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«KNUT WICKSELL WORKING PAPER 2013:4 Working papers Editor: F. Lundtofte The Knut Wicksell Centre for Financial Studies Lund University School of ...»

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Importance of the macroeconomic

variables for variance prediction

A GARCH-MIDAS approach

HOSSEIN ASGHARIAN | AI JUN HOU | FARRUKH JAVED

KNUT WICKSELL WORKING PAPER 2013:4

Working papers

Editor: F. Lundtofte

The Knut Wicksell Centre for Financial Studies

Lund University

School of Economics and Management

Importance of the macroeconomic variables for variance prediction

A GARCH-MIDAS approach

Hossein Asgharian *: Department of Economics, Lund University and Knut Wicksell Center for Financial Studies Ai Jun Hou: Department of Business and Economics, Southern Denmark University Farrukh Javed: Department of Statistics, Lund University Abstract This paper applies the GARCH-MIDAS (Mixed Data Sampling) model to examine whether information contained in macroeconomic variables can help to predict short-term and longterm components of the return variance. A principal component analysis is used to incorporate the information contained in different variables. Our results show that including low-frequency macroeconomic information in the GARCH-MIDAS model improves the prediction ability of the model, particularly for the long-term variance component. Moreover, the GARCH-MIDAS model augmented with the first principal component outperforms all other specifications, indicating that the constructed principal component can be considered as a good proxy of the business cycle.

Keywords: Mixed data sampling, long-term variance component, macroeconomic variables, principal component, variance prediction.

* Tel.: +46 46 222 8667; fax: +46 46 222 4118;

E-mail address: Hossein.Asgharian@nek.lu.se; Department of Economics, Lund University, Box 7082, SLund, Sweden.

We are very grateful to the Jan Wallanders and Tom Hedelius Foundation (P2009-0041:1 and P2010-0077:1) for funding this research.

Importance of the macroeconomic variables for variance prediction A GARCH-MIDAS approach Abstract This paper applies the GARCH-MIDAS (Mixed Data Sampling) model to examine whether information contained in macroeconomic variables can help to predict short-term and longterm components of the return variance. A principal component analysis is used to incorporate the information contained in different variables. Our results show that including low-frequency macroeconomic information in the GARCH-MIDAS model improves the prediction ability of the model, particularly for the long-term variance component. Moreover, the GARCH-MIDAS model augmented with the first principal component outperforms all other specifications, indicating that the constructed principal component can be considered as a good proxy of the business cycle.

Keywords: Mixed data sampling, long-term variance component, macroeconomic variables, principal component, variance prediction.

1. Introduction A correct assessment of future volatility is crucial for asset allocation and risk management.

Countless studies have examined the time-variation in volatility and the factors behind this time variation, and documented a clustering pattern. Different variants of the GARCH model have been pursued in different directions to deal with these phenomena. Simultaneously, a vast literature has investigated the linkages between volatility and macroeconomic and financial variables. Schwert (1989) relates the changes in the volatility of returns to the macroeconomic variables and addresses how bond returns, the short-term interest rate, producer prices or industrial production growth rate provide incremental information on monthly market volatility. Glosten et al. (1993) find evidence that short-term interest rates play an important role for the future market variance. Whitelaw (1994) finds statistical significance for a commercial paper spread and the one year treasury rate, while Brandt and Kang (2002) use the short-term interest rate, term premium, and default premium and find a significant effect. Other research including Hamilton and Lin (1996) and Perez-Quiros and Timmermann (2000) have found evidence that the state of the economy is an important determinant in the volatility of the returns.

Since the analyses of the time-varying volatility are mostly based on high frequency data, the previous studies are mostly limited to variables such as short-term interest rates, term premiums, and default premiums, for which daily data are available. Therefore, the impacts of variables such as unemployment rate and inflation on volatility have not been sufficiently examined. Ghysels et al. (2006) introduce a regression scheme, namely MIDAS (Mixed Data Sampling) which allows inclusion of data from different frequencies in the same model. This makes it possible to combine the high-frequency return data with macroeconomic data that are only observed at lower frequencies, such as monthly or quarterly. Engle et al. (2009) propose the GARCH-MIDAS model within the MIDAS framework to analyze time-varying market volatility. Within this framework, the conditional variance is divided into long-term and short-term components. The low frequency variables affect the conditional variance via the long-term component. This approach combines the component model suggested by Engle and Lee (1999) 1 with the MIDAS framework of Ghysels et al. (2006). The main advantage of the GARCH-MIDAS model is that it allows us to link the daily observations of stock returns For the component model see also Ding and Granger, 1996; Chernov et al., 2003.





with macroeconomic variables, sampled at lower frequencies, in order to examine directly the macroeconomic variables’ impact on the stock volatility.

In this paper, we apply the recently proposed GARCH-MIDAS methodology to examine the effect of the macroeconomic variables on stock market volatility. Departing from Engle et al.

(2009), our investigation mainly focuses on variance predictability and aims to analyze if adding economic variables can improve the forecasting abilities of the traditional volatility models. Using GARCH-MIDAS we decompose the return volatility into its short-term and long-term component, where the latter is affected by the smoothed realized volatility and/or by macroeconomic variables. We examine a large group of macroeconomic variables which include unexpected inflation, term premium, per capita labour income growth, default premium, unemployment rate, short-term interest rate, per capita consumption. We investigate the ability of the GARCH-MIDAS models with economic variables to predict both short-term and long-term volatilities. The performances of these models are then compared with the GARCH (1, 1) model as a benchmark. In order to capture the information contained in different economic variables and investigate their combined effect, we perform a principal component analysis. The advantage of this approach is to reduce the number of parameters and increase the computational efficiency.

