Forecasting GDP Growth using Financial Information

The shocks that occur in periods of instability in financial markets affect the effective implementation that would be subject to appropriate macroeconomic policies. Researchers have developed several approaches to monitor macroeconomic policies concerned with the goal of stabilizing and strengthening the global financial system. The 2007 financial crisis revealed the limits of the proposed approaches, which designed to analyse and forecast the economic fluctuations. Other approaches, including the mixed frequency data models, have been put forward to address the limitations the existing forecasting models by taking into account the interactions between the real and financial sectors. The information on the equity and commodity markets increase the predictive capacities of models and thereby can be used to forecast the fluctuations of GDP growth. The present paper applies a model-independent data assimilation (MIDAS), which is embedded in the mixed frequency data models, to forecast the fluctuations in the economic growth of five developed countries, namely the United States, France, Germany, United Kingdom and Japan. The results show that, taking into account the volatility of financial market indicators enable to provide accurate projections of the economic growth. Furthermore, the integration of the autoregressive component in the MIDAS model strengthens its predictive capacity over the forecast period.


INTRODUCTION
The relationship between the real economy and financial markets has been and continues to be an issue of considerable interest and concern to all countries, drawing attention of the economic researchers, policymakers, and international institutions, including the International Monetary Fund (IMF) and World Bank. The analysis of the role of financial markets in explaining the real economy took off in the early 1980s, notably with the work of Bernanke (1983). The financial crises 2 that have occurred have reinforced this renewed interest and raised questions about taking into account the role of financial markets in forecasts production growth, fostering a better control of systemic risk.
Drawing on the work of Friedman & Schwartz (1963) on explaining the Great Depression of the 1930s, Bernanke (1983) has concluded that shocks in the financial markets are responsible for macroeconomic fluctuations. Other researchers, including Fama (1985), Hamilton (1987), Haubrich (1987), Gertler (1988), Bernanke, Gertler & Gilchrist (BGG, 1996, 1999, have highlighted that financial information is an important component that explains economic fluctuations and macroeconomic balance. In his seminal work, Stock & Watson (2003) has shown that financial aggregates (share and commodity prices, money supply) improve the performance of models forecasting GDP growth and inflation. Hamilton (2003) has analyzed the non-linear relationship between commodity prices and GDP growth using an autoregressive Markov-Switching model and found that oil shocks affect economic activity, through the consumer spending of households and businesses. Moreover, Kilian (2008) has found that notes more generally that shocks from the energy sector generally help reduce economic fluctuations. The issue relating to the financial accelerator has also been raised several researchers (Jerman & Quadrini, 2012 ;Costas, 2018). Foroni and Massimiliano (2012) have considered weekly financial variables in the banking market to illustrate the relationship between the interest rate market and economic activity in the euro area. Others (Ferrara &Marsilli, 2013 andFerrara, Marsilli &Ortega, 2014) have inspired from the studies on forecasting GDP growth during the Great Recession to show the performance of forecasting models in industrialized countries. Their findings reveal that the GDP growth forecasting steadily improve when the volatility of financial variables is taken into account, using mixed frequency data models. Recently, Yan-ran & Qiang Ji (2019) have found, through a multidimensional analysis, that forecasting the volatility of oil prices allows better anticipation of macroeconomic fluctuations.
Two mechanisms of transmitting financial market fluctuations on economic activity flowing from the above-mentioned studies are worthy of consideration. The first is based on the intrinsic relationship between financial and economic activity indicators, by the linear and/or non-linear modelling (Stock & Watson, 2003;Ahn & Lee, 2006;Hamilton & Lin, 1996). The second mechanism refers to the incorporation of volatility into models for forecasting macroeconomic fluctuations (Ferrara, Marsilli & Ortega, 2014). The present paper relates to this second approach, which considers the financial volatility of equity and commodity prices to anticipate quarterly GDP growth.
In empirical work, two types of approaches could be distinguished: i) the technique of aggregating high-frequency financial variables (daily or weekly) explaining the evolution of low-frequency variables (monthly or quarterly); ii) the mixed frequency data models (MIDAS) proposed by Ghysels & al (2004Ghysels & al ( , 2007. The MIDAS models are based on the combination of simultaneous economic and/or financial indicators at different frequencies. More specifically, the present study is inspired from the work of Clements and Galvão (2008), Senyuz & al. (2012) and Ferrara, Marsilli & Ortega (2014), which constitute useful references for the enrichment of this work.
Thus, the methodology consists to use the mixed frequency data models for assessing the impact of (daily) financial volatility on economic activity while taking into account its interactions with other (monthly) economic indicators. The analysis is carried out using data from the financial markets of the United States, France, Great Britain (UK), Germany and Japan. This paper is structured as follow: the first step is to justify the relevance of adopting MIDAS models to perform forecasts of GDP growth, using only economic variables (monthly). The second step consists to show that the performance of MIDAS models when the volatility of financial indicators is also taken into account, in addition.

