MIDAS Regressions Research Articles

Nowcasting Norwegian household consumption with debit card transaction data

SummaryWe use a novel data set covering all domestic debit card transactions in physical terminals by Norwegian households, to nowcast quarterly Norwegian household consumption. These card payments data are not subject to revisions and are available weekly without delays, providing a valuable early indicator of household spending. To account for mixed‐frequency data, we estimate various quantile mixed‐data sampling (QMIDAS) regressions using predictors sampled at monthly and weekly frequency. We evaluate both point and density forecasting performance over the sample 2011Q4–2019Q4. Our results show that MIDAS regressions with debit card transactions data improve both point and density forecast accuracy over competitive standard benchmark models that use alternative high‐frequency predictors. Finally, we illustrate the benefits of using the card payments data by obtaining a timely and relatively accurate nowcast of 2020Q1, a quarter characterized by heightened uncertainty due to the COVID‐19 pandemic. We further show how debit card data have been useful in nowcasting consumption during the four subsequent quarters.

Forecasting innovative start-ups through automatic variable selection and MIDAS regressions

ABSTRACT The paper focuses on the role that both macroeconomic indicators and financial factors play as drivers for the birth and the evolution of the Italian innovative start-ups over time. The analysis makes use of a novel machine learning algorithm, working in high-dimensional graphical models, to select, among the multitude of potential determinants, the relevant explanatory variables for the number of innovative start-ups. Being the variables involved in the analysis sampled at different frequencies, mixed data sampling models are employed for estimation and forecasting purposes. The need to reduce the number of regressors of these models, for reasons related to their estimability, is met by resorting to principal component analysis of the potential determinants. An empirical application to the set of Italian innovative start-ups, either in their entirety or split according to some specific requirements, highlights the effectiveness of this approach. The analysis results provides useful information for the assessment of national innovation policies and for the evaluation of the capability of the innovative start-ups to persist and contribute at the recovery during the actual crisis still affected by the pandemic.

Another look at the energy-growth nexus: New insights from MIDAS regressions

Abstract In this paper, we offer the following contributions to the extant literature on the energy-growth nexus. First, we test the predictability of the energy components in the predictive growth model using the autoregressive distributed lag mixed data sample (ADL-MIDAS) approach. Second, we compare the in-sample and out-of-sample forecast performances of the MIDAS approach with the uniform frequency approach involving the autoregressive (AR) model as well as the autoregressive distributed lag (ARDL) model. Third, we consider an array of energy proxies ranging from aggregate data to sectoral data of energy consumption (residential, commercial, industrial and transportation) and those defined by energy sources (petroleum, natural gas, coal, electricity, nuclear electricity and renewable energy). Fourth, we test whether accounting for asymmetries matters in the ADL-MIDAS regression model for the energy-growth nexus. The results support the significant predictability of energy for growth regardless of the measures of energy. In addition, the in-sample and out-of-sample forecast results overwhelmingly favour the ADL-MIDAS over other competing models. Thus, allowing for high frequency data for energy in the low frequency growth model will enhance the forecast accuracy of the model. However, we find that accounting for asymmetries does not matter in the energy-growth nexus.

The new MIBA model: Real-time nowcasting of French GDP using the Banque de France's monthly business survey

This paper introduces a new nowcasting model of the French quarterly real GDP growth rate (MIBA), developed at the Banque de France and based on monthly business surveys. The model is designed to target initial announcements of GDP in a mixed-frequency framework. The selected equations for each forecast horizon are consistent with the time frame of real-time nowcasting exercises: the first one includes mainly information on the expected evolution of economic activity, while the second and third equations rely more on information on observed business outcomes. The predictive accuracy of the model increases over the forecast horizon, consistent with the gradual increase in available information. Furthermore, the model outperforms a wide set of alternatives, such as its previous version and MIDAS regressions, although not a specification including also hard data. Further research should evaluate the performance of the MIBA model with respect to promising alternative approaches for nowcasting GDP (e.g. mixed-frequency factor models with targeted predictors), and consider forecast combinations and density forecasts.

