where t−1 ≤u≤t. First and second moments are obtained, based on the assumption that dσu and dWu are uncorrelated (no leverage effect). Since standard Brownian Motion has increments distributed according to Wt −Ws ~ N(0, t−s) for 0 ≤s≤t, the mean of rt conditional on information set Ω t−1 is given by Accordingly, conditional variance, or Integrated Volatility IVt , is given by Of course, return and volatility computations in practice are restricted to discrete time intervals, hence IVt is latent and can only be approximated. As parametric models of estimating IVt are prone to misspecification, an elegant non-parametric method is to estimate volatility of daily changes by a monthly realized volatility series<sup>6</sup> . Realized volatility is defined as the summation of squared daily changes over the period from the first to the last day (Dm) of a given month: <!-- Start of picture text --> Dm Dm 2<br>RVm(ρd ρd2 = ,<br>) = �d=1 �d=1 � πd π − π d−1 d−1 �<br>where RVm(ρd) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic RVm(ρd) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic m(ρd) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic (ρd) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic d) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic ) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic ρd. Crucially, based on the quadratic d. Crucially, based on the quadratic . Crucially, based on the quadratic<br>variation theory, Andersen et al. (2004) demonstrate that a volatility measure RVp(x) converges uniformly in RVp(x) converges uniformly in p(x) converges uniformly in (x) converges uniformly in converges uniformly in<br>probability to IVt as p→0; and hence is an unbiased and efficient estimatorIVt as p→0; and hence is an unbiased and efficient estimatort as p→0; and hence is an unbiased and efficient estimator as p→0; and hence is an unbiased and efficient estimatorp→0; and hence is an unbiased and efficient estimator; and hence is an unbiased and efficient estimator 7 . In practice, increasing the<br>sampling frequency of intra-period changes will yield a more accurate non-parametric estimator of IVtIVtt. This<br>study will therefore be based on monthly data, unlike Guo and Kliesen (2005) and Rafiq et al. (2009), who<br>measure oil price variance only at quarterly frequency, and hence ‘aggregate away’ potentially valuable<br>information on intra-quarter volatility.<br>0.35 0.20 0.20<br>USA 0.18 Germany 0.18 Japan<br>0.30<br>0.16 0.16<br>0.25 0.14 0.14<br>0.20 0.12 0.12<br>0.10 0.10<br>0.15 0.08 0.08<br>0.10 0.06 0.06<br>0.04 0.04<br>0.05<br>0.02 0.02<br>0.00 0.00 0.00<br>0.20 0.20 0.20<br>0.18 Malaysia 0.18 India 0.18 S.Korea<br>0.16 0.16 0.16<br>0.14 0.14 0.14<br>0.12 0.12 0.12<br>0.10 0.10 0.10<br>0.08 0.08 0.08<br>0.06 0.06 0.06<br>0.04 0.04 0.04<br>0.02 0.02 0.02<br>0.00 0.00 0.00<br>1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009<br>1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009<br><!-- End of picture text --> where RVm(ρd) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic RVm(ρd) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic m(ρd) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic (ρd) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic d) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic ) denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic denotes the monthly realized volatility of daily changes ρd. Crucially, based on the quadratic ρd. Crucially, based on the quadratic d. Crucially, based on the quadratic . Crucially, based on the quadratic variation theory, Andersen et al. (2004) demonstrate that a volatility measure RVp(x) converges uniformly in RVp(x) converges uniformly in p(x) converges uniformly in (x) converges uniformly in converges uniformly in probability to IVt as p→0; and hence is an unbiased and efficient estimatorIVt as p→0; and hence is an unbiased and efficient estimatort as p→0; and hence is an unbiased and efficient estimator as p→0; and hence is an unbiased and efficient estimatorp→0; and hence is an unbiased and efficient estimator; and hence is an unbiased and efficient estimator<sup>7</sup> . In practice, increasing the sampling frequency of intra-period changes will yield a more accurate non-parametric estimator of IVtIVtt. This study will therefore be based on monthly data, unlike Guo and Kliesen (2005) and Rafiq et al. (2009), who measure oil price variance only at quarterly frequency, and hence ‘aggregate away’ potentially valuable information on intra-quarter volatility.

**Figure 4.** Monthly Realized Volatility (1983 – 2011). Distinct clusters of high volatility are evident, even though their extent varies across countries due to exchange rate and inflation effects.

> 6 While a RV estimate of higher frequency (e.g. daily RV based on intraday price returns) would capture volatility more accurately, this could not reasonably be analysed against lower frequency macro data. In practice, monthly Industrial Production data is the highest frequency proxy for economic growth.

> 7 Note that Andersen et al. (2004) denote the h-period volatility at date t as  RVt(h), while in this study RVm(ρd) denotes the monthly volatility in month m, based on daily returns ρd.

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