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Journal ArticleDOI

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

01 Aug 2018-Resources Policy (Elsevier)-Vol. 57, pp 196-212

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

Topics: Realized variance (54%), Futures contract (53%), Quantile (51%)

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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Gold Futures Returns and Realized Moments:
A Forecasting Experiment Using a Quantile-Boosting Approach
Matteo Bonato
a
, Riza Demirer
b
, Rangan Gupta
c
, Christian Pierdzioch
d
June 2016
Abstract
This paper proposes an iterative model-building approach known as quantile boosting to
trace out the predictive value of realized volatility and skewness for gold futures returns.
Controlling for several widely studied market- and sentiment-based variables, we examine
the predictive value of realized moments across alternative forecast horizons and across
the quantiles of the conditional distribution of gold futures returns. We find that the real-
ized moments often significantly improve the predictive value of the estimated forecasting
models at intermediate forecast horizons and across quantiles representing distressed mar-
ket conditions. We argue that realized moments carry information that reflects investors’
tradeoff between diversification and skewed payoffs, particularly during periods of market
stress, which may be especially relevant for gold as the traditional accepted safe haven.
JEL classification: C22; C53; Q02
Keywords: Gold futures returns; Realized volatility; Realized skewness; Forecasting; Quan-
tile boosting
Addresses:
a
Department of Economics and Econometrics, University of Johannesburg, Auckland Park,
Johannesburg, South Africa; E-mail: mbonato@uj.ac.za.
b
Department of Economics & Finance, Southern Illinois University Edwardsville, Edwardsville,
IL 62026-1102, USA; E-mail address: rdemire@siue.edu.
c
Corresponding author. Department of Economics, University of Pretoria, Pretoria, 0002,
South Africa; E-mail address: rangan.gupta@up.ac.za.
d
Department of Economics, Helmut Schmidt University, Holstenhofweg 85, P.O.B. 700822,
22008 Hamburg, Germany; Email address: c.pierdzioch@hsu-hh.de.

1 Introduction
The financial market crises and prolonged uncertainty surrounding global economic funda-
mentals have drawn the attention of researchers towards the dynamics of gold returns as
the traditionally accepted safe haven. While the literature has promoted gold as an invest-
ment asset due to its low level of correlation with equity indices (Hillier et al., 2006) and
its counter-cyclical reaction to unexpected macroeconomic news (Roache and Rossi, 2009),
other studies have focused on the determinants of gold returns in the context of its value as
a hedge and/or diversifier for investors (Baur and Lucey, 2010; Ciner et al., 2013). Classic
determinants of gold returns that have been discussed in earlier literature include stock market
returns, exchange-rate movements, oil-price fluctuations, and interest rates (see, for example,
Hammoudeh and Yuan, 2008; Pukthuanthong and Roll, 2011; Reboredo 2013a,b; Pierdzioch
et al. 2014; Beckmann et al., 2015). We contribute to this literature by examining the pre-
dictive value of realized moments for gold futures returns across alternative forecast horizons,
after controlling for well documented market-based variables and widely studied measures of
investor sentiment and uncertainty (Da et al., 2015; Baker et al., 2015). More specifically, we
trace out the incremental predictive value of realized volatility and skewness for gold futures
returns using a recursively estimated quantile-boosting approach recently used in the litera-
ture on gold-price dynamics by Pierdzioch et al. (2016). The approach accounts for model
uncertainty as well as model instability and allows the predictive value of realized moments
to be analyzed across the quantiles of the conditional distribution of gold futures returns that
represent different market conditions. By doing so, the analysis provides new insights to the
predictability of gold futures return that can be useful in hedging and safe-haven analyses.
Research in gold price dynamics and how they relate to stock and bond market returns has
recently experienced renewed interest, particularly following the 2007/08 financial crisis. Con-
sequently, a number of papers have been published in recent years examining the diversification
benefits of gold investments. Traditionally, gold has been studied as a hedge against inflation
and currency depreciation (e.g., Christie-David et al., 2000; Capie et al., 2005; Worthington
and Pahlavani, 2007; Blose, 2010). Following the market turmoil experienced during the credit
crunch of 2008, a number of recent studies have also looked into the diversification and safe-
haven benefits of gold for stock and bond portfolios (e.g., Baur and Lucey, 2010; Baur and
McDermott, 2010; Hood and Malik, 2013; Bredin et al., 2015). While recent studies present
mixed evidence in regards to the dominance of gold as a safe haven compared to other assets
(e.g., Hood and Malik, 2013; Agyei-Ampomah et al., 2014), the literature generally suggests
that gold can work as a hedge and/or safe haven for stock and bond investors both in the U.S.
and in other developed markets. Clearly, modeling gold returns and identifying the market
variables that might have predictive value for gold-price fluctuations is of practical concern for
1