Indirect Inference Estimation of Mixed Frequency Stochastic Volatility State Space Models using MIDAS Regressions and ARCH Models

We examine the relationship between MIDAS regressions and the estimation of state space models applied to mixed frequency data. While in some cases the binding function is known, in general it is not, and therefore indirect inference is called for. The approach is appealing when we consider state space models which feature stochastic volatility, or other non-Gaussian settings where maximum likelihood methods are infeasible. The stochastic volatility feature is particularly relevant when considering high frequency nancial series. In addition, we propose a ltering

Expected Returns and Idiosyncratic Risk: Industry-Level Evidence from Russia

ABSTRACTWe explore a relation between expected returns and idiosyncratic risk in Russia. Investors in the Russian stock market cannot fully diversify their portfolios due to transaction costs, information gathering and processing costs, and shortcomings in investor protection. This implies that investors demand a premium for idiosyncratic risk. We estimate the price of idiosyncratic risk using MIDAS regressions and a cross section of Russian industry portfolios. We find that idiosyncratic risk is economically significant and commands a negative (positive) premium, on average, of 10.0% (8.0) per year before (after) the global financial crisis in 2008. The results remain unaffected after controlling for global pricing factors and return reversal.

On the use of high frequency measures of volatility in MIDAS regressions

Many empirical studies link mixed data frequency variables such as low frequency macroeconomic or financial variables with high frequency financial indicators’ volatilities, especially within a predictive regression model context. The objective of this paper is threefold: First, we relate the standard Least Squares (LS) regression model with high frequency volatility predictors, with the corresponding Mixed Data Sampling Nonlinear LS (MIDAS-NLS) regression model (Ghysels et al., 2005, 2006), and evaluate the properties of the regression estimators of these models. We also consider alternative high frequency volatility measures as well as various continuous time models using their corresponding relevant higher-order moments to further analyze the properties of these estimators. Second, we derive the relative MSE efficiency of the slope estimator in the standard LS and MIDAS regressions, we provide conditions for relative efficiency and present the numerical results for different continuous time models. Third, we extend the analysis of the bias of the slope estimator in standard LS regressions with alternative realized measures of risk such as the Realized Covariance, Realized beta and the Realized Skewness when the true DGP is a MIDAS model.

Macroeconomics and the reality of mixed frequency data

Many time series are sampled at different frequencies. When we study co-movements between such series we usually analyze the joint process sampled at a common low frequency. This has consequences in terms of potentially mis-specifying the co-movements and hence the analysis of impulse response functions—a commonly used tool for economic policy analysis. We introduce a class of mixed frequency VAR models that allows us to measure the impact of high frequency data on low frequency and vice versa. Our approach does not rely on latent processes/shocks representations. As a consequence, the mixed frequency VAR is an alternative to commonly used state space models for mixed frequency data. State space models are parameter-driven whereas mixed frequency VAR models are observation-driven models as they are formulated exclusively in terms of observable data and do not involve latent processes as well as shocks and thus avoid the need to formulate measurement equations, filtering, etc. We also propose various parsimonious parameterizations, in part inspired by recent work on MIDAS regressions. We also explicitly characterize the mis-specification of a traditional common low frequency VAR and its implied mis-specified impulse response functions. The class of mixed frequency VAR models can also characterize the timing of information releases for a mixture of sampling frequencies and the real-time updating of predictions caused by the flow of high frequency information. Various estimation procedures for mixed frequency VAR models are also proposed, both classical and Bayesian. Numerical and empirical examples quantify the consequences of ignoring mixed frequency data.