METHODOLOGY
The methodology outlined below is inspired from the work of Ferrara, Marsilli & Ortega (2014), which considers the volatility of financial variables for the prediction of GDP growth. The MIDAS regression is used for forecasting GDP growth by incorporating the economic and financial variables to measure the performance of each forecasting model across distinct horizons. To this end, the MIDAS and MIDAS-AR models are used, within the framework of forecasts. This enables to show the usefulness of mixed frequency models compared to AR models, but also the importance of taking into account the dynamics of GDP growth in this type of modelling. Furthermore, it will be a question of comparing the forecasts of each model with or without the financial volatilities to assess the relevance of our approach. The style used in this work is in line with that of studies of Kuzin, Marcellino & Schumacher (2009) The MIDAS model can be written follow: Where is the error term of the model such that E (ε t q ) = 0 et E (ε t q , ε ′ t q ) = 2 . 0 , , , are the parameters of the model to be estimated. Adding an autoregressive process to equation (1) gives the MIDAS-AR model in the following form: With , the lag in the quarterly GDP growth rate. In this work ℎ = 1, due to the nature of the series, and also in conformities with the works of Ferrara & al. (2014) and Stock & Watson (2003). Regarding the beta function ( ; ), we take inspiration from the work of Ferrara, Marsilli & Ortega (2014), who have considered only one parameter in the specification of such function. This approach makes it possible to limit the parameters to be estimated, given a large number of monthly and daily data to be used (2 + 2 + 1 + 1). The beta function is defined as: ; ℎ ℎ = ℎ −1 . is the number of variables used in the model and ℎ is the number of times ℎ (ℎ) is observed. The function ( ) allows to weigh the variables according to the number of lags (see Ghysels, 2004, Ghysels;Santa-Clara andValkanov, 2004 and2007). A simplified form of ( . ) was proposed by Ghysels (2004) and gives positive weights that decrease as a function of the number of delays (see Ferrara, Marsilli & Ortega, 2014): As highlighted, the objective of this work is to show the importance of taking into account information from the financial markets to increase our explanation of macroeconomic fluctuations. It consists concretely in measuring volatility from the series relating to the price indices of equities and commodities, which will be used to refine the forecasts. Volatilities are measured using a GARCH (r, s) model 3 .
On the basis of these conditions, it is assumed that the marginal variance ( ) = to ensure the stationarity and the positivity of the volatility  t. is the performance of the financial variable such as = log ( ).
In addition, the forecast for quarterly GDP growth is based on the direct method with several stages. For all t, the forecast horizon makes it possible to define the following relationship, from the MIDAS-AR model at (2 + 2 + 2) parameters estimated by the non-linear least-squares method -NLS, as:

DATA
The series are extracted mainly from the "FRED database" and "Datastream". These are daily, monthly and quarterly data. The quarterly data relate to the seasonally adjusted GDP growth rates, relating to the selected economies. They cover the period from 1970q1 to 2018q4 and are from the "FRED database". The economic variables are observed on a monthly frequency and noted by "ipm", "cos Index", "leadIndex", "capu" and "unemp". They are from the same source as the GDP data. The financial variables with daily frequencies relate to the commodity prices index noted "CRB index" and stock market indices of the United States "S&P 500", France "CAC 40", Great Britain "FTSE 100", Germany "DAX" and Japan "Nikkei 225". These are extracted from the "Datastream" database. Table 1 describes all these data.