hedgers and portfolio managers in the implementation of dynamic diversification and/or hedg-
ing strategies. Identification of primary determinants of gold returns can also help enlarge our
understanding of volatility transmissions between gold and other market segments, which can
especially be useful in cross-hedging strategies. Finally, the findings on gold return dynamics
can be employed in further forecasting exercises given the recent evidence that gold prices can
help forecast real exchange rates, particularly in the case of major commodity exporters (e.g.,
Apergis, 2014).
A significant advantage of the quantile boosting approach utilized in this study is that it
follows an iterative model-building procedure in which the forecasting model is built from
alternative competing predictor variables. In addition to some of the well-documented market-
based variables as well as investor sentiment and uncertainty indicators, we also examine the
predictive value of higher moments measured by the realized volatility and realized skewness,
which we compute using intraday return data. We are particularly interested in the predictive
ability of realized volatility and realized skewness as recent research documents that higher-
order moments may contain significant information regarding future returns and volatility
in stock markets. 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. Earlier studies including Barberis and Huang (2004),
Brunnermeier et al. (2007), Mitton and Vorkink (2007) and Boyer et al. (2010) suggest a
link between the skewness of individual securities and investors’ portfolio decisions, while Bali
et al. (2008) utilize skewness in Value at Risk estimations. In cross-sectional tests, Xing et
al. (2010) find that portfolios sorted on a measure related to idiosyncratic skewness generate
differences in returns while studies including Barberis and Huang (2008), Conrad et al. (2013)
and Amaya et al. (2015) show that realized skewness has predictive value over subsequent
returns. More recently, Kraussl et al. (2016) associate skewness with crash risk, enlarging the
scope of risk proxies skewness may be associated with. Hence, we are primarily motivated by
the evidence suggesting that it is important to account for higher moments when analyzing
return dynamics, and the quantile-boosting approach employed in this study provides an
appropriate framework that allows the predictive value of realized moments to be examined
in the presence of other well documented market- and sentiment-based indicators.
Our findings suggest that realized moments can significantly improve the predictive value
of the estimated forecasting models, even after controlling for widely studied market- and
sentiment-based variables. Comparing alternative model specifications that include market-
based variables such as the nominal interest rate, term spread, exchange rates, oil and stock
market returns as well as popular uncertainty and sentiment indicators, we find that a boosted
model that includes realized volatility and skewness often outperforms a simple boosted AR(1)
2

model as well as a boosted model that excludes the realized moments from the list of predictor
variables. 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. This is especially important for the estimation of tail-risk measures and Value at
Risk projections for periods of market stress.
We organize the remainder of the paper as follows. In Section 2, we explain the quantile-
boosting approach and how we evaluate the accuracy of forecasts. In Section 3, we present
the data, and we explain how we compute the realized moments. In Section 4, we summarize
our empirical results. In Section 5, we conclude with a discussion of practical implications of
our empirical results.
2 Methodology
2.1 The Quantile-Boosting Approach
The starting point of the quantile-boosting approach (see Fenske et al., 2011; Zheng, 2012;
Yuan, 2015; for a least-absolute error boosting approach, see Friedman, 2001) is the following
quantile-regression period-loss function which is standard in the quantile-regression literature
(on quantile regressions, see Koenker, 2005):
L(α, ˆu
t+1,α,h
) = ˆu
t+1,α,h
(α 1(ˆu
t+1,α,h
< 0)), (1)
where 1(·) denotes the indicator function, ˆu
t+1
is the forecast error, and the quantile parameter
can assume values in the interval α (0, 1). A symmetric loss function obtains for α = 0.5,
while for α < 0.5 (α > 0.5), the loss of a negative forecast error exceeds (falls short of)
the loss of a positive forecast error. Because the optimal forecast depends on the quantile
parameter, the forecast error carries an α-index. For a given α-index, the forecast error for a
given forecast horizon, h, is computed as ˆu
t+1,α,h
= r
t+h
F (
ˆ
β
α,h
, x
t
), where F (β
α,h
, x
t
) =
ˆ
β
0,α,h
+
ˆ
β
1,α,h
x
1,t
... +
ˆ
β
n,α,h
x
n,t
, where r
t+h
denotes gold futures returns between period of
time t and t + h and
ˆ
β
j,α,h
, j = 0, 1, 2, ..., n denote estimates of quantile-specific regression
coefficients of the predictors, x
t
.
Similar to Pierdzioch et al. (2016), we use the quantile-boosting approach to estimate the
regression coefficients and to decide which predictors to include in the optimal forecasting
model. To this end, we select for any given α an optimal F (
ˆ
β
α,h
, x
t
)
by solving
F (
ˆ
β
α,h
, x
t
)
= arg min
F (
ˆ
β
α,h
,x
t
)
E [L(α, h, t)] , (2)
3

