Interpreting Skewness and Histograms of Hourly EURUSD Returns

Summary

The document describes an exploratory check of hourly EURUSD percentage returns. The author removes zero-return observations because their concentration overwhelms the plotted histogram, standardizes the remaining returns by subtracting the mean and dividing by the standard deviation, and compares the resulting distribution with a standard normal density and central reference bounds. The reported skewness is close to zero, which appears consistent with a roughly symmetric histogram.

The post also mentions a much more negative skewness estimate for USDCHF despite a histogram that looks similarly symmetric, raising a useful question about how summary statistics relate to visual shape. It does not provide the underlying plot, sample size, time period, or further explanation, so the observations cannot establish whether either distribution is plausible or whether the estimates are reliable. Removing zero returns also changes the distribution being examined, and standardization does not make returns normally distributed.

Key ideas

• The analysis plots standardized hourly percentage returns for EURUSD.
• Zero returns are excluded because their frequency dominates the histogram display.
• The reported EURUSD skewness is close to zero and the plotted shape appears roughly symmetric.
• A highly negative USDCHF skewness estimate seems inconsistent with its visually symmetric histogram.
• Without the sample period, sample size, or plot, the observations are not enough to validate a return model.

Tags

# How skewed are FX returns? Does this look like a plausible histogram of EURUSD?


# How skewed are FX returns? Does this look like a plausible histogram of EURUSD?












I'm reading about volatility. I've charted the histogram of EURUSD and I am wondering if this looks plausible? What I've charted are the 1-hour percent change returns (not log returns). I've removed 0 returns because it completely destroys the plot (you get an impulse centred on 0) and I've standardised the returns by doing `ret = (ret-mean)/std`

I've added a N(0,1) density and the 5% conf intervals (at 0.025 and 0.975). The skewness is -0.12248942201701185 - pretty much symmetric. The histogram for USDCHF has newgative skew of -13 but still looks pretty much symmetric.

Legend: $\mu$ is mean, $\sigma$ is std, $\kappa$ is skew, $\gamma$ is kurtosis.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.