# Gold futures returns and realized moments : a forecasting experiment using a quantile-boosting approach

Abstract: The German Science Foundation (Project Macroeconomic Forecasting in Great Crises; Grant number: FR 2677/4-1).

## Summary (3 min read)

### 1 Introduction

- The financial market crises and prolonged uncertainty surrounding global economic fundamentals have drawn the attention of researchers towards the dynamics of gold returns as the traditionally accepted safe haven.
- While studies including Bollerslev et al. (2013) and Corsi et al. (2013) use realized volatility for forecasting stock-market returns and to develop option-valuation models, a number of studies in the asset-pricing literature underline the predictive ability of realized skewness for stock returns.
- The predictive value of realized moments is particularly evident for intermediate forecast horizons and holds in many cases for lower quantiles, suggesting that realized moments must be taken into account in forecasting exercises that target distressed market periods in particular.

### 2.1 The Quantile-Boosting Approach

- Like Fenske et al. (2011), the authors choose the median of the response variable as a starting value.
- The authors determine the final iteration, m∗, as the one that minimizes the loss function.
- Because the optimal forecasting model may change over time the authors use a recursively expanding estimation window to implement the quantileboosting approach (see Pierdzioch et al., 2016).

### 2.2 Forecast Evaluation

- The authors check the informational value of the boosted forecasts by comparing them with the forecasts from a recursively estimated boosted benchmark model, b.
- In doing so, the authors account for the fact that the quantile-boosting algorithm adjusts forecasts depending on the shape of the loss function given in Equation (1) (see Pierdzioch et al., 2015, 2016).
- Similarly, a quantile parameter of α < 0.5 implies that the loss of a negative forecast error exceeds the loss of a positive forecast error, requiring a downward adjustment of forecasts relative to the symmetric benchmark case.
- If both forecasts contain non-overlapping information for rt+h then both coefficients, γ1,α,h and γ2,α,h, should be significantly different from zero.
- Because of the overlapping structure of the data in case of multiperiod forecasts, the authors use bootstrap simulations to assess the significance of the coefficients.

### 3.1 Gold Futures Returns and Realized Moments

- 1-minute returns are then computed by taking the log-differences of these prices and these intra-day returns are used to compute the realized moments.
- Based on the Jarque-Bera test statistic (not reported), the authors can reject normality of the sampling distribution of returns at the highest levels of significance, which provides some preliminary justification for modeling the quantiles rather than simply the mean of the conditional distribution of returns.

### 3.2 Other Predictor Variables

- In addition to realized volatility and realized skewness, the authors consider several market- and sentiment-based predictors in the construction of the forecasting models.
- Da et al. (2015) show that the FEARS index has predictive power over short-term stock market reversals as well as temporary increases in volatility.
- Naturally, their analysis is restricted to this sample period.
- The role of exchange rate movements for gold returns has been examined in a number of studies including Pukthuanthong and Roll (2011), Reboredo (2013b), and Reboredo and Rivera-Castro (2014).
- The primary measure for this index equals the number of articles that contain at least one term from each of three sets of terms (economic or economy, uncertain or uncertainty, and legislation, regulation, Congress, Federal Reserve, or White House).

### 4.1 Structure of the Forecasting Models

- For computing their baseline results, the authors use 75% of the data (1,222 observations; the initialization period ends in July 2009; as a robustness check, they shall present results for an extended out-of-sample period in Section 4.4) to initialize the quantile-boosting approach, and the remaining data for out-of-sample forecasting.
- For the longer forecasting horizon (ten-days-ahead), this pattern becomes asymmetric insofar as the lower quantiles require more iterations than the upper quantiles.
- In line with this pattern, the quantile-boosting approach selects more predictors for the longer forecast horizons.
- For one-day-ahead returns, realized volatility mainly enters the boosted forecasting models for several upper and the two lower quantiles.
- The importance of realized skewness increases for the quantiles in the range 0.55 ≤ α ≤ 0.7 and remains strong, and in some cases strengthens even further relative to the results for five-days-ahead returns, for quantiles below α = 0.4.

### 4.2 Fair-Shiller Regressions

- For ten-days-ahead returns the dominance of the quantile-boosting approach becomes stronger for the lower quantiles, while results for the quantiles above the median are not significant for the quantile-boosting approach.
- Table 2 summarizes the results of Fair-Shiller regressions that compare a boosted model that excludes the realized moments from the list of predictors and a boosted AR(1) model.
- Nevertheless, whatever the underlying economic rationale might be, their findings clearly point to the significant predictive value of realized moments during distressed market periods, even in the presence of other well cited market- and sentimentbased predictors for gold returns.

### 4.3 Alternative Realized Moments

- The authors consider two alternative measures of realized moments.
- For this estimator the authors use 10-minute returns as slow scale and 1-minute returns as fast scale.
- Please include Tables 4 and 5 about here.

### 4.4 Extended Forecasting Period

- Having presented evidence on the predictive ability of realized moments for the selected baseline sample period discussed in Section 4.1, the authors next analyze an extended out-of-sample forecasting period for a robustness check.
- Specifically, the authors reserve 50% of the data for out-of-sample forecasting (the initialization period ends in November 2007) such that the out-of-sample forecasting period comprises the onset of the financial crisis of 2008/2009.
- The coefficient is significant also for a few of the other quantiles during some periods of time.
- When the authors exclude the realized moments from the list of predictor variables, they still obtain forecasts that yield a significant coefficient for the two upper quantiles at the beginning of the out-of-sample period, but the significance of the coefficient becomes fragile and more scattered across the quantiles as they move the rolling window forward in time.
- In particular, the authors do not observe a systematically significant coefficient for the lower quantiles in the second half of the out-of-sample period, which is in stark contrast to the results for a boosted model that inlcudes the realized moments in the list of potential predictors.

### 5 Concluding Remarks

- The authors find that realized moments often significantly improve the predictive value of the estimated forecasting models, even after controlling for widely-studied market-based variables including the nominal interest rate, term spread, exchange rates, oil and stock market returns as well as popular uncertainty and sentiment indicators.
- By the same token, the findings may also serve as a guideline in regime-based asset-allocation strategies in which gold is utilized as a hedge (or safe haven) in order to protect portfolio value during distressed market conditions.

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##### Frequently Asked Questions (2)

###### Q2. What future works have the authors mentioned in the paper "Gold futures returns and realized moments: a forecasting experiment using a quantile-boosting approach" ?

Furthermore, as Shrestha ( 2014 ) notes, one can expect price discovery to take place primarily in the futures market as the futures price responds to new information faster than the spot price due to lower transaction costs and ease of short selling associated with the futures contracts. The futures price data, in continuous format, are obtained from www. Based on the Jarque-Bera test statistic ( not reported ), the authors can reject normality of the sampling distribution of returns at the highest levels of significance, which provides some preliminary justification for modeling the quantiles rather than simply the mean of the conditional distribution of returns. By the same token, an analysis by means of the BDS test ( Brock et al., 1996 ; results are available upon request ) indicates, for various embedding dimensions, the presence of nonlinearity in the returns series, further strengthening the case for a quantiles-based modeling approach.