FORECASTING RESULTS
This part of the work involves commenting on the main results from the MIDAS and MIDAS-AR forecast models for the selected countries. The Autoregressive (AR) model based on GDP growth is considered as a reference model, that is to say, a scenario of comparison with forecasts. Using the information criterion BIC has allowed validating the existence of a single lag for the AR model, regardless of the selected economy.
Concerning the MIDAS models, the crb and stock market indices were used to measure the corresponding volatility, using an ARMA model (1.1) -GARCH (1.1).
Bayes Information Criterion (BIC) determined the number of lags. The volatility profiles relating to the returns of the , , , , and index are represented by the graphs above. Outliers were treated using the "Winsorising" method at 5% of the lowest The second peak observed in 2008 relates to the financial crisis, which led to large fluctuations in the commodities prices, especially food, metals and energy. Finally, a last less significant peak was observed in 2016, following the drop in oil and metal prices. Fluctuations in volatility relative to the CRB index can also be explained by imbalances in emerging countries.
As has already been confirmed in the work of Stock & Watson (2003), Ferrara (2014), these indicators have also helped in this study to improve the explanation of fluctuations in economic activity. In fact, in applications, these volatilities were initially omitted in the process of explaining economic fluctuations. Then, the financial variables were introduced one by one in the different models. A third specification consisted of simultaneously mobilizing the monthly activity variables and daily financial information (volatilities). The objective of using this procedure is to obtain more precise forecasts and justify their ability to explain economic fluctuations.

Forecast evaluation
This section is intended to compare the models used for predicting the GDP growth.
By Assessing goodness of forecasts using the mean square forecasting errors (MSFE) for each forecast horizon H. Let H=0, 1/3, 2/3,1, …,11/3, the forecast horizons; the different models = AR, MIDAS and MIDAS-AR; is relative to the GDP growth of country , the MSFE is computed as: Where T is the number of observations, is the initial in-sample period to computing the first forecasts, + , is the realized value of GDP at time + , and ̂+ , , is the model forecast of + , made at time . So the expression of RMSFE is given by: Thus, the comparison of the performance of forecasting models relates to that of RMSFE criterion. The lower the RMSFE, the better the forecasting performance of the model. Moreover, to give a better explanation of the performance of models, comparisons of their predictive power were applied for H horizons, in accordance with the indicators (economic and/or financial) used.

Out-of-sample comparison
Regarding the performance of the models, the sample is divided into two sub-periods In addition, in the context of nowcasting (H = 0), the results show the power of the MIDAS models and in especially MIDAS-AR models, compared to the AR reference model. This is explained by the non-aggregation of data with MIDAS models and also by taking into account the lags publication of data, in the case of MIDAS-AR models.  Furthermore, the RMSFE of each model was also computed to have a better appreciation of these results, in accordance with the indicators used for each selected economy. The inherent results are set out in Tables 3, 4, 5, 6, 7 (Appendix A) As highlighted above, the performance of the different models is measured by considering a single economic indicator, see "

CONCLUSION
This work has shown that financial information, generally omitted from economic forecasts, has a significant explanatory power that can improve the results of these This work led to two important results that are in line with the literature concerning the forecast of macroeconomic fluctuations, see Stock & Watson (2003), Ghysels (2004Ghysels ( , 2007, Ferrara et al. (2014). The first result concerns econometric models and the second relates to economic theory on the explanation of economic fluctuations. First, the relevance of mixed frequency models has been proven compared to models based on a single frequency as the Autoregressive (AR) model used as a reference in this work. Then, the second result relating to the enrichment of economic theory enable to understand that information from the financial sphere relevant to explain macroeconomic fluctuations.
However, like Stock & Watson (2003), this work did not consider the banking market, through monetary and credit aggregates. It could then be deepened by highlighting more information from the banking sector. In addition, only a few developed economies were Selected. Other developed economies could be considered, or emerging countries, or even OCDE economies for example, given the availability of information.