arbitrary choice of the heteroscedasticity parameter influences this relationship significantly. JEL classification: C22, E31. Keywords: GARCH-in-mean; inflation; level effect; nominal uncertainty; power transformation. 1. INTRODUCTION The issue of the welfare costs of inflation has been one of the most researched

driving the risk premium, which is in line with the standard C-CAPM model. In addition, growth in international oil prices influences the risk premium, reflecting the important role played by the hydrocarbon sector in GCC economies. The methodology employed in this paper can be used for forecasting the risk premium on a monthly basis, which has important practical implications for policymakers interested in the timely monitoring of risks in the GCC. KEYWORDS: foreign exchange risk, time-varying risk premium, multivariate GARCH-in-Mean, GCC Author Notes: I would like to

Abstract

This paper examines the mixture of distribution properties associated with heteroskedastic excess Bitcoin return data, using the volume of Google search queries as a proxy for the information arrival time, from a monthly data sampling period of June 2010 to May 2019. The results show that the volatility coefficients become highly statistically insignificant when the lagged volume of search queries is included in the conditional variance equation of the GJR-GARCH-M model. This clearly suggests that the volume of search queries is shown to provide significant explanatory power regarding the variance of heteroskedastic excess Bitcoin return, which can be traced from the ARCH process defined in the GJR-GARCH-M specification. A significant negative relationship between the conditional volatility and the volume of search queries indicates that Internet (online) information arrival reduces the risk premium in the Bitcoin market, which may improve market stability.

error terms (i.e., the return residuals). The process { h k } k = 0 N $\{h_k\}_{k=0}^{N}$ (where h k = σ k 2 ) $h_k = \sigma_k^2)$ is the hidden variance process, which needs to be estimated from the data. Model (1.2), (1.3) is, in fact, a GARCH-in-Mean(1,1) model, first introduced in the form of an ARCH-in-Mean model for risk-return tradeoffs in the term structure of US interest rates in [ 6 ]. The main feature of these models is that the conditional first moment of some time series is assumed to be a function of its conditional second moment, which in turn follows

References BAELE, L. (2005). Volatility Spillover Effects in European Equity Markets , Journal of Financial and Quantitative Analysis 40(2), Pp. 373-401. BEINE, J., CAPORALE, G.M., GHATTAS, M. S., SPAGNOLO, N. (2010). Global and regional spillovers in emerging stock markets: A multivariate GARCH-in-mean analysis. Emerging Markets Review , 11(2) Pp. 250-260. BEKAERT, G., HARVEY, C.R. (1997). Emerging Equity Market Volatility, Journal of Financial Economics, 43(1), Pp. 29-77. BOLLERSLEV, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity

US and UK. Journal of Banking & Finance, 19(7), 1191-1210. https://doi.org/10.1016/0378-4266(94)00079-I Beirne, J., Caporale, G. M., Schulze - Ghattas, M., & Spagnolo, N. (2010). Global and Regional Spillovers in Emerging Stock Markets: A Multivariate GARCH - in - Mean Analysis. Emerging Markets Review, 11(3), 250-260. https://doi.org/10.1016/j.ememar.2010.05.002 Bernanke, B. S. (1983). Irreversibility, Uncertainty and Cyclical Investment. Quarterly Journal of Economics, 98(1), 85-106. https://doi.org/10.2307/1885568 Boako, G., & Alagidede, P. (2018). African Stock

correlation in the squared data provides strong evidence of conditional heteroscedasticity in the data. Finally, Engle and Granger (1987) cointegration tests (not reported here) suggest that the null hypothesis of no cointegration between electricity and natural gas prices is rejected at conventional significance levels, suggesting an error correction representation between these series. 3 The Model We use a general asymmetric GARCH-in Mean model of natural gas and elec- tricity price changes that allows for the possibilities of spillovers and asymme- tries in the variance

versions of this work. Thanks also to Lisa Crosato for helping me with the final copyediting. 1. INTRODUCTION It is quite common for financial assets returns to show conditional heteroskedas- ticity, leptokurtosis and skewness. The first two properties are usually dealt with GARCH or Stochastic Volatility models, possibly with fat-tailed distributions. How- ever, skewness has received much less attention in the literature and is usually obtained as a byproduct of GARCH-in-mean models (Engle, Lilien, and Robins, 1987) with leverage effects such as the Exponential GARCH

. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 1986, 31(3): 307–327. Bollerslev T. Generalized autoregressive conditional heteroskedasticity Journal of Econometrics 1986 31 3 307 327 [17] Christensen B J, Dahl C M, Iglesias E M. Semiparametric inference in a GARCH-in-mean model. Journal of Econometrics, 2012, 167(2): 458–472. Christensen B J Dahl C M Iglesias E M. Semiparametric inference in a GARCH-in-mean model Journal of Econometrics 2012 167 2 458 472 [18] Zhang X F, Wong H, Li Y, et al. An alternative GARCH-in-mean model: Structure

-return tradeoff relationships in speculative asset prices, much of it based on GARCH-in-Mean models. Motivated by the largely futile empirical efforts at establishing such a relationship in the data, the paper “Modeling the Volatility-Return Trade-off when Volatility may be Non- stationary” by Christian Dahl and Emma Iglesias proposes a new GARCH- M type model, termed GARCH-AR, in which the conditional mean is effectively a function of the ratio of the volatility this period to last period’s volatility. A complete characterization of the statistical properties of the