Real-Time Forecasting With a Mixed-Frequency VAR

This article develops a vector autoregression (VAR) for time series which are observed at mixed frequencies—quarterly and monthly. The model is cast in state-space form and estimated with Bayesian methods under a Minnesota-style prior. We show how to evaluate the marginal data density to implement a data-driven hyperparameter selection. Using a real-time dataset, we evaluate forecasts from the mixed-frequency VAR and compare them to standard quarterly frequency VAR and to forecasts from MIDAS regressions. We document the extent to which information that becomes available within the quarter improves the forecasts in real time. This article has online supplementary materials.

Real-time forecasting of the US federal government budget: A simple mixed frequency data regression approach

This paper proposes a real-time forecasting procedure involving a combination of MIDAS-type regression models constructed with predictors of different sampling frequencies for predicting the annual U.S. federal government current expenditures and receipts. The evidence shows that forecast combinations of MIDAS regression models provide forecast gains over traditional models, which suggests the use of mixed frequency data consisting of fiscal series and macroeconomic indicators for forecasting the annual federal budget. It is also shown that, although this was not statistically significant, MIDAS regressions with quarterly leads that are employed to include real-time forecast updates of the current year federal expenditures and receipts are found to have improved forecast performances compared to MIDAS regressions without leads.

Nowcasting UK GDP During the Depression: Model Comparisons

This paper reviews the performance of several statistical techniques in nowcasting preliminary estimates of UK GDP, particularly during the recent depression. Traditional bridging equations, MIDAS regressions and factor models are all considered. While there are various theoretical differences and perceived advantages for each technique, replicated real-time out-of-sample testing shows that, in practice, there is in fact little to choose between methods in terms of end-of-period nowcasting accuracy. The analysis also reveals that none of the aforementioned statistical models can consistently beat a consensus of professional economists in nowcasting preliminary GDP estimates. This inability of statistical models to beat the consensus may reflect several factors, one of which is the revisions and re-appraisal of trends inherent in UK GDP statistics. The suggestion is that such changes impact on observed relationships between GDP and indicator variables such as business surveys, which impairs nowcasting performance. Indeed, using a synthetic series based purely on observed preliminary GDP estimates, which introduces stability to the target variable series, the nowcasting accuracy of regressions including closely-watched PMI data is improved by 25-40 percentage points relative to a naive benchmark.

State Space Models and MIDAS Regressions

We examine the relationship between Mi(xed) Da(ta) S(ampling) (MIDAS) regressions and the Kalman filter when forecasting with mixed frequency data. In general, state space models involve a system of equations, whereas MIDAS regressions involve a single equation. As a consequence, MIDAS regressions might be less efficient, but could also be less prone to parameter estimation error and/or specification errors. We examine how MIDAS regressions and Kalman filters match up under ideal circumstances, that is in population, and in cases where all the stochastic processes—low and high frequency—are correctly specified. We characterize cases where the MIDAS regression exactly replicates the steady state Kalman filter weights. We compare MIDAS and Kalman filter forecasts in population where the state space model is misspecified. We also compare MIDAS and Kalman filter forecasts in small samples. The paper concludes with an empirical application. Overall we find that the MIDAS and Kalman filter methods give similar forecasts. In most cases, the Kalman filter is a bit more accurate, but it is also computationally much more demanding.

Changes in predictive ability with mixed frequency data

Abstract When assessing the predictive power of financial variables for economic activity, researchers usually aggregate higher-frequency data before estimating a forecasting model that assumes the relationship between the financial variable and the dependent variable to be linear. This paper proposes a model called smooth transition mixed data sampling (STMIDAS) regression, which relaxes both of these assumptions. Simulation exercises indicate that the improvements in forecasting accuracy from the use of mixed data sampling are larger in nonlinear than in linear specifications. When forecasting output growth with financial variables in real time, statistically significant improvements over a linear regression are more likely to arise from forecasting with STMIDAS than with MIDAS regressions.