where expectations, E, are computed in terms of L(α, h, t) =
P
t
j=0
L(α, ˆu
j+1,α,h
). The min-
imization problem given in Equation (2) is solved by means of a functional-gradient-descent
boosting algorithm (Friedman, 2001; Fenske et al., 2011; for a survey of boosting algorithms,
see Bühlmann and Hothorn, 2007). The algorithm is implemented by iterating over the fol-
lowing steps:
1. Set m = 1 and choose a starting value. Like Fenske et al. (2011), we choose the median
of the response variable as a starting value. We use demeaned data (see Bühlmann and
Hothorn, 2007).
2. Compute the negative gradient vector ˆu
t+1,α,h
= L(α, t) /∂F (
ˆ
β
[m1]
α,h
, α, x
t
), where
ˆu
t+1,α,h
= α if ˆu
t+1,α,h
0 and ˆu
t+1,α,h
= α 1 if ˆu
t+1,α,h
< 0.
3. Fit the individual elements of x
t
to the negative gradient vector. Choose the best
element, κ, as the one that solves min L
2
(see Friedman, 2001).
4. Update the vector of regression coefficients
ˆ
β
[m]
α,h
=
ˆ
β
[m1]
α,h
+ vˆγ
[κ,m]
α,h
, where v (0, 1]
denotes a step-size parameter, and ˆγ
[κ,m]
α,h
contains as the only non-zero element the
coefficient estimated for κ. Like Fenske et al. (2011) and others, we set v = 0.1. Smaller
values of v lead to more boosting iterations.
5. Update m. Terminate the updating when a final iteration is reached. We determine
the final iteration, m
, as the one that minimizes the loss function. Similar to Mayr
et al. (2012) and Pierdzioch et al. (2016), we run the algorithm m
break
times. If
m
= arg min
m
L
m
(α, h, t) satisfies m
0.75×m
break
, we stop, where L
m
(α, h, t) denotes
the loss in iteration m, given α and h. Otherwise, we set m
break
= m
break
+ 10, and
check again if m
0.75 × m
break
. We continue until we reach m
max
= 500, but the
algorithm typically stops much earlier.
Finally, we insert the updated predictors, x
t+1
, into F (
ˆ
β
[m
]
α,h
, x
t+1
)
, and compute an out-of-
sample forecast of gold futures returns. Because the optimal forecasting model may change
over time we use a recursively expanding estimation window to implement the quantile-
boosting approach (see Pierdzioch et al., 2016).
2.2 Forecast Evaluation
We 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, we account for the
fact that the quantile-boosting algorithm adjusts forecasts depending on the shape of the loss
4

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Frequently Asked Questions (2)
Q1. What have the authors contributed in "Gold futures returns and realized moments: a forecasting experiment using a quantile-boosting approach" ?

This paper proposes an iterative model-building approach known as quantile boosting to trace out the predictive value of realized volatility and skewness for gold futures returns. Controlling for several widely studied marketand sentiment-based variables, the authors examine the predictive value of realized moments across alternative forecast horizons and across the quantiles of the conditional distribution of gold futures returns. The authors find that the realized moments often significantly improve the predictive value of the estimated forecasting models at intermediate forecast horizons and across quantiles representing distressed market conditions. 

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.