Abstract

There are many time series data in macroeconomic time series can reflect the states and trends of current macroeconomy, such as, the quarterly GDP data, the monthly CPI and PPI data, daily financial market return data, intraday stock market volatility data, and so on. These data are focused by individuals, enterprises, organizations, countries, and even the international community. They try to use different data processing methods and build a variety of models to grab information from these complex data, and use them to do model estimates and projections, and then use the information to do savings, investment, decision-making and some other economic behaviors. However, the time series data listed above are complex, for example, the data length, sampling frequency, as well as the data attributions are not the same, while, we mainly use the same frequency data in our time series models. In order to use the mixed frequency date, pret-reatment are used. Some studies aggregate the high-frequency data to low frequency data, and some interpolate the low-frequency data into high-frequency data. However, the aggregation destroys sample information, and the interpolations make some artificial data and lack economic theory support. In empirical study, the aggregation is more common than interpolation, and interpolation methods are used due to the data shortage or the need of the models. The appearance of mixed frequency data can directly use the different frequencies data, and solve the above dilemma.

Mixed frequency models are developed and widely used, since the accumulation of various frequency time data, and the development of scientific computing. For example, using mixed frequency model to improve prediction accuracy, prediction timely forecasting and nowcasting, combining the mixed frequency model with econometric models to improve the accuracy of model estimates and achieve the improvement by comparing the model with same frequency model. In my opinion, empirical study should use the original mixed frequency data with mixed frequency model when the data exsit different frequencies. We use mixed frequency data model to do empirical studies in China’s macroeconomic. On one hand, we focus on the application of the mixed frequency data model in Chinese macroeconomic forecasts, including the applications of mixed frequency model in prediction, the effectiveness of the mixed frequency model and the evaluation issues. On the other hand, we pay attention to the combination of mixed frequency and econometric models, such as factor mixed frequency model, Markov switching mixed frequency model, and mixed frequency vector regression model.

We illustrate the research and application by the construction, estimation, and prediction of mixed frequency models. It includes the following parts.

First, Chapter 3 preliminarily analyzes the effectiveness and prediction accuracy by real-time forecasting and short-term prediction of China’s macroeconomic aggregates variables. Then, we explore the selection problem of the lag of high-frequency data, forecast horizon, and the lag of auto regression. And then, use the results to build multivariate MIDAS models to do real-time forecasting and short-term nowcasting. The empirical results show that the mixed frequency data model has a significant comparative advantage, when compared with same frequency models.

Secondly, Chapter 4 comparatively analyzes the effectiveness and the prediction accuracy of mixed frequency vector autoregressive (MF-VAR). MF-VAR model not only has the ability to reflect the dynamic relationship between variables, but also can use the kalman filter to do estimation and prediction. It is not enough to use a single or a few economic variables to predict and forecast macroeconomic trends, when the economic data have become increasingly diverse, and the condition of economic become complicate. Therefore, we use a pool of Chinese macroeconomic data to anylize the MF-VAR model and compare the results with MIDAS models. The empirical results show that there are differences between the results with a single variable prediction, while it is still valid and applicable in general. The comparative analysis of the MIDAS models and the MF-VAR models show that the prediction of MF-VAR has better results in the longer periods, while the MIDAS models have relative advantage in a short-term. So it is useful to combine these two mixed frequency model to provide more accurate predictions in real-time forecasting and short-term forecasts of real GDP in China.

Thirdly, Chapter 5 checkes and compares the effectiveness and the prediction accuracy with factor mixed frequency model. It is not enough to forecast and nowcast the economy with single or a few economic variables in a complex economic situation. Therefore, we adopt factor model to extract macroeconomic factor with a large number of macroeconomic aggregates economic data (including the data of leading indicator data, consistent indicator data and lagging indicators), and combined with MIDAS and MF-VAR models to do real-time forecasting and nowcasting, and then compare these two mixed frequency data model with each other. The empirical results show that, the two mixed frequency models, which using combined factor model has a comparative advantage compared to the traditional autoregressive model, so the projections and forecasts of the two mixed frequency models are applicable and effective. For the compare of the forecast results of the two models, we find there are not have a perfect model. MF-VAR model has an overall comparative advantage in the short-term forecasting and nowcasting, while the MIDAS model has a relatively good performance in the longer forecast period.

Fourth, Chapter 6 characterizes the long-run equilibrium and short-term fluctuation with cointergration MIDAS (CoMIDAS) model and uses it for analysis and prediction. For the reason of information loss when we difference the series for stationary, and cannot get the long-run equilibrium cointegration relationship, we use the CoMIDAS model to analyze the long-term cointegration relationship between the output and the money supply, and show the influence of short-term high-frequency changes in the money supply on the change in output. The empirical results show the existence of long-run equilibrium relationship between money supply and output in China, and reflect the important reason between output volatility and short-term money supply.

Fifth, Chapter 7 monitors and dates the business cycle with Markov Switching MIDAS (MS-MIDAS) models. We combine the mixed frequency model with nonlinear econometric models to characterize the non-linear and non-stationary relationship in Chinese economy, since linear mixed frequency regression model cannot characterize the non-stationary and non-linear relationship between the mixed frequency data. MS-MIDAS model not only has the same ability with traditional regime switching in characteristic the regime changes in the mean and variance, but also can measure the ability change in forecasting low frequency data series with high frequency data, as the regime and market conditions change. Thus, we have more accurate results in the nowcasting and short-term forecasts with this model. The empirical results show the advantage of MS-MIDAS model, when compared with the results of the traditional same frequency model, and it also precise dating the turning points and phases of business cycle.

Sixth, Chapter 8 analyzes the supply and demand shocks based on Bayesian mixed Frequency V AR (BMF-VAR) model. We apply Bayesian approach to get the impact of supply and demand in China and its effect on the monthly level, and the results show that China's output is mainly affected by supply factors, while inflation is mainly affected by demand factors.

In short, based on the theory and estimation of mixed frequency data model, we do real-time forecasting and short-term forecasting with mixed frequency data in China. Then, we build nonlinear mixed frequency models with nonlinear and a pool of series to analyze the macroeconomic theory and laws, such as business cycle, monetary policy and AS-AD model.

Key words

Mixed Frequency Data Model, MIDAS, MF-VAR, Macroeconomic Forecasts, GDP

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