State Space Models and MIDAS Regressions

State Space Models and MIDAS Regressions

Real-Time Predictions of the U.S. Federal Government Budget: Expenditures, Revenues and Deficits

This paper proposes a forecasting procedure involving a combination of MIDAS-type regression models, allowing one to use high frequency predictors with different sampling frequencies to predict the U.S. Federal Government Expenditures (Net Outlays), Revenues and Deficits all of which are low frequency (quarterly/annual) variables. Evidence shows that forecast combinations of MIDAS regression models provide forecast gains over the traditional models. It is also shown that one-step ahead real-time predictions from MIDAS regressions of annual expenditures and revenues have smaller forecast errors than one-step ahead projections provided by the Congressional Budget Office (CBO) for the fiscal years of 1998-2010. Moreover, MIDAS regressions with leads employed to have real-time forecast updates of the current quarter (nowcasting) federal expenditures and revenues are found to have improved forecast performance compared to MIDAS regressions without leads.

Macroeconomics and the Reality of Mixed Frequency Data

Many time series are sampled at different frequencies. When we study co-movements between such series we usually analyze the joint process sampled at a common low frequency. This has consequences in terms of potentially mis-specifying the comovements and hence the analysis of impulse response functions - a commonly used tool for economic policy analysis. We introduce a class of mixed frequency VAR models that allows us to measure the impact of high frequency data on low frequency and vice versa. Our approach does not rely on latent processes/shocks representations. As a consequence, the mixed frequency VAR is an alternative to commonly used state space models for mixed frequency data. State space models are parameter-driven whereas mixed frequency VAR models are observation-driven models as they are formulated exclusively in terms of observable data and do not involve latent processes as well as shocks and thus avoid the need to formulate measurement equations, filtering etc. We also propose various parsimonious parameterizations, in part inspired by recent work on MIDAS regressions. We also explicitly characterize the mis-specification of a traditional common low frequency VAR and its implied mis-specified impulse response functions. The class of mixed frequency VAR models can also characterize the timing of information releases for a mixture of sampling frequencies and the real-time updating of predictions caused by the flow of high frequency information. Various estimation procedures for mixed frequency VAR models are also proposed, both classical and Bayesian. Numerical and empirical examples quantify the consequences of ignoring mixed frequency data.

The Low-Frequency Impact of Daily Monetary Policy Shocks

With rare exception, studies of monetary policy tend to neglect the timing of the innovations to the monetary policy instrument. Models which do take timing seriously are often difficult to compare to standard VAR models of monetary policy because of the differences in the frequency that they use. We propose an alternative model using MIDAS regressions which nests both ideas: Accurate (daily) timing of innovations to the monetary policy instrument are embedded in a monthly frequency VAR to determine the macroeconomic effects of high frequency changes to policy. We find that taking into account the timing of the shocks is important and can alleviate some of the puzzles in standard monthly VARs [e.g., the price puzzle]. We find that policy shocks are most important to variables thought of as being heavily expectations-oriented and that, contrary to some VAR studies, the effects of FOMC shocks on real variables are small.>

MIDAS Regressions: Further Results and New Directions

MIDAS Regressions: Further Results and New Directions

MIDAS Regressions: Further Results and New Directions

We explore mixed data sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Volatility and related processes are our prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. The regressions combine recent developments regarding estimation of volatility and a not-so-recent literature on distributed lag models. We study various lag structures to parameterize parsimoniously the regressions and relate them to existing models. We also propose several new extensions of the MIDAS framework. The paper concludes with an empirical section where we provide further evidence and new results on the risk–return trade-off. We also report empirical evidence on microstructure noise and volatility forecasting.

MIDAS Regressions: Further Results and New Directions

We explore Mixed Data Sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Volatility and related processes are our prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. The regressions combine recent developments regarding estimation of volatility and a not so recent literature on distributed lag models. We study various lag structures to parameterize parsimoniously the regressions and relate them to existing models. We also propose several new extensions of the MIDAS framework. The paper concludes with an empirical section where we provide further evidence and new results on the risk-return tradeoff. We also report empirical evidence on microstructure noise and volatility forecasting.