Our results show that including low-frequency macroeconomic information in the GARCHMIDAS model improves the prediction ability of the model, particularly for the long-term variance component. Moreover, the GARCH-MIDAS model augmented with the first principal component outperforms all other specifications. Among the individual macroeconomic variables, the short-term interest rate and the default rate perform better than the other variables when included in the MIDAS equation.

To our knowledge this is the first study that investigates the out-of-sample forecast performance of the GARCH-MIDAS model. The paper also differs from Engle et al. (2009) and contributes to existing literature by investigating a number of macroeconomic variables in the GARCH-MIDAS framework.

The rest of the paper is organized as follows: Section 2 presents the empirical models, and the data and the econometric methods are described in Section 3, while section 4 contains the empirical results, and Section 5 concludes.

2. GARCH-MIDAS In this paper, we use a new class of component GARCH model based on the MIDAS (Mixed Data Sampling) regression. MIDAS regression models are introduced by Ghysels et al.

(2006). MIDAS offers a framework to incorporate macroeconomic variables sampled at different frequency along with the financial series. This new component GARCH model is referred to as MIDAS-GARCH, where macroeconomic variables enter directly into the specification of the long-term component.

This new class of MIDAS structure has gained much attention in recent years by Ghysels et al. (2004), Ghysels et al. (2006) and Andreaou et al. (2010). Chen and Ghysels (2007) extend the MIDAS setting to a multi-horizon semi-parametric framework. Chen and Ghysels (2009) provide a comprehensive study and a novel method to analyze the impact of news on forecasting volatility. Ghysels et al. (2009) discuss the Granger causality with mixed frequency data. Kotze (2007) uses the MIDAS regression with high frequency data on asset prices and low frequency inflation forecasts. In addition, a number of papers use MIDAS regression to obtain quarterly forecasts with monthly and daily data. For instance, Bai et al.

(2009) and Tay (2007) use monthly data to improve quarterly forecasts. Alper et al. (2008) compare the stock market volatility forecasts across emerging markets using MIDAS regression. Clements and Galavao (2006) study the forecasts of the US output growth and inflation in this context. Forsberg and Ghysels (2006) show, through simulation, the relative advantage of MIDAS over the HAR-RV (Heterogeneous Autoregressive Realized Volatility) model proposed in Anderson et al. (2007).

The GARCH-MIDAS model can formally be described as below. Assume the return on day i

in month t follows the following process:

–  –  –

where N t is the number of trading days in month t and Φ i −1,t is the information set up to the (i − 1) th day of period t. Equation (1) expresses the variance into a short-term component defined by gi,t and a long-term component defined by τ t.

The conditional variance dynamics of the component gi,t is a (daily) GARCH (1,1) process,

as:

–  –  –

where X tl−k represents the level of a macroeconomic variable and X tv−k represents the variance of that macroeconomic variable. The component τ t used in our analysis does not change within a fixed time span (e.g. a month).

Finally, the total conditional variance can be defined as:

–  –  –

A potential problem one might face is to ensure non-negative τ t. A possible solution can be the log form (log τ t ) specification. However, we do not face the problem of negativity during our estimation. Therefore, we use the above formulation of τ t throughout our analysis.

3. Data and Estimation Method 3.1. Data We use the US, S&P 500 composite, daily price index to calculate stock returns. In our conditional variance model we use a number of financial and macroeconomic factors which have been found by previous studies to be important for return variance. The

following variables are used:

• Short-term interest rate is a yield on the three-month US Treasury bill.

• Slope of the yield curve is measured as the yield spread between a ten-year bond and a three-month Treasury bill.

• Default rate is measured as the spread between Moody’s Baa and Aaa corporate bond yields of the same maturity.

• Exchange rate is the nominal major currencies dollar index from the Federal Reserve.

• Inflation is measured as the monthly changes in the seasonally adjusted consumer price index (CPI).

• Growth rate in the Industrial Production index.

• Unemployment rate.

Data cover the period from January 1991 to June 2008. All the items except the exchange rate are collected from DataStream©.

3.2. Estimation Method 3.2.1 Various model specifications We use three different model specifications. The models differ with respect to the definition of the long-term variance component, τt, while the equation for the short-term variance, git,

remains the same in all three cases. The three specifications are:

• The RV model: In this specification, we solely use the monthly realized volatility (RV) in the long-term component of the variance, defined by the MIDAS equation, τt, in equation (3). We have no economic variables in this model.

• The RV + Xl + Xv model: Here, we augment the model by adding both the level and the variance of an economic variable to the MIDAS equation, τt. This modification is supposed to capture the information explained by both the macroeconomic factor and the monthly RV.

• The Xl + Xv model: In this specification, we only study the effect of macroeconomic variables, both level and variance, on the long-term variance component, i.e., the equation for τt.

By analyzing these three alternatives, we can investigate to what extent the long-term variance can be explained by the past realized return volatility and the macroeconomic variables. 3 3.2.2 Estimation strategy Our estimations are based on the daily observations on returns, while we use monthly frequency in the MIDAS equation to capture the long-term component. The realized volatility is our preferred measure of the monthly variance, but since daily data are not available for most macroeconomic variables, it is not possible to use this measure. We select the squared first differences as the measure of the variance of the economic variables.

We estimate the models described above using an estimation window and then use the estimated parameters to make out-of-sample variance prediction. 4 We use a ten-year We have also estimated the model with only the level or the variance of the economic variables in the MIDAS equation. In order to save space, these results are not reported but are available upon request.



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