Econometric Methods For Mixed-Frequency Data: Theory And Application

Recently, econometric models considering the information contained in "Big Data" have received extensive attention. On the one hand, economic decision-makers need to evaluate the current economic situation; on the other hand, the available information is incomplete. The generation of real-time big data is mainly due to the following two characteristics:First, the available indicators have different sampling frequencies; second, the so called "ragged-edge" issue, which is due to delay in the publication of variables and thus causes missing values at the end of the sample.Chapter 1 is the preface. We first introduce the background, purpose and significance of the theme studied in the thesis. Then we explain the research framework and analytical methods employed and introduce the main innovations and shortcomings of my research. Last but not the least, we summarize and pave the way for specific studies in the following chapters.In Chapter 2 we review the major econometric models proposed so far in the literature to deal with mixed-frequency data. The typical approach is to aggregate the data to the same frequency and to work with a "frozen" final vintage dataset, which eliminates the ragged edge problem. In what follows, we depict the main features of the bridge models, often employed in central banks and other policy-making institutions, especially for nowcasting and short-term forecasting. We then move to one of the main strands of the literature, mixed-data sampling (MIDAS) models, parsimonious specifications based on distributed lag polynomials, which flexibly deal with data sampled at different frequencies and provide a direct forecast of the low-frequency variable. Finally, we consider the state-space approaches, presenting mixed-frequency VAR (MF-VAR) and factor models. Both are system approaches that jointly describe the dynamics of the variable to be explained and of the indicators, where the use of the Kalman filter provides not only predictions of the future observations but also estimates of the current latent state. A natural extension in the literature is the combination of the factors with the MIDAS models, and it is based on the use of factors as explanatory variables to exploit the information in large mixed-frequency datasets. The resulting model is called Factor-MIDAS. In Chapter 3, we study the predictive power of daily stock returns on output growth and inflation with Mixed Data Sampling (henceforth, MIDAS) regression models both in forecasting and nowcasting contexts. We filter the daily stock returns with a newly proposed frequency domain filter, and aggregate the daily data with MIDAS weights using estimated parameter values. We find that predictors with MIDAS regressions perform quite well in inflation forecasting. For Singapore inflation, filtered stock returns forecast better than unfiltered stock returns; for US inflation, on the other hand, unfiltered stock returns forecast better than filtered stock returns. Predictors with MIDAS regressions perform fairly well in Singapore output growth forecasting in that contemporary stock returns have higher forecasting accuracy than the benchmark model, but for the US output growth, we don’t see any improvements with our MIDAS regressions.In Chapter 4, we focus on using MIDAS method to forecast on volatility. The three main applications of volatility forecasting are in asset pricing, risk management and portfolio management. A focal issue in risk management is the measure of potential future losses in the portfolio, and in order to measure the potential losses correctly, we must predict future volatility and correlation. The MIDAS regression models allow us to carry out regressions on observations at different frequencies with compact parameterization. In the empirical part, we analyzed the weekly stock market volatilities through four developed countries and four emerging economies. We found that Merton (1973)’s ICAPM model has good applicability in mature markets, while it is not necessarily valid in the relatively more volatile markets. We also analyzed and compared three predictors which are commonly adopted in volatility forecasting literature by using the actual data of eight stock markets and found that "Daily Absolute Return" has the highest prediction accuracy among all the three predictors, followed by the "Daily Range". While the most widely adopted predictor "Daily Squared Return" has, sadly, the lowest prediction accuracy.In Chapter 5, we introduced methods to estimate MF-VAR models and factor models in the case of missing observations, and several econometric models for nowcasting or forecasting output growth by exploiting mixed frequency data (including possible ragged-edged structure) and compared the pros and cons of various methods. The models we described in detail in this chapter are:Mixed Data Sampling (MIDAS), Mixed Frequency-VAR, and Mixed Frequency Factors models. We also introduced the methodology for how to get the monthly estimates of output growth under these three analyzing frameworks.In Chapter 6 we summarize. Our studies show that mixed frequency data play a very important role in forecasting, and the use of different frequency and real-time data improve our predictions. The state-space model is a systematic approach, and by the benefit of the Kalman filter it allows the estimation of the missing values of the high frequency data. MIDAS is more robust compared to bridge equation and state-space method when the model is wrongly specified and the computation load of MIDAS method is relatively light. In short, the study of econometrics models dealing with mixed frequency data is a very popular research topic, especially in nowadays when the concept of "Big Data" enjoys popular support. On the one hand, the volume of data we can get is increasing exponentially and the frequencies of different data are not necessarily the same; on the other hand, how to handle these data which are huge, with varied frequencies and missing values, to be used for the purpose of research, while keeping the useful information in its original data as much as possible, this is still a very challenging but exciting task. We have reasons to believe that, as more and more in-depth researches are conducted in this area, our ability to deal with these challenges will increase correspondingly.